7. We will use the Pulse.txt dataset for this question. This dataset is from an observational study where subjects had their resting pulse rate (beats per minute), height (in inches), weight (in pounds), smoking status (1 for smoker and 0 for non-smoker), and active pulse rate (beats per minute) recorded. We will use resting pulse rate as the response variable Y, and explanatory variables of weight as X] and smoking status as X2. Run the following line in R after you have imported the data set to create a new variable called "Smoker" with categories Yes and No. pulse$Smoker = ifelse (pulse$Smoke==1, "Yes", "No") a A. Fit a model in R using response variable Y and only the covariate Xy of smoking status. Test if the coefficient on X2 is equal to 0. State the null and alternative hypothesis, the test statistic, p-value and make a conclusion. b. Now conduct a two sample t-test with equal varaince in R, where the response is resting pulse rate and the two groups/samples are smokers and non-smokers. How does this test correspond to the test from part a. ? c. Write out the population model where we have response Y and covariates/explanatory variables Xi and X2 with no interaction term in context of the study. d. With respect to the effect of weight on resting pulse rate, what does it mean in context of the study that we do not have an interaction term (with smoking status) in the model from part c. ? Explain in a sentence or two. e. Fit the model from part c. in R and report the coefficient of determination (multiple R2 value) and report the estimate of or. f. How many observations are there in the dataset? g. Using the model output from part e., test the coefficient on Smoking yes (X2) being equal to 0 or not. Write the null and alternative hypothesis, test statistic, p-value, and make a conclusion in context of the study (be careful of your wording). h. Can we conclude that smoking causes lower resting pulse rates? Why or why not? i. Create a scatterplot where X=Weight and Y=Resting pulse rate, and have different colors and symbols for the different smoking groups. Interpret this scatterplot