WalMart Revenue Data
Date | Wal Mart Revenue | CPI | Personal Consumption | Retail Sales Index | December |
11/28/03 | 14.764 | 552.7 | 7868495 | 301337 | 0 |
12/30/03 | 23.106 | 552.1 | 7885264 | 357704 | 1 |
1/30/04 | 12.131 | 554.9 | 7977730 | 281463 | 0 |
2/27/04 | 13.628 | 557.9 | 8005878 | 282445 | 0 |
3/31/04 | 16.722 | 561.5 | 8070480 | 319107 | 0 |
4/29/04 | 13.98 | 563.2 | 8086579 | 315278 | 0 |
5/28/04 | 14.388 | 566.4 | 8196516 | 328499 | 0 |
6/30/04 | 18.111 | 568.2 | 8161271 | 321151 | 0 |
7/27/04 | 13.764 | 567.5 | 8235349 | 328025 | 0 |
8/27/04 | 14.296 | 567.6 | 8246121 | 326280 | 0 |
9/30/04 | 17.169 | 568.7 | 8313670 | 313444 | 0 |
10/29/04 | 13.915 | 571.9 | 8371605 | 319639 | 0 |
11/29/04 | 15.739 | 572.2 | |||
12/31/04 | 26.177 | 570.1 | 8462026 | 386918 | 1 |
1/21/05 | 13.17 | 571.2 | 8469443 | 293027 | 0 |
2/24/05 | 15.139 | 574.5 | 8520687 | 294892 | 0 |
3/30/05 | 18.683 | 579 | 8568959 | 338969 | 0 |
4/29/05 | 14.829 | 582.9 | 8654352 | 335626 | 0 |
5/25/05 | 15.697 | 582.4 | 8644646 | 345400 | 0 |
6/28/05 | 20.23 | 582.6 | 8724753 | 351068 | 0 |
7/28/05 | 15.26 | 585.2 | 8833907 | 351887 | 0 |
8/26/05 | 15.709 | 588.2 | 8825450 | 355897 | 0 |
9/30/05 | 18.618 | 595.4 | 8882536 | 333652 | 0 |
10/31/05 | 15.397 | 596.7 | 8911627 | 336662 | 0 |
11/28/05 | 17.384 | 592 | 8916377 | 344441 | 0 |
12/30/05 | 27.92 | 589.4 | 8955472 | 406510 | 1 |
1/27/06 | 14.555 | 593.9 | 9034368 | 322222 | 0 |
2/23/06 | 18.684 | 595.2 | 9079246 | 318184 | 0 |
3/31/06 | 16.639 | 598.6 | 9123848 | 366989 | 0 |
4/28/06 | 20.17 | 603.5 | 9175181 | 357334 | 0 |
5/25/06 | 16.901 | 606.5 | 9238576 | 380085 | 0 |
6/30/06 | 21.47 | 607.8 | 9270505 | 373279 | 0 |
7/28/06 | 16.542 | 609.6 | 9338876 | 368611 | 0 |
8/29/06 | 16.98 | 610.9 | 9352650 | 382600 | 0 |
9/28/06 | 20.091 | 607.9 | 9348494 | 352686 | 0 |
10/20/06 | 16.583 | 604.6 | 9376027 | 354740 | 0 |
11/24/06 | 18.761 | 603.6 | 9410758 | 363468 | 0 |
12/29/06 | 28.795 | 604.5 | 9478531 | 424946 | 1 |
1/26/07 | 20.473 | 606.348 | 9540335 | 332797 | 0 |
(a)
(a) | Linear regression model to predict Wal-Mart revenue, using CPI as the only independent variable. | ||||||||||||||||
Wal Mart Revenue | CPI | ||||||||||||||||
14.764 | 552.7 | SUMMARY OUTPUT | |||||||||||||||
23.106 | 552.1 | ||||||||||||||||
12.131 | 554.9 | Regression Statistics | |||||||||||||||
13.628 | 557.9 | Multiple R | 0.3371520645 | ||||||||||||||
16.722 | 561.5 | R Square | 0.1136715146 | ||||||||||||||
13.98 | 563.2 | Adjusted R Square | 0.0897166907 | ||||||||||||||
14.388 | 566.4 | Standard Error | 3.6894006147 | ||||||||||||||
18.111 | 568.2 | Observations | 39 | ||||||||||||||
13.764 | 567.5 | ||||||||||||||||
14.296 | 567.6 | ANOVA | |||||||||||||||
17.169 | 568.7 | df | SS | MS | F | Significance F | |||||||||||
13.915 | 571.9 | Regression | 1 | 64.5907452267 | 64.5907452267 | 4.7452452569 | 0.0358255646 | ||||||||||
15.739 | 572.2 | Residual | 37 | 503.6320451322 | 13.6116768955 | ||||||||||||
26.177 | 570.1 | Total | 38 | 568.222790359 | |||||||||||||
13.17 | 571.2 | ||||||||||||||||
15.139 | 574.5 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
18.683 | 579 | Intercept | -24.4085437609 | 19.2484821488 | -1.2680762863 | 0.2126922535 | -63.4096732156 | 14.5925856938 | -63.4096732156 | 14.5925856938 | |||||||
14.829 | 582.9 | X Variable 1 | 0.0717915502 | 0.0329567213 | 2.1783583858 | 0.0358255646 | 0.0050148899 | 0.1385682105 | 0.0050148899 | 0.1385682105 | |||||||
15.697 | 582.4 | ||||||||||||||||
20.23 | 582.6 | ||||||||||||||||
15.26 | 585.2 | ||||||||||||||||
15.709 | 588.2 | RESIDUAL OUTPUT | |||||||||||||||
18.618 | 595.4 | ||||||||||||||||
15.397 | 596.7 | Observation | Predicted Y | Residuals | |||||||||||||
17.384 | 592 | 1 | 15.2706460301 | -0.5066460301 | |||||||||||||
27.92 | 589.4 | 2 | 15.2275711 | 7.8784289 | |||||||||||||
14.555 | 593.9 | 3 | 15.4285874405 | -3.2975874405 | |||||||||||||
18.684 | 595.2 | 4 | 15.6439620911 | -2.0159620911 | |||||||||||||
16.639 | 598.6 | 5 | 15.9024116718 | 0.8195883282 | |||||||||||||
20.17 | 603.5 | 6 | 16.0244573071 | -2.0444573071 | |||||||||||||
16.901 | 606.5 | 7 | 16.2541902677 | -1.8661902677 | |||||||||||||
21.47 | 607.8 | 8 | 16.3834150581 | 1.7275849419 | |||||||||||||
16.542 | 609.6 | 9 | 16.3331609729 | -2.5691609729 | |||||||||||||
16.98 | 610.9 | 10 | 16.3403401279 | -2.0443401279 | |||||||||||||
20.091 | 607.9 | 11 | 16.4193108331 | 0.7496891669 | |||||||||||||
16.583 | 604.6 | 12 | 16.6490437938 | -2.7340437938 | |||||||||||||
18.761 | 603.6 | 13 | 16.6705812588 | -0.9315812588 | |||||||||||||
28.795 | 604.5 | 14 | 16.5198190034 | 9.6571809966 | |||||||||||||
20.473 | 606.348 | 15 | 16.5987897086 | -3.4287897086 | |||||||||||||
SUMMARY OUTPUT | 16 | 16.8357018243 | -1.6967018243 | ||||||||||||||
17 | 17.1587638001 | 1.5242361999 | |||||||||||||||
Regression Statistics | 18 | 17.4387508459 | -2.6097508459 | ||||||||||||||
Multiple R | 0.3371520645 | 19 | 17.4028550708 | -1.7058550708 | |||||||||||||
R Square | 0.1136715146 | 20 | 17.4172133808 | 2.8127866192 | |||||||||||||
Adjusted R Square | 0.0897166907 | 21 | 17.6038714113 | -2.3438714113 | |||||||||||||
Standard Error | 3.6894006147 | 22 | 17.8192460619 | -2.1102460619 | |||||||||||||
Observations | 39 | 23 | 18.3361452233 | 0.2818547767 | |||||||||||||
24 | 18.4294742385 | -3.0324742385 | |||||||||||||||
ANOVA | 25 | 18.0920539526 | -0.7080539526 | ||||||||||||||
df | SS | 26 | 17.9053959221 | 10.0146040779 | |||||||||||||
Regression | 1 | 64.5907452267 | 27 | 18.228457898 | -3.673457898 | ||||||||||||
Residual | 37 | 503.6320451322 | 28 | 18.3217869132 | 0.3622130868 | ||||||||||||
Total | 38 | 568.222790359 | 29 | 18.5658781839 | -1.9268781839 | ||||||||||||
30 | 18.9176567798 | 1.2523432202 | |||||||||||||||
Coefficients | Standard Error | 31 | 19.1330314304 | -2.2320314304 | |||||||||||||
Intercept | -24.4085437609 | 19.2484821488 | 32 | 19.2263604456 | 2.2436395544 | ||||||||||||
X Variable 1 | 0.0717915502 | 0.0329567213 | 33 | 19.355585236 | -2.813585236 | ||||||||||||
34 | 19.4489142512 | -2.4689142512 | |||||||||||||||
35 | 19.2335396007 | 0.8574603993 | |||||||||||||||
the x-variable= 0.071792, the intercept= -24.4085 | 36 | 18.996627485 | -2.413627485 | ||||||||||||||
The regression equation is: | 37 | 18.9248359348 | -0.1638359348 | ||||||||||||||
38 | 18.98944833 | 9.80555167 | |||||||||||||||
Revenue= 0.071792*CPI-24.4085 | 39 | 19.1221191148 | 1.3508808852 | ||||||||||||||
Regression equation | y= 0.071792x-24.4085 |
X Variable 1 Residual Plot
552.70000000000005 552.1 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 570.1 571.20000000000005 574.5 579 582.9 582.4 582.6 585.2000 0000000005 588.20000000000005 595.4 596.70000000000005 592 589.4 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 604.5 606.34799999999996 -0.50664603008153364 7.8784289000335299 -3.2975874405033956 -2.0159620910786664 0.81958832823100281 -2.0444573070949943 -1.8661902677086193 1.7275849419462119 -2.5691609729195548 -2.0443401279387281 0.74968916685033093 -2.7340437937632878 -0.93158125882082032 9.6571809965818751 -3.4287897086290595 -1.696701824261865 1.5242361998752223 -2.6097508458726288 -1.7058550707767566 2.8127866191848909 -2.34387141131368 -2.110246061888958 0.28185477673038406 -3.032474238518903 -0.70805395261763593 10.014604077880936 -3.6734578979819794 0.36221308676873321 -1.9268781838832467 1.2523432201771421 -2.2320314303981377 2.2436395543525798 -2.813585235992587 -2.4689142512418698 0.85746039933340157 -2.4136274850337962 -0.16383593484204084 9.8055516699853804 1.3508808852310104X Variable 1
Residuals
Y 552.70000000000005 552.1 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 570.1 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 589.4 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 604.5 606.34799999999996 14.763999999999999 23.106000000000002 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 26.177 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 27.92 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 28.795000000000002 20.472999999999999 Predicted Y 552.70000000000005 552.1 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 570.1 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 589.4 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 604.5 606.34799999999996 15.270646030081533 15.227571099966472 15.428587440503396 15.643962091078667 15.902411671768999 16.024457307094995 16.254190267708619 16.383415058053789 16.333160972919554 16.340340127938727 16.41931083314967 16.649043793763287 16.670581258820821 16.519819003418124 16.598789708629059 16.835701824261864 17.158763800124778 17.438750845872629 17.402855070776756 17.41721338081511 17.60387141131368 17.819246061888958 18.336145223269614 18.429474238518903 18.092053952617636 17.905395922119066 18.228457897981979 18.321786913231268 18.565878183883246 18.91765677982286 19.133031430398137 19.226360445647419 19.355585235992589 19.44891425124187 19.2335396006666 18.996627485033795 18.92483593484204 18.989448330014621 19.122119114768989
(b)
(b) | Linear regression model to predict Wal-Mart revenue, using Personal Consumption as the only independent variable. | ||||||||||||||||
Wal Mart Revenue | Personal Consumption | ||||||||||||||||
14.764 | 7868495 | ||||||||||||||||
23.106 | 7885264 | SUMMARY OUTPUT | |||||||||||||||
12.131 | 7977730 | ||||||||||||||||
13.628 | 8005878 | Regression Statistics | |||||||||||||||
16.722 | 8070480 | Multiple R | 0.3940240291 | ||||||||||||||
13.98 | 8086579 | R Square | 0.1552549355 | ||||||||||||||
14.388 | 8196516 | Adjusted R Square | 0.1324239879 | ||||||||||||||
18.111 | 8161271 | Standard Error | 3.6018140987 | ||||||||||||||
13.764 | 8235349 | Observations | 39 | ||||||||||||||
14.296 | 8246121 | ||||||||||||||||
17.169 | 8313670 | ANOVA | |||||||||||||||
13.915 | 8371605 | df | SS | MS | F | Significance F | |||||||||||
15.739 | 8410820 | Regression | 1 | 88.219392691 | 88.219392691 | 6.8001967182 | 0.0130666987 | ||||||||||
26.177 | 8462026 | Residual | 37 | 480.003397668 | 12.9730648018 | ||||||||||||
13.17 | 8469443 | Total | 38 | 568.222790359 | |||||||||||||
15.139 | 8520687 | ||||||||||||||||
18.683 | 8568959 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
14.829 | 8654352 | Intercept | -8.8950748025 | 10.139008405 | -0.8773121046 | 0.3859782812 | -29.4386572154 | 11.6485076104 | -29.4386572154 | 11.6485076104 | |||||||
15.697 | 8644646 | X Variable 1 | 0.0000030282 | 0.0000011612 | 2.6077186808 | 0.0130666987 | 0.0000006753 | 0.000005381 | 0.0000006753 | 0.000005381 | |||||||
20.23 | 8724753 | ||||||||||||||||
15.26 | 8833907 | ||||||||||||||||
15.709 | 8825450 | ||||||||||||||||
18.618 | 8882536 | RESIDUAL OUTPUT | |||||||||||||||
15.397 | 8911627 | ||||||||||||||||
17.384 | 8916377 | Observation | Predicted Y | Residuals | |||||||||||||
27.92 | 8955472 | 1 | 14.932038192 | -0.168038192 | |||||||||||||
14.555 | 9034368 | 2 | 14.9828175161 | 8.1231824839 | |||||||||||||
18.684 | 9079246 | 3 | 15.2628199601 | -3.1318199601 | |||||||||||||
16.639 | 9123848 | 4 | 15.3480567908 | -1.7200567908 | |||||||||||||
20.17 | 9175181 | 5 | 15.5436824033 | 1.1783175967 | |||||||||||||
16.901 | 9238576 | 6 | 15.5924328558 | -1.6124328558 | |||||||||||||
21.47 | 9270505 | 7 | 15.9253403968 | -1.5373403968 | |||||||||||||
16.542 | 9338876 | 8 | 15.8186126683 | 2.2923873317 | |||||||||||||
16.98 | 9352650 | 9 | 16.0429331866 | -2.2789331866 | |||||||||||||
20.091 | 9348494 | 10 | 16.0755525962 | -1.7795525962 | |||||||||||||
16.583 | 9376027 | 11 | 16.2801022153 | 0.8888977847 | |||||||||||||
18.761 | 9410758 | 12 | 16.4555390417 | -2.5405390417 | |||||||||||||
28.795 | 9478531 | 13 | 16.5742885912 | -0.8352885912 | |||||||||||||
20.473 | 9540335 | 14 | 16.7293488852 | 9.4476511148 | |||||||||||||
15 | 16.7518087961 | -3.5818087961 | |||||||||||||||
SUMMARY OUTPUT | 16 | 16.9069841605 | -1.7679841605 | ||||||||||||||
17 | 17.0531598139 | 1.6298401861 | |||||||||||||||
Regression Statistics | 18 | 17.3117440362 | -2.4827440362 | ||||||||||||||
Multiple R | 0.3940240291 | 19 | 17.2823526521 | -1.5853526521 | |||||||||||||
R Square | 0.1552549355 | 20 | 17.5249299862 | 2.7050700138 | |||||||||||||
Adjusted R Square | 0.1324239879 | 21 | 17.8554664728 | -2.5954664728 | |||||||||||||
Standard Error | 3.6018140987 | 22 | 17.8298572687 | -2.1208572687 | |||||||||||||
Observations | 39 | 23 | 18.0027231817 | 0.6152768183 | |||||||||||||
24 | 18.0908155735 | -2.6938155735 | |||||||||||||||
ANOVA | 25 | 18.1051993644 | -0.7211993644 | ||||||||||||||
df | SS | 26 | 18.2235855338 | 9.6964144662 | |||||||||||||
Regression | 1 | 88.219392691 | 27 | 18.4624957583 | -3.9074957583 | ||||||||||||
Residual | 37 | 480.003397668 | 28 | 18.5983938147 | 0.0856061853 | ||||||||||||
Total | 38 | 568.222790359 | 29 | 18.7334560971 | -2.0944560971 | ||||||||||||
30 | 18.8889009682 | 1.2810990318 | |||||||||||||||
Coefficients | Standard Error | 31 | 19.0808715837 | -2.1798715837 | |||||||||||||
Intercept | -8.8950748025 | 10.139008405 | 32 | 19.177557912 | 2.292442088 | ||||||||||||
X Variable 1 | 0.0000030282 | 0.0000011612 | 33 | 19.3845966841 | -2.8425966841 | ||||||||||||
34 | 19.4263066495 | -2.4463066495 | |||||||||||||||
the x-variable is 3.0281E-06 or 0.000003028 | 35 | 19.4137215895 | 0.6772784105 | ||||||||||||||
the intercept is -8.895 | 36 | 19.4970960978 | -2.9140960978 | ||||||||||||||
regrssion equation | 37 | 19.6022673487 | -0.8412673487 | ||||||||||||||
based on personal consumption | y=0.000003028x-8.895 | 38 | 19.8074952772 | 8.9875047228 | |||||||||||||
39 | 19.9946480798 | 0.4783519202 |
X Variable 1 Residual Plot
7868495 7885264 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8462026 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825 450 8882536 8911627 8916377 8955472 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9478531 9540335 -0.16803819200906389 8.1231824838883462 -3.1318199600540702 -1.7200567908036568 1.178317596716429 -1.6124328558286045 -1.537340396759296 2.2923873316679142 -2.2789331866022202 -1.7795525961813929 0.88889778465192748 -2.5405390417470066 -0.83528859119439147 9.4476511148108955 -3.5818087961479552 -1.7679841604698154 1.6298401860576845 -2.4827440362031972 -1.585352652117102 2.7050700137612225 -2.5954664727969767 -2.120857268674154 0.6152768182886561 -2.6938 155734740317 -0.72119936436718746 9.6964144661658906 -3.9074957583196621 8.5606185321811523E-2 -2.0944560970816646 1.2810990317776358 -2.1798715837321687 2.2924420879672951 -2.8425966840655228 -2.4463066494891699 0.67727841050071547 -2.914096097849022 -0.84126734869326825 8.9875047228431981 0.47835192024097495X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 7868495 7885264 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8462026 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825450 8882536 8911627 8916377 8955472 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9478531 9540335 14.763999999999999 23.106000000000002 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 26.177 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 27.92 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 28.795000000000002 20.472999999999999 Predicted Y 7868495 7885264 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8462026 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825450 8882536 8911627 8916377 8955472 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9478531 9540335 14.932038192009063 14.982817516111655 15.26281996005407 15.348056790803657 15.543682403283572 15.592432855828605 15.925340396759296 15.818612668332086 16.04293318660222 16.075552596181392 16.280102215348073 16.455539041747006 16.574288591194392 16.729348885189104 16.751808796147955 16.906984160469815 17.053159813942315 17.311744036203198 17.282352652117101 17.524929986238778 17.855466472796977 17.829857268674154 18.002723181711342 18.090815573474032 18.105199364367188 18.223585533834111 18.462495758319662 18.59839381467819 18.733456097081664 18.888900968222366 19.080871583732169 19.177557912032704 19.384596684065524 19.42630664948917 19.413721589499286 19.49709609784902 19.602267348693267 19.807495277156804 19.994648079759024X Variable 1
Y
(c)
c) | Linear regression model to predict Wal-Mart revenue, using Retail Sales Index as the only independent variable. | ||||||||||||||||
Wal Mart Revenue | Retail Sales Index | ||||||||||||||||
14.764 | 301337 | ||||||||||||||||
23.106 | 357704 | ||||||||||||||||
12.131 | 281463 | SUMMARY OUTPUT | |||||||||||||||
13.628 | 282445 | ||||||||||||||||
16.722 | 319107 | Regression Statistics | |||||||||||||||
13.98 | 315278 | Multiple R | 0.7574074001 | ||||||||||||||
14.388 | 328499 | R Square | 0.5736659697 | ||||||||||||||
18.111 | 321151 | Adjusted R Square | 0.5621434283 | ||||||||||||||
13.764 | 328025 | Standard Error | 2.5587830317 | ||||||||||||||
14.296 | 326280 | Observations | 39 | ||||||||||||||
17.169 | 313444 | ||||||||||||||||
13.915 | 319639 | ANOVA | |||||||||||||||
15.739 | 324067 | df | SS | MS | F | Significance F | |||||||||||
26.177 | 386918 | Regression | 1 | 325.9700780358 | 325.9700780358 | 49.7864101155 | 0.0000000239 | ||||||||||
13.17 | 293027 | Residual | 37 | 242.2527123232 | 6.5473706033 | ||||||||||||
15.139 | 294892 | Total | 38 | 568.222790359 | |||||||||||||
18.683 | 338969 | ||||||||||||||||
14.829 | 335626 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
15.697 | 345400 | Intercept | -13.803967588 | 4.455669125 | -3.098068371 | 0.0037083535 | -22.8320107869 | -4.7759243891 | -22.8320107869 | -4.7759243891 | |||||||
20.23 | 351068 | X Variable 1 | 0.0000918587 | 0.0000130186 | 7.0559485624 | 0.0000000239 | 0.0000654805 | 0.000118237 | 0.0000654805 | 0.000118237 | |||||||
15.26 | 351887 | ||||||||||||||||
15.709 | 355897 | ||||||||||||||||
18.618 | 333652 | ||||||||||||||||
15.397 | 336662 | RESIDUAL OUTPUT | |||||||||||||||
17.384 | 344441 | ||||||||||||||||
27.92 | 406510 | Observation | Predicted Y | Residuals | |||||||||||||
14.555 | 322222 | 1 | 13.8764695716 | 0.8875304284 | |||||||||||||
18.684 | 318184 | 2 | 19.0542711737 | 4.0517288263 | |||||||||||||
16.639 | 366989 | 3 | 12.0508689712 | 0.0801310288 | |||||||||||||
20.17 | 357334 | 4 | 12.141074254 | 1.486925746 | |||||||||||||
16.901 | 380085 | 5 | 15.5087993828 | 1.2132006172 | |||||||||||||
21.47 | 373279 | 6 | 15.157072267 | -1.177072267 | |||||||||||||
16.542 | 368611 | 7 | 16.3715366696 | -1.9835366696 | |||||||||||||
16.98 | 382600 | 8 | 15.6965586475 | 2.4144413525 | |||||||||||||
20.091 | 352686 | 9 | 16.3279956268 | -2.5639956268 | |||||||||||||
16.583 | 354740 | 10 | 16.1677021254 | -1.8717021254 | |||||||||||||
18.761 | 363468 | 11 | 14.9886033377 | 2.1803966623 | |||||||||||||
28.795 | 424946 | 12 | 15.5576682325 | -1.6426682325 | |||||||||||||
20.473 | 332797 | 13 | 15.9644187336 | -0.2254187336 | |||||||||||||
14 | 21.7378324064 | 4.4391675936 | |||||||||||||||
15 | 13.1131234415 | 0.0568765585 | |||||||||||||||
SUMMARY OUTPUT | 16 | 13.2844399917 | 1.8545600083 | ||||||||||||||
17 | 17.3332976783 | 1.3497023217 | |||||||||||||||
Regression Statistics | 18 | 17.0262139102 | -2.1972139102 | ||||||||||||||
Multiple R | 0.7574074001 | 19 | 17.9240412357 | -2.2270412357 | |||||||||||||
R Square | 0.5736659697 | 20 | 18.4446965745 | 1.7853034255 | |||||||||||||
Adjusted R Square | 0.5621434283 | 21 | 18.5199288826 | -3.2599288826 | |||||||||||||
Standard Error | 2.5587830317 | 22 | 18.8882824303 | -3.1792824303 | |||||||||||||
Observations | 39 | 23 | 16.8448847573 | 1.7731152427 | |||||||||||||
24 | 17.1213795649 | -1.7243795649 | |||||||||||||||
ANOVA | 25 | 17.835948704 | -0.451948704 | ||||||||||||||
df | SS | 26 | 23.537528842 | 4.382471158 | |||||||||||||
Regression | 1 | 325.9700780358 | 27 | 15.7949393581 | -1.2399393581 | ||||||||||||
Residual | 37 | 242.2527123232 | 28 | 15.4240137657 | 3.2599862343 | ||||||||||||
Total | 38 | 568.222790359 | 29 | 19.9071795753 | -3.2681795753 | ||||||||||||
30 | 19.0202834398 | 1.1497165602 | |||||||||||||||
Coefficients | Standard Error | 31 | 21.1101616354 | -4.2091616354 | |||||||||||||
Intercept | -13.803967588 | 4.455669125 | 32 | 20.4849710504 | 0.9850289496 | ||||||||||||
X Variable 1 | 0.0000918587 | 0.0000130186 | 33 | 20.0561744517 | -3.5141744517 | ||||||||||||
34 | 21.3411863667 | -4.3611863667 | |||||||||||||||
the x-variable is 9.19E-05 or 0.0000919 | 35 | 18.5933240159 | 1.4976759841 | ||||||||||||||
the intercept is -13.804 | 36 | 18.7820018681 | -2.1990018681 | ||||||||||||||
37 | 19.5837449515 | -0.8227449515 | |||||||||||||||
38 | 25.2310365741 | 3.5639634259 | |||||||||||||||
Regression equation | y=0.0000919x-13.804 | 39 | 16.7663455345 | 3.7066544655 |
X Variable 1 Residual Plot
301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 0.8875304284375396 4.0517288263375875 8.0131028791196712E-2 1.4869257460324512 1.2132006172125998 -1.1770722670203604 -1.9835366696205252 2.4144413524886978 -2.5639956268225177 -1.871702125382587 2.1803966622867037 -1.6426682325100614 -0.22541873358512987 4.439167593634977 5.6876558503899943E-2 1.8545600082543494 1.3497023217399082 -2.1972139101720245 -2.2270412357157809 1.7853034255097135 -3.2599288826159576 -3.179282430337512 1.7731152427462646 -1.7243795648951004 -0.45194870397888209 4.3824711579839359 -1.2399393581371854 3.2599862343066164 -3.2681795753069629 1.1497165601672563 -4.2091616353970984 0.98502894958865994 -3.5141744517170252 -4.3611863666987709 1.4976759840599669 -2.199001868064741 -0.82274495148461924 3.5639634258655875 3.706654465514827X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 14.763999999999999 23.106000000000002 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 26.177 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 27.92 14.555 18.68400000000000 1 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 28.795000000000002 20.472999999999999 Predicted Y 301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 13.87646957156246 19.054271173662414 12.050868971208804 12.141074253967549 15.508799382787402 15.157072267020361 16.371536669620525 15.696558647511303 16.327995626822517 16.167702125382586 14.988603337713297 15.557668232510061 15.964418733585131 21.737832406365023 13.1131234414961 13.28443999174565 17.333297678260092 17.026213910172025 17.92404123571578 18.444696574490287 18.519928882615957 18.888282430337512 16.844884757253734 17.121379564895101 17.835948703978882 23.537528842016066 15.794939358137185 15.424 013765693385 19.907179575306962 19.020283439832745 21.110161635397098 20.484971050411339 20.056174451717027 21.341186366698771 18.593324015940034 18.782001868064739 19.583744951484618 25.231036574134414 16.766345534485172X Variable 1
Y
(d)
(d) | Which of these three models is the best? Use R-square values, Significance F values, p-values and other appropriate criteria to explain your answer. | |||
The regression equation with the highest R-square value is the best regression equation because it means the data is closest to the regression equation | ||||
For Revenue versus CPI | ||||
R-squared value=0.1137 | ||||
For Revenue and personal consumption: | ||||
R-squared value=0.115 | ||||
For Revenue and Retails sales index | ||||
R-squared value=0.5737 | ||||
From R-squared value, the Revenue and the Retails Sales index gives the best regression equation because it has the highest value of the R-squared value | ||||
It has also the lowest p-value, meaning it is the best regression equation | ||||
It also has the highest value of the F-statistic | ||||
Regresion equation of the Revenue and the Retails Sales Index has the best regression equation |
(e)
e) | Residual plot of the revenue vs retails sales index | |||||||||||||
Wal Mart Revenue | Retail Sales Index | |||||||||||||
14.764 | 301337 | |||||||||||||
23.106 | 357704 | |||||||||||||
12.131 | 281463 | |||||||||||||
13.628 | 282445 | |||||||||||||
16.722 | 319107 | |||||||||||||
13.98 | 315278 | |||||||||||||
14.388 | 328499 | |||||||||||||
18.111 | 321151 | |||||||||||||
13.764 | 328025 | |||||||||||||
14.296 | 326280 | |||||||||||||
17.169 | 313444 | |||||||||||||
13.915 | 319639 | |||||||||||||
15.739 | 324067 | |||||||||||||
26.177 | 386918 | |||||||||||||
13.17 | 293027 | |||||||||||||
15.139 | 294892 | |||||||||||||
18.683 | 338969 | |||||||||||||
14.829 | 335626 | |||||||||||||
15.697 | 345400 | |||||||||||||
20.23 | 351068 | |||||||||||||
15.26 | 351887 | |||||||||||||
15.709 | 355897 | |||||||||||||
18.618 | 333652 | |||||||||||||
15.397 | 336662 | |||||||||||||
17.384 | 344441 | |||||||||||||
27.92 | 406510 | |||||||||||||
14.555 | 322222 | |||||||||||||
18.684 | 318184 | |||||||||||||
16.639 | 366989 | |||||||||||||
20.17 | 357334 | |||||||||||||
16.901 | 380085 | |||||||||||||
21.47 | 373279 | |||||||||||||
16.542 | 368611 | |||||||||||||
16.98 | 382600 | |||||||||||||
20.091 | 352686 | |||||||||||||
16.583 | 354740 | |||||||||||||
18.761 | 363468 | |||||||||||||
28.795 | 424946 | |||||||||||||
20.473 | 332797 | |||||||||||||
Regression Statistics | COMMENTS | |||||||||||||
Multiple R | 0.7574074001 | They line plot indicates a strong correlation between Y and the predicted Y, meaning the regression equation is strong | ||||||||||||
R Square | 0.5736659697 | The residual plot indicates the residuals are almost evenly distributed above and below 0, indicating the regression equation is strong | ||||||||||||
Adjusted R Square | 0.5621434283 | |||||||||||||
Standard Error | 2.5587830317 | |||||||||||||
Observations | 39 | |||||||||||||
ANOVA | ||||||||||||||
df | SS | MS | F | Significance F | ||||||||||
Regression | 1 | 325.9700780358 | 325.9700780358 | 49.7864101155 | 0.0000000239 | |||||||||
Residual | 37 | 242.2527123232 | 6.5473706033 | |||||||||||
Total | 38 | 568.222790359 | ||||||||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||||
Intercept | -13.803967588 | 4.455669125 | -3.098068371 | 0.0037083535 | -22.8320107869 | -4.7759243891 | -22.8320107869 | -4.7759243891 | ||||||
X Variable 1 | 0.0000918587 | 0.0000130186 | 7.0559485624 | 0.0000000239 | 0.0000654805 | 0.000118237 | 0.0000654805 | 0.000118237 | ||||||
RESIDUAL OUTPUT | ||||||||||||||
Observation | Predicted Y | Residuals | ||||||||||||
1 | 13.8764695716 | 0.8875304284 | ||||||||||||
2 | 19.0542711737 | 4.0517288263 | ||||||||||||
3 | 12.0508689712 | 0.0801310288 | ||||||||||||
4 | 12.141074254 | 1.486925746 | ||||||||||||
5 | 15.5087993828 | 1.2132006172 | ||||||||||||
6 | 15.157072267 | -1.177072267 | ||||||||||||
7 | 16.3715366696 | -1.9835366696 | ||||||||||||
8 | 15.6965586475 | 2.4144413525 | ||||||||||||
9 | 16.3279956268 | -2.5639956268 | ||||||||||||
10 | 16.1677021254 | -1.8717021254 | ||||||||||||
11 | 14.9886033377 | 2.1803966623 | ||||||||||||
12 | 15.5576682325 | -1.6426682325 | ||||||||||||
13 | 15.9644187336 | -0.2254187336 | ||||||||||||
14 | 21.7378324064 | 4.4391675936 | ||||||||||||
15 | 13.1131234415 | 0.0568765585 | ||||||||||||
16 | 13.2844399917 | 1.8545600083 | ||||||||||||
17 | 17.3332976783 | 1.3497023217 | ||||||||||||
18 | 17.0262139102 | -2.1972139102 | ||||||||||||
19 | 17.9240412357 | -2.2270412357 | ||||||||||||
20 | 18.4446965745 | 1.7853034255 | ||||||||||||
21 | 18.5199288826 | -3.2599288826 | ||||||||||||
22 | 18.8882824303 | -3.1792824303 | ||||||||||||
23 | 16.8448847573 | 1.7731152427 | ||||||||||||
24 | 17.1213795649 | -1.7243795649 | ||||||||||||
25 | 17.835948704 | -0.451948704 | ||||||||||||
26 | 23.537528842 | 4.382471158 | ||||||||||||
27 | 15.7949393581 | -1.2399393581 | ||||||||||||
28 | 15.4240137657 | 3.2599862343 | ||||||||||||
29 | 19.9071795753 | -3.2681795753 | ||||||||||||
30 | 19.0202834398 | 1.1497165602 | ||||||||||||
31 | 21.1101616354 | -4.2091616354 | ||||||||||||
32 | 20.4849710504 | 0.9850289496 | ||||||||||||
33 | 20.0561744517 | -3.5141744517 | ||||||||||||
34 | 21.3411863667 | -4.3611863667 | ||||||||||||
35 | 18.5933240159 | 1.4976759841 | ||||||||||||
36 | 18.7820018681 | -2.1990018681 | ||||||||||||
37 | 19.5837449515 | -0.8227449515 | ||||||||||||
38 | 25.2310365741 | 3.5639634259 | ||||||||||||
39 | 16.7663455345 | 3.7066544655 |
X Variable 1 Residual Plot
301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 0.8875304284375396 4.0517288263375875 8.0131028791196712E-2 1.4869257460324512 1.2132006172125998 -1.1770722670203604 -1.9835366696205252 2.4144413524886978 -2.5639956268225177 -1.871702125382587 2.1803966622867037 -1.6426682325100614 -0.22541873358512987 4.439167593634977 5.6876558503899943E-2 1.8545600082543494 1.3497023217399082 -2.1972139101720245 -2.2270412357157809 1.7853034255097135 -3.2599288826159576 -3.179282430337512 1.7731152427462646 -1.7243795648951004 -0.45194870397888209 4.3824711579839359 -1.2399393581371854 3.2599862343066164 -3.2681795753069629 1.1497165601672563 -4.2091616353970984 0.98502894958865994 -3.5141744517170252 -4.3611863666987709 1.4976759840599669 -2.199001868064741 -0.82274495148461924 3.5639634258655875 3.706654465514827X Variable 1
Residuals
Y 301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 14.763999999999999 23.106000000000002 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 26.177 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 27.92 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 28.795000000000002 20.472999999999999 Predicted Y 301337 357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 406510 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 424946 332797 13.87646957156246 19.054271173662414 12.050868971208804 12.141074253967549 15.508799382787402 15.157072267020361 16.371536669620525 15.696558647511303 16.327995626822517 16.167702125382586 14.988603337713297 15.557668232510061 15.964418733585131 21.737832406365023 13.1131234414961 13.28443999174565 17.333297678260092 17.026213910172025 17.92404123571578 18.444696574490287 18.519928882615957 18.888282430337512 16.844884757253734 17.121379564895101 17.835948703978882 23.537528842016066 15.7949393581371 85 15.424013765693385 19.907179575306962 19.020283439832745 21.110161635397098 20.484971050411339 20.056174451717027 21.341186366698771 18.593324015940034 18.782001868064739 19.583744951484618 25.231036574134414 16.766345534485172
(f)
(f) | Identify and remove the four cases corresponding to December revenue. | |||||||||||||
Develop a linear regression model to predict Wal-Mart revenue, using CPI as the only independent variable. | ||||||||||||||
We remove the values with 1 | ||||||||||||||
After removing, the new data is as follows: | ||||||||||||||
Wal Mart Revenue | CPI | |||||||||||||
14.764 | 552.7 | |||||||||||||
12.131 | 554.9 | |||||||||||||
13.628 | 557.9 | |||||||||||||
16.722 | 561.5 | |||||||||||||
13.98 | 563.2 | |||||||||||||
14.388 | 566.4 | |||||||||||||
18.111 | 568.2 | |||||||||||||
13.764 | 567.5 | |||||||||||||
14.296 | 567.6 | |||||||||||||
17.169 | 568.7 | |||||||||||||
13.915 | 571.9 | |||||||||||||
15.739 | 572.2 | |||||||||||||
13.17 | 571.2 | |||||||||||||
15.139 | 574.5 | |||||||||||||
18.683 | 579 | |||||||||||||
14.829 | 582.9 | |||||||||||||
15.697 | 582.4 | |||||||||||||
20.23 | 582.6 | |||||||||||||
15.26 | 585.2 | |||||||||||||
15.709 | 588.2 | |||||||||||||
18.618 | 595.4 | |||||||||||||
15.397 | 596.7 | |||||||||||||
17.384 | 592 | |||||||||||||
14.555 | 593.9 | |||||||||||||
18.684 | 595.2 | |||||||||||||
16.639 | 598.6 | |||||||||||||
20.17 | 603.5 | |||||||||||||
16.901 | 606.5 | |||||||||||||
21.47 | 607.8 | |||||||||||||
16.542 | 609.6 | |||||||||||||
16.98 | 610.9 | |||||||||||||
20.091 | 607.9 | |||||||||||||
16.583 | 604.6 | |||||||||||||
18.761 | 603.6 | |||||||||||||
20.473 | 606.348 | |||||||||||||
SUMMARY OUTPUT | ||||||||||||||
Regression Statistics | ||||||||||||||
Multiple R | 0.6447522354 | |||||||||||||
R Square | 0.4157054451 | |||||||||||||
Adjusted R Square | 0.3979995495 | |||||||||||||
Standard Error | 1.8267603919 | |||||||||||||
Observations | 35 | |||||||||||||
ANOVA | ||||||||||||||
df | SS | MS | F | Significance F | ||||||||||
Regression | 1 | 78.3485542745 | 78.3485542745 | 23.4783630486 | 0.0000290663 | |||||||||
Residual | 33 | 110.1227664683 | 3.3370535293 | |||||||||||
Total | 34 | 188.4713207429 | ||||||||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||||
Intercept | -33.1342186173 | 10.2426576417 | -3.2349239598 | 0.0027654609 | -53.9730622759 | -12.2953749587 | -53.9730622759 | -12.2953749587 | ||||||
X Variable 1 | 0.0848979804 | 0.0175211841 | 4.8454476624 | 0.0000290663 | 0.0492508634 | 0.1205450974 | 0.0492508634 | 0.1205450974 | ||||||
Regression equation | y=0.0849x-33.1342 | |||||||||||||
RESIDUAL OUTPUT | ||||||||||||||
Observation | Predicted Y | Residuals | ||||||||||||
1 | 13.7888951429 | 0.9751048571 | ||||||||||||
2 | 13.9756706998 | -1.8446706998 | ||||||||||||
3 | 14.2303646409 | -0.6023646409 | ||||||||||||
4 | 14.5359973703 | 2.1860026297 | ||||||||||||
5 | 14.680323937 | -0.700323937 | ||||||||||||
6 | 14.9519974742 | -0.5639974742 | ||||||||||||
7 | 15.1048138389 | 3.0061861611 | ||||||||||||
8 | 15.0453852527 | -1.2813852527 | ||||||||||||
9 | 15.0538750507 | -0.7578750507 | ||||||||||||
10 | 15.1472628291 | 2.0217371709 | ||||||||||||
11 | 15.4189363664 | -1.5039363664 | ||||||||||||
12 | 15.4444057605 | 0.2945942395 | ||||||||||||
13 | 15.3595077801 | -2.1895077801 | ||||||||||||
14 | 15.6396711154 | -0.5006711154 | ||||||||||||
15 | 16.0217120271 | 2.6612879729 | ||||||||||||
16 | 16.3528141506 | -1.5238141506 | ||||||||||||
17 | 16.3103651604 | -0.6133651604 | ||||||||||||
18 | 16.3273447565 | 3.9026552435 | ||||||||||||
19 | 16.5480795055 | -1.2880795055 | ||||||||||||
20 | 16.8027734467 | -1.0937734467 | ||||||||||||
21 | 17.4140389055 | 1.2039610945 | ||||||||||||
22 | 17.52440628 | -2.12740628 | ||||||||||||
23 | 17.1253857721 | 0.2586142279 | ||||||||||||
24 | 17.2866919349 | -2.7316919349 | ||||||||||||
25 | 17.3970593094 | 1.2869406906 | ||||||||||||
26 | 17.6857124427 | -1.0467124427 | ||||||||||||
27 | 18.1017125466 | 2.0682874534 | ||||||||||||
28 | 18.3564064878 | -1.4554064878 | ||||||||||||
29 | 18.4667738623 | 3.0032261377 | ||||||||||||
30 | 18.619590227 | -2.077590227 | ||||||||||||
31 | 18.7299576015 | -1.7499576015 | ||||||||||||
32 | 18.4752636603 | 1.6157363397 | ||||||||||||
33 | 18.195100325 | -1.612100325 | ||||||||||||
34 | 18.1102023446 | 0.6507976554 | ||||||||||||
35 | 18.3435019947 | 2.1294980053 |
X Variable 1 Residual Plot
552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 606.34799999999996 0.97510485708523831 -1.8446706997674127 -0.60236464093012643 2.1860026296746184 -0.70032393698425821 -0.56399747422448421 3.0061861610778884 -1.2813852526508107 -0.75787505068957017 2.0217371708840979 -1.5039363663561218 0.29459423952760133 -2.1895077800848259 -0.50067111536381148 2.6612879728921186 -1.5238141506194012 -0.61336516042561939 3.9026552434968629 -1.2880795055108205 -1.0937734466735343 1.2039610945359591 -2.1274062799678912 0.25861422785369825 -2.7316919348826829 1.2869406906134664 -1.0467124427042727 2.0682874533966285 -1.4554064877660799 3.0032261377300742 -2.0775902269675512 -1.7499576014713902 1.6157363396913169 -1.6121003250297008 0.65079765535787359 2.1294980052528274X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.200 00000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 606.34799999999996 14.763999999999999 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 20.472999999999999 Predicted Y 552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.7999999999999 5 609.6 610.9 607.9 604.6 603.6 606.34799999999996 13.788895142914761 13.975670699767413 14.230364640930127 14.535997370325383 14.680323936984259 14.951997474224484 15.104813838922112 15.04538525265081 15.05387505068957 15.147262829115903 15.418936366356121 15.444405760472399 15.359507780084826 15.639671115363811 16.021712027107881 16.352814150619402 16.310365160425619 16.327344756503138 16.54807950551082 16.802773446673534 17.414038905464039 17.524406279967891 17.125385772146302 17.286691934882683 17.397059309386535 17.685712442704272 18.101712546603373 18.35640648776608 18.466773862269925 18.619590226967553 18.729957601471391 18.475263660308684 18.195 100325029699 18.110202344642126 18.343501994747172X Variable 1
Y
(g)
(g) | Develop a linear regression model to predict Wal-Mart revenue, using Personal Consumption as the only independent variable. | ||||||||||||||||
Wal Mart Revenue | Personal Consumption | ||||||||||||||||
14.764 | 7868495 | ||||||||||||||||
12.131 | 7977730 | ||||||||||||||||
13.628 | 8005878 | SUMMARY OUTPUT | |||||||||||||||
16.722 | 8070480 | ||||||||||||||||
13.98 | 8086579 | Regression Statistics | |||||||||||||||
14.388 | 8196516 | Multiple R | 0.6352809133 | ||||||||||||||
18.111 | 8161271 | R Square | 0.4035818388 | ||||||||||||||
13.764 | 8235349 | Adjusted R Square | 0.3855085612 | ||||||||||||||
14.296 | 8246121 | Standard Error | 1.8456149387 | ||||||||||||||
17.169 | 8313670 | Observations | 35 | ||||||||||||||
13.915 | 8371605 | ||||||||||||||||
15.739 | 8410820 | ANOVA | |||||||||||||||
13.17 | 8469443 | df | SS | MS | F | Significance F | |||||||||||
15.139 | 8520687 | Regression | 1 | 76.0636021829 | 76.0636021829 | 22.330307066 | 0.0000413258 | ||||||||||
18.683 | 8568959 | Residual | 33 | 112.40771856 | 3.4062945018 | ||||||||||||
14.829 | 8654352 | Total | 34 | 188.4713207429 | |||||||||||||
15.697 | 8644646 | ||||||||||||||||
20.23 | 8724753 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
15.26 | 8833907 | Intercept | -10.0401404897 | 5.6194273236 | -1.7866839291 | 0.083178865 | -21.4729513425 | 1.3926703632 | -21.4729513425 | 1.3926703632 | |||||||
15.709 | 8825450 | X Variable 1 | 0.0000030407 | 0.0000006435 | 4.7254954307 | 0.0000413258 | 0.0000017316 | 0.0000043498 | 0.0000017316 | 0.0000043498 | |||||||
18.618 | 8882536 | ||||||||||||||||
15.397 | 8911627 | ||||||||||||||||
17.384 | 8916377 | ||||||||||||||||
14.555 | 9034368 | RESIDUAL OUTPUT | |||||||||||||||
18.684 | 9079246 | ||||||||||||||||
16.639 | 9123848 | Observation | Predicted Y | Residuals | |||||||||||||
20.17 | 9175181 | 1 | 13.8855277296 | 0.8784722704 | |||||||||||||
16.901 | 9238576 | 2 | 14.2176776983 | -2.0866776983 | |||||||||||||
21.47 | 9270505 | 3 | 14.3032670911 | -0.6752670911 | |||||||||||||
16.542 | 9338876 | 4 | 14.4997018627 | 2.2222981373 | |||||||||||||
16.98 | 9352650 | 5 | 14.54865396 | -0.56865396 | |||||||||||||
20.091 | 9348494 | 6 | 14.8829384943 | -0.4949384943 | |||||||||||||
16.583 | 9376027 | 7 | 14.7757693118 | 3.3352306882 | |||||||||||||
18.761 | 9410758 | 8 | 15.0010176789 | -1.2370176789 | |||||||||||||
20.473 | 9540335 | 9 | 15.033772011 | -0.737772011 | |||||||||||||
10 | 15.2391677014 | 1.9298322986 | |||||||||||||||
11 | 15.4153301807 | -1.5003301807 | |||||||||||||||
12 | 15.5345709097 | 0.2044290903 | |||||||||||||||
13 | 15.712825385 | -2.542825385 | |||||||||||||||
14 | 15.8686425956 | -0.7296425956 | |||||||||||||||
15 | 16.0154228701 | 2.6675771299 | |||||||||||||||
SUMMARY OUTPUT | 16 | 16.2750766649 | -1.4460766649 | ||||||||||||||
17 | 16.2455637103 | -0.5485637103 | |||||||||||||||
Regression Statistics | 18 | 16.4891444083 | 3.7408555917 | ||||||||||||||
Multiple R | 0.6352809133 | 19 | 16.8210480809 | -1.5610480809 | |||||||||||||
R Square | 0.4035818388 | 20 | 16.7953329504 | -1.0863329504 | |||||||||||||
Adjusted R Square | 0.3855085612 | 21 | 16.9689138825 | 1.6490861175 | |||||||||||||
Standard Error | 1.8456149387 | 22 | 17.0573706476 | -1.6603706476 | |||||||||||||
Observations | 35 | 23 | 17.0718139336 | 0.3121860664 | |||||||||||||
24 | 17.4305881997 | -2.8755881997 | |||||||||||||||
ANOVA | 25 | 17.5670483663 | 1.1169516337 | ||||||||||||||
df | SS | 26 | 17.7026693019 | -1.0636693019 | |||||||||||||
Regression | 1 | 76.0636021829 | 27 | 17.8587571341 | 2.3112428659 | ||||||||||||
Residual | 33 | 112.40771856 | 28 | 18.0515217907 | -1.1505217907 | ||||||||||||
Total | 34 | 188.4713207429 | 29 | 18.1486080391 | 3.3213919609 | ||||||||||||
30 | 18.3565031781 | -1.8145031781 | |||||||||||||||
Coefficients | Standard Error | 31 | 18.398385667 | -1.418385667 | |||||||||||||
Intercept | -10.0401404897 | 5.6194273236 | 32 | 18.3857485519 | 1.7052514481 | ||||||||||||
X Variable 1 | 0.0000030407 | 0.0000006435 | 33 | 18.4694679192 | -1.8864679192 | ||||||||||||
34 | 18.5750741861 | 0.1859258139 | |||||||||||||||
x-variable is 3.04E-06 or 0.00000304 | 35 | 18.9690779073 | 1.5039220927 | ||||||||||||||
intercept is -10.04 | |||||||||||||||||
Regression equation | y=0.00000304x-10.04 |
X Variable 1 Residual Plot
7868495 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825450 8882536 8911 627 8916377 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9540335 0.87847227039468123 -2.0866776983009174 -0.6752670910673686 2.2222981373148087 -0.56865395996198487 -0.49493849430068515 3.3352306881653391 -1.2370176789425713 -0.73777201100453738 1.9298322986451275 -1.5003301807468219 0.20442909034396806 -2.5428253850058926 -0.72964259556878375 2.6675771298958217 -1.446076664921069 -0.54856371031714701 3.7408555917170183 -1.5610480809428378 -1.0863329503962298 1.6490861175494196 -1.6603706475837665 0.31218606636960189 -2.8755881997205925 1.1169516337108085 -1.0636693019211876 2.311 2428659457862 -1.1505217906702931 3.3213919608701303 -1.8145031781392191 -1.4183856669826618 1.7052514481351935 -1.8864679191746987 0.18592581394411312 1.5039220926673309X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 7868495 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825450 8882536 8911627 8916377 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9540335 14.763999999999999 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 20.472999999999999 Predicted Y 7868495 7977730 8005878 8070480 8086579 8196516 8161271 8235349 8246121 8313670 8371605 8410820 8469443 8520687 8568959 8654352 8644646 8724753 8833907 8825450 8882536 8911627 8916377 9034368 9079246 9123848 9175181 9238576 9270505 9338876 9352650 9348494 9376027 9410758 9540335 13.885527729605318 14.217677698300918 14.303267091067369 14.499701862685193 14.548653959961985 14.882938494300685 14.775769311834662 15.001017678942571 15.033772011004537 15.239167701354873 15.415330180746821 15.534570909656033 15.712825385005893 15.868642595568783 16.015422870104178 16.27507666492107 16.245563710317146 16.489144408282982 16.821048080942838 16.795332950396229 16.968913882450579 17.057370647583767 17.071813933630398 17.430588199720592 17.567048366289193 17.702669301921187 17.858757134054215 18.051521790670293 18.148608039129869 18.356503178139221 18.398385666982662 18.385748551864808 18.469467919174697 18.575074186055886 18.969077907332668X Variable 1
Y
(h)
(h) | Develop a linear regression model to predict Wal-Mart revenue, using Retail Sales Index as the only independent variable. | ||||||||||||||||
Wal Mart Revenue | Retail Sales Index | ||||||||||||||||
14.764 | 301337 | ||||||||||||||||
12.131 | 281463 | ||||||||||||||||
13.628 | 282445 | SUMMARY OUTPUT | |||||||||||||||
16.722 | 319107 | ||||||||||||||||
13.98 | 315278 | Regression Statistics | |||||||||||||||
14.388 | 328499 | Multiple R | 0.5699442193 | ||||||||||||||
18.111 | 321151 | R Square | 0.3248364131 | ||||||||||||||
13.764 | 328025 | Adjusted R Square | 0.3043769105 | ||||||||||||||
14.296 | 326280 | Standard Error | 1.9636775405 | ||||||||||||||
17.169 | 313444 | Observations | 35 | ||||||||||||||
13.915 | 319639 | ||||||||||||||||
15.739 | 324067 | ANOVA | |||||||||||||||
13.17 | 293027 | df | SS | MS | F | Significance F | |||||||||||
15.139 | 294892 | Regression | 1 | 61.2223478005 | 61.2223478005 | 15.8770434896 | 0.0003514832 | ||||||||||
18.683 | 338969 | Residual | 33 | 127.2489729423 | 3.8560294831 | ||||||||||||
14.829 | 335626 | Total | 34 | 188.4713207429 | |||||||||||||
15.697 | 345400 | ||||||||||||||||
20.23 | 351068 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
15.26 | 351887 | Intercept | -0.6013362599 | 4.2980384153 | -0.1399094661 | 0.8895819742 | -9.3457611648 | 8.143088645 | -9.3457611648 | 8.143088645 | |||||||
15.709 | 355897 | X Variable 1 | 0.000051012 | 0.0000128023 | 3.9846007943 | 0.0003514832 | 0.0000249656 | 0.0000770585 | 0.0000249656 | 0.0000770585 | |||||||
18.618 | 333652 | ||||||||||||||||
15.397 | 336662 | ||||||||||||||||
17.384 | 344441 | ||||||||||||||||
14.555 | 322222 | RESIDUAL OUTPUT | |||||||||||||||
18.684 | 318184 | ||||||||||||||||
16.639 | 366989 | Observation | Predicted Y | Residuals | |||||||||||||
20.17 | 357334 | 1 | 14.7704766892 | -0.0064766892 | |||||||||||||
16.901 | 380085 | 2 | 13.7566635479 | -1.6256635479 | |||||||||||||
21.47 | 373279 | 3 | 13.8067573642 | -0.1787573642 | |||||||||||||
16.542 | 368611 | 4 | 15.6769605133 | 1.0450394867 | |||||||||||||
16.98 | 382600 | 5 | 15.4816354394 | -1.5016354394 | |||||||||||||
20.091 | 352686 | 6 | 16.156065526 | -1.768065526 | |||||||||||||
16.583 | 354740 | 7 | 15.7812291084 | 2.3297708916 | |||||||||||||
18.761 | 363468 | 8 | 16.1318858224 | -2.3678858224 | |||||||||||||
20.473 | 332797 | 9 | 16.042869825 | -1.746869825 | |||||||||||||
10 | 15.3880793711 | 1.7809206289 | |||||||||||||||
11 | 15.7040989147 | -1.7890989147 | |||||||||||||||
12 | 15.9299801963 | -0.1909801963 | |||||||||||||||
13 | 14.346566696 | -1.176566696 | |||||||||||||||
14 | 14.4417041373 | 0.6972958627 | |||||||||||||||
15 | 16.6901615101 | 1.9928384899 | |||||||||||||||
SUMMARY OUTPUT | 16 | 16.5196282842 | -1.6906282842 | ||||||||||||||
17 | 17.0182198935 | -1.3212198935 | |||||||||||||||
Regression Statistics | 18 | 17.3073560958 | 2.9226439042 | ||||||||||||||
Multiple R | 0.5699442193 | 19 | 17.3491349508 | -2.0891349508 | |||||||||||||
R Square | 0.3248364131 | 20 | 17.5536932026 | -1.8446932026 | |||||||||||||
Adjusted R Square | 0.3043769105 | 21 | 16.4189305314 | 2.1990694686 | |||||||||||||
Standard Error | 1.9636775405 | 22 | 16.5724767503 | -1.1754767503 | |||||||||||||
Observations | 35 | 23 | 16.969299354 | 0.414700646 | |||||||||||||
24 | 15.8358629957 | -1.2808629957 | |||||||||||||||
ANOVA | 25 | 15.6298764069 | 3.0541235931 | ||||||||||||||
df | SS | 26 | 18.1195186712 | -1.4805186712 | |||||||||||||
Regression | 1 | 61.2223478005 | 27 | 17.6269974938 | 2.5430025062 | ||||||||||||
Residual | 33 | 127.2489729423 | 28 | 18.7875722536 | -1.8865722536 | ||||||||||||
Total | 34 | 188.4713207429 | 29 | 18.4403843579 | 3.0296156421 | ||||||||||||
30 | 18.2022601885 | -1.6602601885 | |||||||||||||||
Coefficients | Standard Error | 31 | 18.9158675163 | -1.9358675163 | |||||||||||||
Intercept | -0.6013362599 | 4.2980384153 | 32 | 17.389893565 | 2.701106435 | ||||||||||||
X Variable 1 | 0.000051012 | 0.0000128023 | 33 | 17.4946722805 | -0.9116722805 | ||||||||||||
34 | 17.9399053034 | 0.8210946966 | |||||||||||||||
x-variable is 0.000051 | 35 | 16.3753152433 | 4.0976847567 | ||||||||||||||
Intercept is -0.60134 | |||||||||||||||||
Regression equation is y=0.000051x-0.60134 |
X Variable 1 Residual Plot
301337 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 332797 -6.4766891549918881E-3 -1.6256635478893529 -0.17875736416805132 1.0450394867386201 -1.5016354394007507 -1.7680655259798481 2.3297708915515933 -2.3678858223992982 -1.746869825040509 1.7809206288834982 -1.7890989147484149 -0.19098019629839058 -1.1765666960022561 0.69729586269451183 1.9928384898674274 -1.6906282842469409 -1.3212198935218922 2.9226439041688792 -2.0891349507519497 -1.8446932025621159 2.1990694686391592 -1.1754767503006409 0.41470064600078871 -1.2808629956525657 3.0541235930779678 -1.4805186711602047 2.5430025062031731 -1.8865722536305078 3.0296156420851972 -1.6602601884759345 -1.9358675162994743 2.7011064349846308 -0.9116722805311035 0.82109469657634904 4.0976847567433197X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 301337 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 332797 14.763999999999999 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 20.472999999999999 Predicted Y 301337 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 293027 294892 338969 335626 345400 351068 351887 355897 333652 336662 344441 322222 318184 366989 357334 380085 373279 368611 382600 352686 354740 363468 332797 14.770476689154991 13.756663547889353 13.806757364168051 15.676960513261381 15.481635439400751 16.156065525979848 15.781229108448407 16.131885822399298 16.042869825040508 15.388079371116502 15.704098914748414 15.929980196298391 14.346566696002256 14.441704137305488 16.690161510132572 16.519628284246942 17.018219893521891 17.307356095831121 17.349134950751949 17.553693202562116 16.418930531360839 16.572476750300641 16.969299353999212 15.835862995652565 15.629876406922033 18.119518671160204 17.626997493796829 18.787572253630508 18.440384357914802 18.202260188475936 18.915867516299475 17.38989356501537 17.494672280531102 17.93990530342365 16.375315243256679X Variable 1
Y
(i)
(i) Which of these three models is the best? Use R-square values, Significance F values, p-values and other appropriate criteria to explain your answer. | |||||
We indentify the regression equation with the highest R-squared value, the highest F value and the lowest p-value | |||||
The regression equation with the highest R-square value is the best regression equation because it means the data is closest to the regression equation | |||||
For Revenue versus CPI | |||||
R-squared value = | 0.416 | ||||
For Revenue and personal consumption: | |||||
R-squared value= | 0.4036 | ||||
For Revenue and Retails sales index | |||||
R-squared value= | 0.3248 | ||||
The regression with the highest R-squared value, the highest F value, and the lowest p-value is the regression equation of Revenue on CPI | |||||
Best Regression | The regression of revenue on CPI |
(j)
(j) Generate a residual plot and a line fit plot for the best model in part (i) and comment on what you see. | ||||||||||||||
Wal Mart Revenue | CPI | |||||||||||||
14.764 | 552.7 | |||||||||||||
12.131 | 554.9 | |||||||||||||
13.628 | 557.9 | |||||||||||||
16.722 | 561.5 | |||||||||||||
13.98 | 563.2 | |||||||||||||
14.388 | 566.4 | |||||||||||||
18.111 | 568.2 | |||||||||||||
13.764 | 567.5 | |||||||||||||
14.296 | 567.6 | |||||||||||||
17.169 | 568.7 | |||||||||||||
13.915 | 571.9 | |||||||||||||
15.739 | 572.2 | |||||||||||||
13.17 | 571.2 | |||||||||||||
15.139 | 574.5 | |||||||||||||
18.683 | 579 | |||||||||||||
14.829 | 582.9 | |||||||||||||
15.697 | 582.4 | |||||||||||||
20.23 | 582.6 | |||||||||||||
15.26 | 585.2 | |||||||||||||
15.709 | 588.2 | |||||||||||||
18.618 | 595.4 | |||||||||||||
15.397 | 596.7 | |||||||||||||
17.384 | 592 | |||||||||||||
14.555 | 593.9 | |||||||||||||
18.684 | 595.2 | |||||||||||||
16.639 | 598.6 | |||||||||||||
20.17 | 603.5 | |||||||||||||
16.901 | 606.5 | |||||||||||||
21.47 | 607.8 | |||||||||||||
16.542 | 609.6 | |||||||||||||
16.98 | 610.9 | |||||||||||||
20.091 | 607.9 | |||||||||||||
16.583 | 604.6 | |||||||||||||
18.761 | 603.6 | Comment on the line plot and the residual plot | ||||||||||||
20.473 | 606.348 | |||||||||||||
The line fit plot indicates that the points are close to the regression equation | ||||||||||||||
Therefore, the regression equation is a good model for the data | ||||||||||||||
The residual plots indicate the residuals are almost evenly distributed around 0, meaning the regression equation is a good model | ||||||||||||||
SUMMARY OUTPUT | ||||||||||||||
Regression Statistics | ||||||||||||||
Multiple R | 0.6447522354 | |||||||||||||
R Square | 0.4157054451 | |||||||||||||
Adjusted R Square | 0.3979995495 | |||||||||||||
Standard Error | 1.8267603919 | |||||||||||||
Observations | 35 | |||||||||||||
ANOVA | ||||||||||||||
df | SS | MS | F | Significance F | ||||||||||
Regression | 1 | 78.3485542745 | 78.3485542745 | 23.4783630486 | 0.0000290663 | |||||||||
Residual | 33 | 110.1227664683 | 3.3370535293 | |||||||||||
Total | 34 | 188.4713207429 | ||||||||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||||
Intercept | -33.1342186173 | 10.2426576417 | -3.2349239598 | 0.0027654609 | -53.9730622759 | -12.2953749587 | -53.9730622759 | -12.2953749587 | ||||||
X Variable 1 | 0.0848979804 | 0.0175211841 | 4.8454476624 | 0.0000290663 | 0.0492508634 | 0.1205450974 | 0.0492508634 | 0.1205450974 | ||||||
RESIDUAL OUTPUT | ||||||||||||||
Observation | Predicted Y | Residuals | ||||||||||||
1 | 13.7888951429 | 0.9751048571 | ||||||||||||
2 | 13.9756706998 | -1.8446706998 | ||||||||||||
3 | 14.2303646409 | -0.6023646409 | ||||||||||||
4 | 14.5359973703 | 2.1860026297 | ||||||||||||
5 | 14.680323937 | -0.700323937 | ||||||||||||
6 | 14.9519974742 | -0.5639974742 | ||||||||||||
7 | 15.1048138389 | 3.0061861611 | ||||||||||||
8 | 15.0453852527 | -1.2813852527 | ||||||||||||
9 | 15.0538750507 | -0.7578750507 | ||||||||||||
10 | 15.1472628291 | 2.0217371709 | ||||||||||||
11 | 15.4189363664 | -1.5039363664 | ||||||||||||
12 | 15.4444057605 | 0.2945942395 | ||||||||||||
13 | 15.3595077801 | -2.1895077801 | ||||||||||||
14 | 15.6396711154 | -0.5006711154 | ||||||||||||
15 | 16.0217120271 | 2.6612879729 | ||||||||||||
16 | 16.3528141506 | -1.5238141506 | ||||||||||||
17 | 16.3103651604 | -0.6133651604 | ||||||||||||
18 | 16.3273447565 | 3.9026552435 | ||||||||||||
19 | 16.5480795055 | -1.2880795055 | ||||||||||||
20 | 16.8027734467 | -1.0937734467 | ||||||||||||
21 | 17.4140389055 | 1.2039610945 | ||||||||||||
22 | 17.52440628 | -2.12740628 | ||||||||||||
23 | 17.1253857721 | 0.2586142279 | ||||||||||||
24 | 17.2866919349 | -2.7316919349 | ||||||||||||
25 | 17.3970593094 | 1.2869406906 | ||||||||||||
26 | 17.6857124427 | -1.0467124427 | ||||||||||||
27 | 18.1017125466 | 2.0682874534 | ||||||||||||
28 | 18.3564064878 | -1.4554064878 | ||||||||||||
29 | 18.4667738623 | 3.0032261377 | ||||||||||||
30 | 18.619590227 | -2.077590227 | ||||||||||||
31 | 18.7299576015 | -1.7499576015 | ||||||||||||
32 | 18.4752636603 | 1.6157363397 | ||||||||||||
33 | 18.195100325 | -1.612100325 | ||||||||||||
34 | 18.1102023446 | 0.6507976554 | ||||||||||||
35 | 18.3435019947 | 2.1294980053 |
X Variable 1 Residual Plot
552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 606.34799999999996 0.97510485708523831 -1.8446706997674127 -0.60236464093012643 2.1860026296746184 -0.70032393698425821 -0.56399747422448421 3.0061861610778884 -1.2813852526508107 -0.75787505068957017 2.0217371708840979 -1.5039363663561218 0.29459423952760133 -2.1895077800848259 -0.50067111536381148 2.6612879728921186 -1.5238141506194012 -0.61336516042561939 3.9026552434968629 -1.2880795055108205 -1.0937734466735343 1.2039610945359591 -2.1274062799678912 0.25861422785369825 -2.7316919348826829 1.2869406906134664 -1.0467124427042727 2.0682874533966285 -1.4554064877660799 3.0032261377300742 -2.0775902269675512 -1.7499576014713902 1.6157363396913169 -1.6121003250297008 0.65079765535787359 2.1294980052528274X Variable 1
Residuals
X Variable 1 Line Fit Plot
Y 552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 606.34799999999996 14.763999999999999 12.131 13.628 16.722000000000001 13.98 14.388 18.111000000000001 13.763999999999999 14.295999999999999 17.169 13.914999999999999 15.739000000000001 13.17 15.138999999999999 18.683 14.829000000000001 15.696999999999999 20.23 15.26 15.709 18.617999999999999 15.397 17.384 14.555 18.684000000000001 16.638999999999999 20.170000000000002 16.901 21.47 16.542000000000002 16.98 20.091000000000001 16.582999999999998 18.760999999999999 20.472999999999999 Predicted Y 552.70000000000005 554.9 557.9 561.5 563.20000000000005 566.4 568.20000000000005 567.5 567.6 568.70000000000005 571.9 572.20000000000005 571.20000000000005 574.5 579 582.9 582.4 582.6 585.20000000000005 588.20000000000005 595.4 596.70000000000005 592 593.9 595.20000000000005 598.6 603.5 606.5 607.79999999999995 609.6 610.9 607.9 604.6 603.6 606.34799999999996 13.788895142914761 13.975670699767413 14.230364640930127 14.535997370325383 14.680323936984259 14.951997474224484 15.104813838922112 15.04538525265081 15.05387505068957 15.147262829115903 15.418936366356121 15.444405760472399 15.359507780084826 15.639671115363811 16.021712027107881 16.352814150619402 16.310365160425619 16.327344756503138 16.54807950551082 16.802773446673534 17.414038905464039 17.524406279967891 17.125385772146302 17.286691934882683 17.397059309386535 17.685712442704272 18.101712546603373 18.35640648776608 18.466773862269925 18.619590226967553 18.729957601471391 18.475263660308684 18.195100325029699 18.110202344642126 18.343501994747172X Variable 1
Y
(k)
(k) Comparing the results of parts (d) and (i), which of these two models is better? Use R-square values, Significance F values, p-values and other appropriate criteria to explain your answer | |||
We choose the regression equation with the highest R-squared value because it will be the best regression model for the data | |||
Comparing the two regression equations, the | |||
R-squared value for (d) is 0.5737 | |||
R-squared value for (I) is 0.4157 | |||
Therefore, (d) is the better regression model |
Paper:
Discuss at least two historical challenges urban planners have overcome. Be sure to include lessons learned for today’s public planners. Discuss the background, evolution, current status of each challenge, and lessons learned for today’s public planners. Explain the reasoning for your selections as a viable tool for today’s public planner.
NOTES: (below is information lifted for reference from the websites listed in the reference section.
· Agreements signed in 1977, including subsequent amendments, allow the Tribe and the City of Palm Springs to work closely together on development projects on reservation lands. These agreements define the process by which development projects on the reservation are reviewed.
· the Palm Springs area has been home to the Agua Caliente Band of Cahuilla Indians for generations. Archaeological research has discovered that the Cahuilla have occupied Tahquitz Canyon for at least 5,000 years, mirroring the migration stories of the Cahuilla people.
· Later, in 1877, President Hayes extended it to cover the even numbered sections in three townships, which totaled some 30,000+ acres. All of the land was tribally-owned. The Government had previously given the odd-numbered sections to the railroad in the early 1870s as an incentive to build a cross-country rail line. On January 12, 1891, the US Congress passed the Mission Indian Relief Act, authorizing allotments from the acreage comprising the Reservation. However, more than 50 years passed before the allotment elections were approved by the Secretary of the Interior. An allotment is a land parcel owned by a Tribal Member. The Equalization Act of September 21, 1959 finalized the individual Indian allotments. On a combined basis, the Tribe and its members currently represent the largest single land owner in Palm Springs.
Referenced Websites:
http://www.visionaguacaliente.com/history/
http://www.visitpalmsprings.com/palm-springs-history
http://www.aguacaliente.org/content/History%20&%20Culture/
http://www.ci.palm-springs.ca.us/government/departments/planning/for-land-development
HISTORICAL URBAN CHALLENGES – PALM SPRINGS
Historical Urban Challenges
Leigh Gileno
PPA401: Urban Management
Professor Angela McCormick
December 11, 2017
There is no question that when it comes to establishing a territory for people to live, there is great consideration and planning that must take place in order to provide life sustaining quality for not only people but also for the environment that includes wildlife and vegetation. This paper will focus on the challenges that the City of Palm Springs has faced over the last one hundred and forty years that incorporates the reservation boundaries and jurisdictional boundaries that overlap. Learning to respect a sovereign nation in order to develop land owned by the state has had many ups and downs.
Due Date: 12/11
Please use one Excel file to complete this case study, and use one spreadsheet for one problem. Finally, upload the Excel file to the submission link for grading.No credit will be granted for problems that are not completed using Excel.
Wal-Mart is the second largest retailer in the world. The data file (WalMart_revenue.xlsx) is included in the Excel data zip file in week one, and it holds monthly data on Wal-Mart’s revenue, along with several possibly related economic variables.
(a) Develop a multiple linear regression model to predict Wal-Mart revenue, using CPI, Personal Consumption, and Retail Sales Index as the independent variables.
(b) Find the residuals and the predicted values for the multiple regression model, and then plot the residuals against the predicted values by Excel’s scatter chart (Insert tab > Charts > Scatter chart). Comment on what you see on the plot.
(c) Does it seem that Wal-Mart’s revenue is closely related to the general state of the economy?
Identify and remove the four cases corresponding to December revenue.
(d) Develop a multiple linear regression model to predict Wal-Mart revenue, using CPI, Personal Consumption, and Retail Sales Index as the independent variables.
(e) Find the residuals and the predicted values for the multiple regression model, and then plot the residuals against the predicted values by Excel’s scatter chart (Insert tab > Charts > Scatter chart). Comment on what you see on the plot.
(f) Does it seem that Wal-Mart’s revenue is closely related to the general state of the economy?
(g) Compare the results of parts (a) and (d), which of these two models is better? Use R-square values, adjusted R-square values, Significance F values, and p-values to explain your answer.
Data
Date | Wal Mart Revenue | CPI | Personal Consumption | Retail Sales Index | December |
11/28/03 | 14.764 | 552.7 | 7868495 | 301337 | 0 |
12/30/03 | 23.106 | 552.1 | 7885264 | 357704 | 1 |
1/30/04 | 12.131 | 554.9 | 7977730 | 281463 | 0 |
2/27/04 | 13.628 | 557.9 | 8005878 | 282445 | 0 |
3/31/04 | 16.722 | 561.5 | 8070480 | 319107 | 0 |
4/29/04 | 13.98 | 563.2 | 8086579 | 315278 | 0 |
5/28/04 | 14.388 | 566.4 | 8196516 | 328499 | 0 |
6/30/04 | 18.111 | 568.2 | 8161271 | 321151 | 0 |
7/27/04 | 13.764 | 567.5 | 8235349 | 328025 | 0 |
8/27/04 | 14.296 | 567.6 | 8246121 | 326280 | 0 |
9/30/04 | 17.169 | 568.7 | 8313670 | 313444 | 0 |
10/29/04 | 13.915 | 571.9 | 8371605 | 319639 | 0 |
11/29/04 | 15.739 | 572.2 | 8410820 | 324067 | 0 |
12/31/04 | 26.177 | 570.1 | 8462026 | 386918 | 1 |
1/21/05 | 13.17 | 571.2 | 8469443 | 293027 | 0 |
2/24/05 | 15.139 | 574.5 | 8520687 | 294892 | 0 |
3/30/05 | 18.683 | 579 | 8568959 | 338969 | 0 |
4/29/05 | 14.829 | 582.9 | 8654352 | 335626 | 0 |
5/25/05 | 15.697 | 582.4 | 8644646 | 345400 | 0 |
6/28/05 | 20.23 | 582.6 | 8724753 | 351068 | 0 |
7/28/05 | 15.26 | 585.2 | 8833907 | 351887 | 0 |
8/26/05 | 15.709 | 588.2 | 8825450 | 355897 | 0 |
9/30/05 | 18.618 | 595.4 | 8882536 | 333652 | 0 |
10/31/05 | 15.397 | 596.7 | 8911627 | 336662 | 0 |
11/28/05 | 17.384 | 592 | 8916377 | 344441 | 0 |
12/30/05 | 27.92 | 589.4 | 8955472 | 406510 | 1 |
1/27/06 | 14.555 | 593.9 | 9034368 | 322222 | 0 |
2/23/06 | 18.684 | 595.2 | 9079246 | 318184 | 0 |
3/31/06 | 16.639 | 598.6 | 9123848 | 366989 | 0 |
4/28/06 | 20.17 | 603.5 | 9175181 | 357334 | 0 |
5/25/06 | 16.901 | 606.5 | 9238576 | 380085 | 0 |
6/30/06 | 21.47 | 607.8 | 9270505 | 373279 | 0 |
7/28/06 | 16.542 | 609.6 | 9338876 | 368611 | 0 |
8/29/06 | 16.98 | 610.9 | 9352650 | 382600 | 0 |
9/28/06 | 20.091 | 607.9 | 9348494 | 352686 | 0 |
10/20/06 | 16.583 | 604.6 | 9376027 | 354740 | 0 |
11/24/06 | 18.761 | 603.6 | 9410758 | 363468 | 0 |
12/29/06 | 28.795 | 604.5 | 9478531 | 424946 | 1 |
1/26/07 | 20.473 | 606.348 | 9540335 | 332797 | 0 |

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