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.

Using the estimated regression line, what is an estimate of the Points Differential for a game with Assists = 15, Rebounds = 40, Turnovers = 10, and Personal Fouls = 20?

(provide one decimal place)

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

answer is 26.871 ( whole number approximation would be 27)

the regression equation is given as y=-23.14+1.169x1+0.863x2-0.0404x3-0.041x4

for Assists =x1 = 15, Rebounds = x2=40, Turnovers = x3=10, and Personal Fouls = x4=20

y=-23.14+1.169*15+0.863*40-0.0404*10-0.041*40=26.871

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT Regression Statistics Multiple R 0.629988265 R Square 0.396885214 Adjusted R Square 0.357336703 Standard Error 12.15639557 Observations 66 ANOVA df SS MS F Significance F Regression 4 5932.044844 1483.011 10.0354 2.62807E-06 Residual 61 9014.455156 147.778 Total 65 14946.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -23.13912998 11.31797927 -2.04446 0.045231 -45.77082805 -0.50743191 Assists (x1) 1.169041317 0.374527531 3.121376 0.00275 0.42012724 1.917955393 Rebounds(x2) 0.863017562 0.212634794 4.058685 0.000143 0.437828017 1.288207108 Turnovers(x3) -0.404138687 0.431534099 -0.93652 0.352701 -1.267044441 0.458767068 Personal Fouls(x4) -0.420941622 0.302206552 -1.39289 0.168708 -1.025240965 0.183357721

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