> lpga.mod1 <- lm(logprzperrnd~rounds+drivedist+frwypct+grnregpct+aveputts+avesandshot+sandsvpct) > summary(lpga.mod1) Call: lm(formula = logprzperrnd ~ rounds + drivedist + frwypct + grnregpct + aveputts + avesandshot + sandsvpct) Residuals: Min 1Q Median 3Q Max -1.44584 -0.30000 0.03416 0.28401 1.18583 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.340504 2.182177 1.073 0.286 rounds 0.026872 0.003333 8.062 2.68e-12 *** drivedist 0.002221 0.008493 0.262 0.794 frwypct 0.002132 0.012828 0.166 0.868 grnregpct 0.090784 0.021281 4.266 4.82e-05 *** aveputts -0.113570 0.022791 -4.983 2.92e-06 *** avesandshot -0.009903 0.236609 -0.042 0.967 sandsvpct 0.005176 0.005674 0.912 0.364 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4573 on 92 degrees of freedom Multiple R-squared: 0.7844, Adjusted R-squared: 0.768 F-statistic: 47.83 on 7 and 92 DF, p-value: < 2.2e-16 > anova(lpga.mod1) Analysis of Variance Table Response: logprzperrnd Df Sum Sq Mean Sq F value Pr(>F) rounds 1 59.132 59.132 282.7483 < 2.2e-16 *** drivedist 1 0.832 0.832 3.9793 0.0490213 * frwypct 1 1.316 1.316 6.2917 0.0138820 * grnregpct 1 3.377 3.377 16.1477 0.0001197 *** aveputts 1 5.186 5.186 24.7956 2.967e-06 *** avesandshot 1 0.000 0.000 3.644e-05 0.9951966 sandsvpct 1 0.174 0.174 0.8322 0.3640320 Residuals 92 19.240 0.209 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > lpga.mod2 <- lm(logprzperrnd~rounds+grnregpct+aveputts) > summary(lpga.mod2) Call: lm(formula = logprzperrnd ~ rounds + grnregpct + aveputts) Residuals: Min 1Q Median 3Q Max -1.46489 -0.29033 0.03662 0.28986 1.20591 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.027677 0.999630 3.029 0.00315 ** rounds 0.027392 0.003063 8.944 2.76e-14 *** grnregpct 0.092986 0.015475 6.009 3.35e-08 *** aveputts -0.112803 0.022237 -5.073 1.91e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4498 on 96 degrees of freedom Multiple R-squared: 0.7824, Adjusted R-squared: 0.7756 F-statistic: 115 on 3 and 96 DF, p-value: < 2.2e-16 > anova(lpga.mod2) Analysis of Variance Table Response: logprzperrnd Df Sum Sq Mean Sq F value Pr(>F) rounds 1 59.132 59.132 292.212 < 2.2e-16 *** grnregpct 1 5.491 5.491 27.136 1.082e-06 *** aveputts 1 5.207 5.207 25.733 1.912e-06 *** Residuals 96 19.427 0.202 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(lpga.mod2,lpga.mod1) Analysis of Variance Table Model 1: logprzperrnd ~ rounds + grnregpct + aveputts Model 2: logprzperrnd ~ rounds + drivedist + frwypct + grnregpct + aveputts + avesandshot + sandsvpct Res.Df RSS Df Sum of Sq F Pr(>F) 1 96 19.427 2 92 19.240 4 0.18629 0.2227 0.9251 > > library(lmtest) > > bptest(logprzperrnd ~ rounds + grnregpct + aveputts) studentized Breusch-Pagan test data: logprzperrnd ~ rounds + grnregpct + aveputts BP = 9.0713, df = 3, p-value = 0.02836