Why does the residual plot of Model 1 appear to have three clusters, while the residual plot of Model 2 appears to have four vertical clusters? Hint: Analyze the coefficients from the regression output / calculate the estimated average response for each combination.

The following data set was collected to study the relationship between factors on the birth weight of babies. The variables included are as follows: 0 hsg rad : is the mother a high school graduate? (1 = yes, 0 = no) 0 smoke : does the mother smoke during pregnancy? (1 = yes, 0 = no) 0 gestate: gestational age in weeks 0 grams : birth weight in grams Two regression models were created. The summary output and residuals vs tted values plot for each are shown below. > im_mode11 summary(1m_mode11) Coefficients: Estimate Std. Error t va'lue Pr{>lt|) (Intercept) 3484.09 29.47 118.217 lm_mode12 summary(1m_mode1 ) Coefficients: Estimate Std. Error 1: value Pr(>|t|) (Intercept) 3498.90 31.66 110.515