Data in Ma (posted on Blackboard) are the 1976 team performance statistics for t

Question

Data in Ma (posted on Blackboard) are the 1976 team performance statistics for the 28 1. teams in the National Football League (Source: pro-football-reference.com). Computer output of a Minitab multiple regression model relating the number of games won (y) to the teams' passing yardage (x2) the percent rushing plays (x7), and the opponents' rushing yards (x8) is shown below: Regression Analysis: y versus x2, x7, x8 Analysis of Variance DF Adj ss Adj Ms F-value P-value Source Regression 3 249.45 83.151 25.75 000 100.28 100.282 31.05 0.000 1 25.05 25.054 7.76 010 1 29.16 29.158 9.03 006 24 77.51 230 Error 27 326.96 Total Model Summary sq (adj) sq (pred) 69.306 1.79711 76.298 73.33 coefficients VIF value T-valu SE Coef Term 0.340 7.63 Constant 06 0.003976 0.000714 5.57 0.000 010 2.79 0890 0.2478 006 3.00 00389 00130 Regression Equation x8 y -7.63 003976 x2 24 78 27 0.00389 Prediction for y 1800 60 Variable setting: x 2 2000 Fit SE Fit 958 CI 958 12.0253) 8.17684 497392 (7.15027 9.20341) (4.32834,

Explanation / Answer

Part-A

R-square is 76.29% which is the variaions in “number of games won” accounted for by this model

Part-B

From ANOVA table the regression model is significant at 1% level of significance as test statistic F(3,24)=25.75 with p-value=0.000.<0.01. this means that at least one of the predictors is significant in explaining the variations in number of games won

Part-C

The coefficient of x2 is 0.003976 which means that corresponding to unit increase in passing yards there is on an average an increase of 0.003976 in the number of games won, holding other predictors fixed. So, for 1000 passing yards, number of games won is approximately increases by 4 on an average.

Part-D

Coefficient of X7 is significant at 0.05 level as test statistic t=2.79 with p-value=0.010<0.05.

Part-E

Error degree of freedom =24

So, critical t at 5% level =2.064

So 95% confidence interval for coefficient of x8 is = -0.00389-2.064*0.00130   , -0.00389+2.064*0.00130

=(-0.0065732      -0.0012068)

This means that we are 95% confident that corresponding to unit increase in opponents’ rushing yards there is on an average a decrease of 0.0012068 to 0.0065732 in the number of games won, holding other predictors fixed.

Part-F

From above results (Minitab output)

95% lower bound of mean number of games won=7.15027

95% upper bound of individual number of games won=4.32834

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