?Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good) cholesterol. He

Chapter 14, Problem 21

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Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL levels. He obtained the following data:

(a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol?

(b) Determine the least-squares regression equation from the sample data.

(c) Plot the residuals against the explanatory variable, age. Does a linear model seem appropriate on the basis of the residual plot? (Hint: See Section 4.3.)

(d) Are there any outliers or influential observations?

(e) Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the  = 0.01 level of significance.

(f) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.

(g) For a 42-year-old male patient who visits the doctor’s office, would you recommend using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient? Why? What would be a good estimate for the HDL cholesterol of this patient?