(16 marks) A sample of 716 adolescent girls from a particular health authority participated in a study of the relationship between systolic blood pressure (SBP) and resting heart rate (RHR). Measurements of SBP (in mm Hg) and RHR (in beats/min.) were taken on each girl. You may assume that the SBP measurements are independent and normally distributed with common SD. The data are available in the file bp_heart_rate.txt.

a. (2 marks) Write down the linear regression model for these data. Be sure to define your variables and to state all assumptions.

b. (1 mark) Fit the model in (a) and provide the table of parameter estimates, standard errors, etc.

c. (2 marks) Produce a scatterplot to illustrate the relationship between SBP and RHR. Be sure to label the axes appropriately. Include the line of best fit.

d. (5 marks) Conduct the test of whether mean SBP is positively associated with RHR. In particular: i. Specify the null and alternative hypotheses. ii. Specify the value of the test statistic. iii. Specify the p-value. iv. Using a significance level of = 0.05, state your conclusions in the language of the problem. e. (2 marks) Provide a 90% confidence interval for the mean SBP of girls with a RHR of 100 beats/min. f. (2 marks) Provide a 90% prediction interval for the SBP of a girl with a RHR of 100 beats/min. g. (2 marks) Given an intuitive (not mathematical) explanation as to why your interval in (f) is so much wider than your interval in (e).