PS 15

11/17/23, 9:35 AM PS 15 https://stat20.datahub.berkeley.edu/user/nathen1076225/rstudio/p/f3e8bb00/ 2/2 <dbl> 1 0.735 # A tibble: 1 × 1 r.squared <dbl> 1 0.992 # A tibble: 1 × 2 Rsq_linear Rsq_poly <dbl> <dbl> 1 0.726 0.889 The testing and training r squared values are greater in the polynomial models compared to the single linear models. Whats driving the difference in statistics of these two models is that polynomial models are more capable of capturing the non linear relationships between variables compared to single linear models. lm_training <- lm (y ~ poly (x, degree = 20 , raw = T), data = train) glance (lm_training) %>% select (r.squared) y_pred_linear <- predict (lm_train, newdata = test) y_pred_poly <- predict (lm_training, newdata = test) test %>% mutate ( y_pred_linear = y_pred_linear, y_pred_poly = y_pred_poly, resid_sq_linear = (y - y_pred_linear) ^ 2 , resid_sq_poly = (y - y_pred_poly) ^ 2 ) %>% summarize ( TSS = sum ((y - mean (y)) ^ 2 ), RSS_linear = sum (resid_sq_linear), RSS_poly = sum (resid_sq_poly)) %>% mutate ( Rsq_linear = 1 - RSS_linear / TSS, Rsq_poly = 1 - RSS_poly / TSS) %>% select (Rsq_linear, Rsq_poly)