3. This question will use the puise.txt dataset we have been using. Let the response Y be Best (resting heart rate), and covariates X1 be Height in inches [Hgt), X; be Weight in pounds (Wgt) and X3 smoking status (Smoke, 1 for smokers and U for nonsmokers). a. Say we want a multiple linear regression model with all the covariates listed in it, along with an interaction between height and weight. Write out this population model. b. Why does it make sense to have an interaction between weight and height in the model? Explain. c. Fit the model from part a. in R. and write out the estimated model. What is the adjusted R-squared value? d. What is the estimated SSE [sum of squared errors) of your model? Use the R. output from the summary(model), along with some formulas, to compute this. e. Test if your model has any significance. Write out the null and alternative hypothesis, the test statistic [and what distribution it follows), p-value, and make a conclusion. f. Test the interaction term between height and weight. State the null and alternative hypothesis and pvalue. Viihat can you conclude with respect to the effect of height and weight on the response of resting heart rate 1