several variables on total winnings of 100 randomly selected

several variables on total winnings of 100 randomly selected PGA golfers in 2004. The are: Variable Age AvgDriveYds Description Player\'s age in years Average length of drive in yards % of drives landing in the fairway % of greens reached in regulation (ie, par-2) Average number of putts taken per round % of pars saved when off the green in regulation Number of golf tournaments played GreensReg AvgNumPutts SavePct NumEvents The dependent variable is: Dependent Var Description TotWinnings1000s Total winnings in thousands of $ results A multiple linear regression model was created using the above variables. Here are the main Regression Analysis R 0.435 Adjusted R2 0.392 R 0.659 n 100 Std. Eror 1058.283 Dep. Var. TotWinningst000s ANOVA table Source Regression Residual Total 79,221,681 103,036,680 182,258,361 11,317,383 10.11 255E-09 1.119.964 92 Regression output t (d-92) p-value 1.625 1075 VIF vanables Intercept Age AvgDriveYds DriveAcc std error 18,021.42 11,087.17 19.34 21.52 33.73 49.95 -13,745.68 4,816.89 21.63 24.25 350 7272 1297 -1.051 2962 2774 2709 0081 2.736 5813 8.78E-08 1775 2.8540053 1.198 1.481 14211201 1069 1.722 6.77 22.61 91.37 290.32 SavePct NumEvents 32.02 1.000 3199 mean VF a) (6 pts) Write down the fitted regression model. Only include variables that are statistically significant

Solution

a. Given the above table, variables whose p-value is less than 0.05, those variables are statistical significant. Here the variables DriveAcc, GreensReg and AvgMumPutts are statistical significant.

Thus, the fitted regression model is

TotWinnings1000s=-91.37DriveAcc+290.32GreenReg-13.745.68AvgMumPutts

h.

Multicollinearity exists whenever two or more of the predictors in a multiple regression model are moderately or highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy. Multicollinearity increases the standard errors of the coefficients. Increased standard errors in turn means that coefficients for some independent variables may be found not to be significantly different from 0. One way to measure multicollinearity is the variance inflation factor (VIF), which assesses how much the variance of an estimated regression coefficient increases if your predictors are correlated. If no factors are correlated, the VIFs will all be 1.

There is some variables the multicollinearity is present because the above given condition is true.

i. In this plot the variance is looks like constant