Using the Villanova_basketball_1 data, run a linear regression with y variable a

Question

Using the Villanova_basketball_1 data, run a linear regression with y variable as "Points Differential", and x variables as Assists, Rebounds, Turnovers, and Personal Fouls.

Having found that the regression is significant overall (i.e. not all slopes are zero - go ahead and change your answer to the previous question if you got it wrong), which of these slopes are significant at 5% level? (i.e. for which of those slopes can we reject the hypothesis that the slope is zero). The slopes with respect to

- Assists

- Rebounds

- Turnovers

- Personal Fouls

Game Points For Points Against Points Differential Assists Rebounds Turnovers Personal Fouls 1 68 52 16 14 38 12 10 2 84 47 37 19 42 9 14 3 82 66 16 21 29 7 13 4 86 41 45 22 46 11 11 5 82 70 12 11 40 7 22 6 68 78 -10 10 31 13 26 7 71 60 11 19 45 11 7 8 65 53 12 16 32 16 14 9 84 81 3 16 27 18 15 10 78 59 19 9 34 17 17 11 76 36 40 16 41 9 17 12 78 34 44 12 29 9 22 13 81 65 16 17 36 13 20 14 83 71 12 21 21 9 22 15 72 61 11 14 34 19 23 16 88 74 14 20 36 18 12 17 74 66 8 12 42 14 17 18 59 61 -2 8 31 8 18 19 83 72 11 15 26 10 10 20 68 83 -15 10 48 11 26 21 66 69 -3 12 20 9 17 22 75 70 5 13 28 12 18 23 66 50 16 12 26 8 18 24 76 77 -1 16 27 12 19 25 54 57 -3 6 33 12 23 26 60 57 3 13 36 20 17 27 77 75 2 7 44 13 13 28 64 69 -5 14 30 12 15 29 68 81 -13 17 23 12 21 30 72 93 -21 18 19 9 18 31 50 60 -10 4 22 8 21 32 69 70 -1 6 21 9 22 33 57 61 -4 10 33 8 19 34 84 61 23 16 39 8 22 35 103 65 38 19 43 15 22 36 69 68 1 9 42 16 26 37 71 65 6 12 38 13 17 38 79 67 12 8 45 22 19 39 81 63 18 17 27 13 26 40 77 58 19 14 39 13 15 41 95 86 9 19 42 14 24 42 97 89 8 16 39 16 25 43 65 75 -10 12 24 9 19 44 96 58 38 19 44 10 19 45 97 63 34 15 39 12 17 46 74 72 2 13 31 7 17 47 99 72 27 19 38 14 19 48 78 76 2 17 24 12 20 49 92 84 8 10 34 21 33 50 82 77 5 16 36 11 27 51 94 68 26 14 49 12 20 52 81 71 10 10 34 20 20 53 90 72 18 20 30 11 23 54 81 71 10 15 43 13 16 55 90 103 -13 11 26 17 38 56 82 75 7 11 37 18 24 57 92 81 11 18 41 15 23 58 75 84 -9 9 26 9 30 59 65 70 -5 8 30 13 26 60 74 49 25 9 33 10 17 61 77 95 -18 15 36 16 25 62 77 73 4 14 28 12 22 63 66 68 -2 16 32 15 24 64 76 80 -4 13 27 14 17 65 73 70 3 9 26 16 19 66 68 75 -7 9 31 7 18

Explanation / Answer

> attach(read.csv("New Microsoft Excel Worksheet.csv"))
The following objects are masked from read.csv("New Microsoft Excel Worksheet.csv") (pos = 3):

Assists, Game, Personal.Fouls, Points.Against, Points.Differential,
Points.For, Rebounds, Turnovers

The following objects are masked from read.csv("New Microsoft Excel Worksheet.csv") (pos = 4):

Assists, Game, Personal.Fouls, Points.Against, Points.Differential,
Points.For, Rebounds, Turnovers

> summary(lm(Points.Differential~Assists+Rebounds+Turnovers+Personal.Fouls))

Call:
lm(formula = Points.Differential ~ Assists + Rebounds + Turnovers +
Personal.Fouls)

Residuals:
Min 1Q Median 3Q Max
-29.586 -6.545 -0.864 6.202 40.981

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) - 23.1391 11.3180 -2.044 0.045231 *  
Assists 1.1690 0.3745 3.121 0.002750 **
Rebounds 0.8630 0.2126 4.059 0.000143 ***
Turnovers -0.4041 0.4315 -0.937 0.352701   
Personal.Fouls -0.4209 0.3022 -1.393 0.168708   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12.16 on 61 degrees of freedom
Multiple R-squared: 0.3969, Adjusted R-squared: 0.3573
F-statistic: 10.04 on 4 and 61 DF, p-value: 2.628e-06

> #The p-values corresponding to the Intercept(0.045) and Regressors i.e. Assists(0.00275) and Rebounds(0.000143)
> #which is less than the level of significance 0.05.
> #so we reject our Null Hypothesis that slopes corresponding to Assists and Rebounds are = 0 and conclude they are significant
> #in estimating Points Differential
> #The P-value corresponding to Turnovers and personal fouls are >0.05 hence their corresponding hypothesis that slopes are equal to 0
> #got accepted and readily tells us to drop those two X values as predictors

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