final

b. OCTrapLM <- lm(voplus ~ oc + trap, data= biomark) summary.lm(OCTrapLM) ## ## Call: ## lm(formula = voplus ~ oc + trap, data = biomark) ## ## Residuals: ## Min 1Q Median 3Q Max ## -708.2 -198.6 -100.2 125.8 1224.8 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 57.704 156.539 0.369 0.71518 ## oc 6.415 5.125 1.252 0.22102 ## trap 53.874 15.393 3.500 0.00158 ** ## --- ## Signif. codes: 0 ' *** ' 0.001 ' ** ' 0.01 ' * ' 0.05 ' . ' 0.1 ' ' 1 ## ## Residual standard error: 376.3 on 28 degrees of freedom ## Multiple R-squared: 0.607, Adjusted R-squared: 0.5789 ## F-statistic: 21.62 on 2 and 28 DF, p-value: 2.096e-06 Our linear regression model is: [ VO+ = 57 . 704 + 6 . 415 OC + 53 . 874 TRAP H 0 : β 1 = β 2 = 0 , there is no linear association between VO+ and OC/Trap (respectively). H a : β 1 ̸ = 0 , β 2 ̸ = 0 , there is a substantial linear association between VO+ and OC/Trap (respectively). For the coefficient of Trap, as shown in the summary, t = 3 . 5 and P = 0 . 00158 < 0 . 05 , so we reject the null hypothesis, concluding that there is enough evidence against the consistency to say that there is a statistically significant linear association between VO+ and Trap. However, for the coefficient of OC, we fail to reject the null hypothesis because t = 1 . 252 and P = 0 . 22102 > 0 . 05 . Thus, we conclude there is not enough evidence against the consistency to say that there is a substantial linear association between VO+ and OC. These results align with our findings in Problem 11.36. We can conclude from these tests that the coefficient of OC is not significantly different from 0 whereas the coefficient of Trap is significantly different from 0. Problem 11.38 a. \ V O + = β 0 + β 1 ( OC ) + β 2 ( TRAP ) + β 3 ( V O − ) + ϵ i b. allLM <- lm(voplus ~ oc + trap + vominus, data= biomark) summary.lm(allLM) ## ## Call: ## lm(formula = voplus ~ oc + trap + vominus, data = biomark) ## ## Residuals: ## Min 1Q Median 3Q Max 6