The Framingham Study was planned as a 20-year cohort study of adult health in Framingham, Massachusetts, USA, commencing in 1948. Fourteen variables were recorded over the period of the study, and the data in the file Framingham.csv contains this information in respect of study participants aged 45-59 inclusive. For the purposes of this question, you are investigating the relationship, if any, between the following variables: AGE The person's age last birthday (i.e., whole years only) CHOL Cholesterol level in milligrams per decilitre (mg/dL) (a) Obtain the following R output, treating AGE as the explanatory variable: (i) scatter plot [3] (ii) standardised residual plot [2] (iii) distribution of residuals [3] (iv) regression analysis summary. [2, total = 10] (b) What statistical model is assumed in the regression analysis? [2] (c) As far as possible, assess the extent to which the model is appropriate to the data. [4] (d) Using a suitable hypothesis test at a 5% significance level, evaluate the evidence that average Cholesterol levels are related to Age in the underlying population. If you find that there is a relationship, describe it. [5] (e) Provide a 95% prediction interval for the cholesterol level that can be expected in a 49-year -old person from this region. [4] (f) Briefly discuss whether a linear relationship with Age provides a useful basis for predicting Cholesterol levels in this region, for adults within the age range of the data.