Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation

Chapter 14, Problem 21

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Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a males age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL cholesterol. He obtained the data on the following page:Age, x HDL Cholesterol, y Age, x HDL Cholesterol, y38 57 38 4442 54 66 6246 34 30 5332 56 51 3655 35 27 4552 40 52 3861 42 49 5561 38 39 2826 47Source: Data based on information obtained from the NationalCenter for Health Statistics(a) Draw a scatter diagram of the data, treating age as theexplanatory variable. What type of relation, if any, appearsto exist between age and HDL cholesterol?(b) Determine the least-squares regression equation from thesample data.(c) Plot the residuals against the explanatory variable, age.Does a linear model seem appropriate on the basis of theresidual plot? (Hint: See Section 4.3.)(d) Are there any outliers or influential observations?(e) Assuming the residuals are normally distributed, test whethera linear relation exists between age and HDL cholesterollevels at the a = 0.01 level of significance.(f) Assuming the residuals are normally distributed, constructa 95% confidence interval for the slope of the true leastsquaresregression line.(g) For a 42-year-old male patient who visits the doctors office,would you recommend using the least-squares regressionline obtained in part (b) to predict the HDL cholesterol ofthis patient? Why? What would be a good estimate for theHDL cholesterol of this patient?