An analyst wants to build a regression model to predict attendance at a baseball

Question

An analyst wants to build a regression model to predict attendance at a baseball game from the following two predictor variables: wins and runs A correlation matrix of the two predictors shows: Wins Runs Homelt-e Wins 1.0000 0.6048 1.0000 0.6966 0.6669 1.0000 HomeAttend-e a. Why might there be cause to be concerned about colinearity in the model? The analyst fits the model with the two explantory variables. The regression output shows: df MS Number of ob5 F( 2, ll)= 7.61 Prob E R-squared Adj R-squared 0.5041 Root MSE Model Residual 650249202 470178035 2 325124601 11 42743457.7 - 0.0084 - 0.5804 Total 11204e+09 13 86186710.6 6527.8 HomeAttend e Coef. Std Err [95% Conf. Interval] 1.58 0.143-23.43767 142.4288 1.89 0.086-59.88548 75.3394 cons47185.75 24339.91-1.940.079-100757.5 386.033 59.49554 37.68004 357.727 189.7389 Wins b) what variables are significant, at -0.10? What variables are not? c) Worried about colinearity, the analyst regresses Wins on Runs. The output shows: df MS Number of ob5 = F( 1, 12)= 6.92 Prob E R-squared Adj R-squared 0.3129 Root MSE Model 684.709536 1 684.70953 6 Residual 1187.29046 1 98.940872 0.02 19 0. 3658 Total 1872 13 144 9.94 69 Wins Coef Std. Err [95% Conf. Interval] 1201034 0456552 2.63 0.022 2195775 66.61454 0206293 cons-13.6146136.82242 -0.37 071893.84377 d) e) What is the VIF for Wins? How do you interpret this?

Explanation / Answer

a) Since there is high correlation so we should be concerned about collinearity between the variables.

b) At alpha = 0.10, boths wins and _cons are significant since their p-value < 0.10

c) Runs is not significant since its p-value > 0.10

d) VIF = 1 / (1-R2) = 1 / (1 - 0.3658) = 1.58

e) Since VIF < 10, WE CAN SAY THERE IS NO MULTICOLLINEARITY.

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