3. This question will use the pulse.txt dataset we have been using. Let the response Y be Rest (resting heart rate), and covariates X1 be Height in inches (Hgt), X2 be Weight in pounds (Wet) and X3 smoking status (Smoke, 1 for smokers and ( for non-smokers). 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 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 p-value. What can you conclude with respect to the effect of height and weight on the response of resting heart rate ? g. Now a researchers states that you do not need weight in the model in any way or form. Write out the null and alternative hypothesis for this (write it out in terms of slope coefficients). h. Conduct the test from part g. Make a conclusion in context of the study. i. Show the output from R for the sequential sum of regressions table (keep the order of X1, X2