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We first explore the relationship between intima-media thickness and age. a) Plot variable measure as a function of variable AGE. Describe this scatter plot. b) Propose a regression model and write down the model by presenting all the assumptions of your model. c) . Estimate the parameters of the model and interpret the regression parameter. d) . Draw the regression line over the scatter plot with the confidence interval of the model. e)  Check the validity of your model by conducting a diagnosis of the residuals. f) Compute a prediction interval for intima-media thickness for a 33 years old person. g) . Compute a confidence interval for the average intima-media thickness of 33 years old people. h) Propose and then fit a parsimonious model to increase the predictive power of intima-media thickness, using only AGE as an explanatory variable. Add the new fitted regression line (with confidence interval) to the scatter plot you obtained in part (d). Part-II We now wish to fit a regression model on all variables which may explain variations in intima-media thickness. The study will rely on the following variables: AGE, SPORT, alcohol, packyear and the variable BMI. which you must create from variables height and weight. We are mostly interested in tobacco, through the variable packyear as main exposure factor. We therefore decide to keep this variable in the model even if it is not significant. 2 Question 2 Create the variable BMI, where Body Mass Index (BMI) = weight (kg) [height (m)]2 and add it to the new data frame excluding variables height, weight & GENDER. Also recall that both Alcohol and SPORT are both categorical variables. Remember to include your code and print out the first few rows of the data frame for checking. b). First, draw scatter plots of pairs of quantitative variables (explained and explanatory). Comment on their relationships. Then, draw plots of pairs of categorical explanatory variables included the response variable as well. Comment the relationship of each categorical explanatory variable with the response variable. Finally do you suspect any issues with collinearity? c) Perform a univariate analysis of intima-media thickness of each explanatory variable. Present your results in a single table with only relevant information from each univariate model. d) We only keep the explanatory variables associated with significance level p < 0.25 in the univariate analysis. One by one, test all possible interactions between the selected explanatory variables and the main exposure variable packyear. e). Estimate the model with all variables which were declared significant in the univariate analyses (  = 25) and all interaction terms significant at the 25% level and then comment on its overall significance and performance. f). Starting with the model obtained from the previous question, obtain your final model by performing backward model selection (using a significance level of 5% level; making sure that the removals do not make a big difference on the estimate of the coefficient associated with tobacco status). Are the interaction terms still significant? [Hint: a number of the variables here are categorical.]= g) . Check the validity of your model by presenting a diagnosis of the residuals and also interpret the final mo

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