2. This question will use the bodymass.txt dataset on our site. The response variable is bodymass (in kilograms) and the covariate is height (in centimeters). a. Create a scatterplot of bodymass (on the Yaxis) and height (on the Xaxis), and overlay the simple linear regression line. Comment on the linear relationship between height and bodymass. b. Now t a simple linear regression of Y:bodymass and X:height. What is the adjusted Rsquared value? c. Using the model from part b., show the tted vs. residual plot and QQplot of the residuals. (1. Based on the plots from part 6., what can you say about the linearity assumption and the normality assumption of the linear regression model? e. Now t the following model where you add a quadratic term of height: Bodymass = 30 + 51 Height + zHeight2 + s, and report the output from the R summary(model) call. f. Using the model from part e., test if we need the quadratic term in the model. State the null and alternative hypothesis, p-value, and conclusion. g. What is the adjusted Rsquared value from the model in part e.? Is it an improvement over the model from part b.? h. Using the model from part 9., present the residual versus tted plot and comment on the shape (if any) seen. i. Conduct a test of all the coefcients in the model from part e. being equal to 0. Report the test statistic, p-value, and make a conclusion in context of the problem. j. Compute the VIF (variance ination factor) for each of the covariates in the model in part e. What do you notice? Explain in a few sentences. k. Say you have a subject who is 170 centimeters tall. Using the model from part e., interpret the effect of increasing the height of this subject by 1 centimeter on the bodymass. Now interpret the effect of increasing the height of this subject by 5 centimeters on the bodymass. 1. Which observation has the highest leverage from the model in part e.? What makes them have such a high leverage