data
| Players | Position | Guard | Forward | Center | Height | Points Scored |
| Ramon Sessions | Guard | 1 | 0 | 0 | 75 | 206 |
| John Wall | Guard | 1 | 1 | 0 | 76 | 1387 |
| Bradley Beal | Center | 1 | 0 | 0 | 77 | 962 |
| Garrett Temple | Center | 1 | 0 | 0 | 78 | 204 |
| Will Bynum | Forward | 1 | 0 | 0 | 74 | 22 |
| Paul Pierce | Forward | 0 | 1 | 0 | 79 | 868 |
| Kris Humphries | Forward | 0 | 1 | 0 | 81 | 509 |
| Otto Porter | Forward | 0 | 1 | 0 | 81 | 445 |
| Martell Webster | Forward | 0 | 1 | 0 | 79 | 106 |
| Rasual Butler | Forward | 0 | 1 | 0 | 79 | 580 |
| Drew Gooden | Forward | 0 | 1 | 0 | 82 | 277 |
| Marcin Gortat | Center | 0 | 0 | 1 | 83 | 1001 |
| DeJuan Butler | Center | 0 | 0 | 1 | 79 | 56 |
| Nene Hiliario | Center | 0 | 0 | 1 | 83 | 737 |
| Kevin Seraphin | Center | 0 | 0 | 1 | 81 | 22 |
| Generate and create bar graphs between the following potential relationships: |
data
regression
Sheet3
| Multiple regression analysis to predict salary from age, forward, guard, height, minutes, playernum, points and weight. | |||||||
| The prediction equation is: | |||||||
| salary = | -19003604.142808 | ||||||
| +General | age | ||||||
| -General | forward | ||||||
| -General | guard | ||||||
| +General | height | ||||||
| +General | minutes | ||||||
| +General | playernum | ||||||
| +General | points | ||||||
| +General | weight | ||||||
| 0.4385566211 | R squared | ||||||
| 3599928.09100962 | Standard error of estimate | ||||||
| 114 | Number of observations | ||||||
| 10.2522460276 | F statistic | ||||||
| 0.0000000002 | p value | ||||||
| 95% | 95% | ||||||
| Coeff | LowerCI | UpperCI | StdErr | t | p | Significant? | |
| Constant | -19003604.142808 | -42001484.7821742 | 3994276.49655825 | 11598600.0304612 | -1.6384394748 | 0.1043232856 | No (p>0.05) |
| age | 389631.1730025 | 234482.039795109 | 544780.306209891 | 78246.8945449255 | 4.9795097335 | 0.0000025135 | Yes (p<0.001) |
| forward | -295116.891250432 | -2339762.87454324 | 1749529.09204238 | 1031183.32232356 | -0.2861924595 | 0.7752946114 | No (p>0.05) |
| guard | -539480.166331768 | -3554041.93858475 | 2475081.60592122 | 1520344.27918677 | -0.3548407908 | 0.7234205886 | No (p>0.05) |
| height | 104482.919180252 | -161881.980459385 | 370847.818819888 | 134336.723523373 | 0.7777688516 | 0.4384542682 | No (p>0.05) |
| minutes | 650.2643161098 | -416.2791831613 | 1716.8078153808 | 537.8935414578 | 1.2089089494 | 0.2294130774 | No (p>0.05) |
| playernum | 22802.6408241651 | -20317.6757363456 | 65922.9573846758 | 21747.0171627962 | 1.0485410782 | 0.2967969176 | No (p>0.05) |
| points | 3658.5708237449 | 1959.4002915409 | 5357.7413559489 | 856.9485030219 | 4.2693006766 | 0.0000431331 | Yes (p<0.001) |
| weight | 6760.0337354336 | -22486.1352928991 | 36006.2027637662 | 14749.8207466234 | 0.4583129417 | 0.6476747848 | No (p>0.05) |
| The R-squared value, 43.9%, indicates the proportion of the variance of salary | |||||||
| that is explained by the regression model. | |||||||
| Thus age, forward, guard, height, minutes, playernum, points and weight together explain | |||||||
| a very highly significant proportion of the variation in salary, based on the F test (p<0.001). | |||||||
| The standard error of estimate, 3599928.091, indicates the typical size | |||||||
| of errors made in predicting salary using the regression model. | |||||||
| Holding the other X variables constant, we estimate that: | |||||||
| 389631.1730025 | is the increase in salary associated with an increase in age of 1 unit. This is very highly significant (p<0.001). | ||||||
| -295116.891250432 | is the increase in salary associated with an increase in forward of 1 unit. This is not significant (p>0.05). | ||||||
| -539480.166331768 | is the increase in salary associated with an increase in guard of 1 unit. This is not significant (p>0.05). | ||||||
| 104482.919180252 | is the increase in salary associated with an increase in height of 1 unit. This is not significant (p>0.05). | ||||||
| 650.2643161098 | is the increase in salary associated with an increase in minutes of 1 unit. This is not significant (p>0.05). | ||||||
| 22802.6408241651 | is the increase in salary associated with an increase in playernum of 1 unit. This is not significant (p>0.05). | ||||||
| 3658.5708237449 | is the increase in salary associated with an increase in points of 1 unit. This is very highly significant (p<0.001). | ||||||
| 6760.0337354336 | is the increase in salary associated with an increase in weight of 1 unit. This is not significant (p>0.05). |
[Title of Research]
|
Dependent Variable |
MPG |
Weight (Ton) |
Drive Ratio |
Horsepower |
Displacement (litres) |
Cylinders |
|
Minimum |
15.50 |
1.92 |
2.26 |
65.00 |
85.00 |
4.00 |
|
Maximum |
37.30 |
4.36 |
3.90 |
155.00 |
360.00 |
8.00 |
|
Mean |
24.76 |
2.86 |
3.09 |
101.74 |
177.29 |
5.39 |
|
Median |
24.25 |
2.69 |
3.08 |
100.00 |
148.50 |
4.50 |
|
Standard Deviation |
6.55 |
0.71 |
0.52 |
26.44 |
88.88 |
1.60 |
|
Range |
21.80 |
2.45 |
1.64 |
90.00 |
275.00 |
4.00 |
|
Number of Observations |
38 |
38 |
38 |
38 |
38 |
38 |
Summary Statistics
(Explain summary statistics. For example, what does this statistics tell you about each variable? What is the shape of the distribution of each variable?)
Correlation Coefficients
(Find correlation coefficient between the dependent variable and each of the independent variables)
|
Dependent Variable |
MPG |
Weight (Ton) |
Drive Ratio |
Horsepower |
Displacement |
Cylinders |
|
MPG (Miles) |
1 |
|
|
|
|
|
|
Weight (Ton) |
-0.90 |
1 |
|
|
|
|
|
Drive Ratio |
0.42 |
-0.69 |
1 |
|
|
|
|
Horsepower |
-0.87 |
0.92 |
-0.59 |
1 |
|
|
|
Displacement |
-0.79 |
0.95 |
-0.80 |
0.87 |
1 |
|
|
Cylinders |
-0.81 |
0.92 |
-0.69 |
0.86 |
0.94 |
1 |
(Explain the correlation coefficients. What does it tell you about the relationship between the dependent and each of the independent variables?)
Scatter Plots
(Explain the scatter plots. What does it tell you about the relationship between the dependent and each of the independent variables? Does there exist any outliers?)
Regression Results
Y = 69.22 – 11.38x – 3.35x + .45x + .03x - .53x
|
Dependent Variable |
Coefficients |
t Stat |
P-value |
|
Intercept |
69.22 |
14.96 |
0.00 |
|
Weight (Ton) |
-11.38 |
-5.60 |
0.00 |
|
Drive Ratio |
-3.35 |
-2.63 |
0.01 |
|
Horsepower |
-0.04 |
-1.30 |
0.20 |
|
Displacement (liters) |
0.03 |
1.65 |
0.11 |
|
Cylinders |
-0.53 |
-0.78 |
0.44 |
(Interpret the coefficients for each of the independent variables, and t-statistic and p-value for each coefficient. For example, does Variable 1 have a significant impact on the dependent variable? Why or why not? How much impact does Variable 1 have on the dependent variable?)
Assess the Model’s Fit
[From Excel regression output, identify and interpret the measures for the fit of the model,
including the Standard Error of the Estimate (Se), Coefficient of Determination (Rsquared),
Adjusted R-squared, and F-statistic. What do these measures tell you about the
model’s fit?]
Regression Diagnosis
[Insert residual plots and histogram of residuals. Based on residual plots, explain
whether the required conditions for the residuals are satisfied. Comment on the
Goodness-of-Fit and validity of the model. Identify outliers if there exists any. Is your
model a valid model?]
Estimation
[Use the regression equation to estimate. For example, given certain values of the
independent variables, what is the predicted value for the dependent variable?]
Recommendations
[Based on the above regression analysis results, provide managerial decisions and/or
recommendations.]
Histogram
Frequency Below 60 60 - 120 120 -180 180 - 240 240 - 300 Above 300 1 151 43 21 3 2 7MPG
Frequency
020400246
Weight (Ton)
Weight (Ton)020400246
Drive Ratio
Drive Ratio020400100200
Horsepower (hp)
Horsepower (hp)020400200400
Displacement
Displacement020400510
Cylinders
Cylinders
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