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

Height

regression

Points Scored

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]

Names

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 7

MPG

Frequency

020400246

Weight (Ton)

Weight (Ton)020400246

Drive Ratio

Drive Ratio020400100200

Horsepower (hp)

Horsepower (hp)020400200400

Displacement

Displacement020400510

Cylinders

Cylinders

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