Question

## ## Call: ## Im(formula = mpg ~ disp + hp + wt + osec, data = mtcars.train.df) ## ## Residuals: Min 1Q Median ## -4.3442 -1.1687 -0.4033 3Q Max 1.0519 5.9623 ## ## Coefficients: Estimate Std. Error t value Pr>t) ## (Intercept) 31.204891 10.909916 2.860 0.00967 ** ## disp 0.009432 0.012308 0.766 0.45245 ## hp -0.032908 0.025528 -1.289 0.21208 ## wt -4.978374 1.434757 -3.470 0.00242 ** ## qsec 0.434043 0.576267 0.753 0.46011 ## --- ## Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 ## ## Residual standard error: 2.713 on 20 degrees of freedom ## Multiple R-squared: 0.8391, Adjusted R-squared: 0.8069 ## F-statistic: 26.07 on 4 and 20 DF, p-value: 1.094e-07

please show your explanation thanks!

Answer 1

Ans a ) from the output of the regression model

the value of the coefficient of determination is 0.8391

about 83.91 % variability in mpg is explained by the model.

Ans b ) from the output and the p-value of the quarter-mile time variable is 0.00242

since p-value for this  variable is less than 0.05 so these this predictor variable is statistically significant