The following table gives the systolic blood pressure (SBP), body size (QUET), age (AGE), and smoking history (SMK = 0 if a nonsmoker, SMK = 1 if a current or previous smoker) for a hypothetical Sample of 32 white males 40 years old from the town Angina.

a. On each of the accompanying scatter diagrams, sketch by eye a line that fits the data reasonably well. Comment on the relationships described.

b. (1) Determine the least-squares estimates of the slope (β1) and intercept (β0) for the straight-line regression of SBP (Y) on QUET (X).
(2) Sketch the estimated regression line on the scatter diagram involving SBP and QUET. Compare this new line with the line you drew in part (a).
(3) Test the null hypothesis of zero slope; be sure to interpret the result.
(4) Based on your test in part (b)(3), would you conclude that blood pressure increases as body size increases?
(5) Find and sketch 95% prediction bands on the appropriate scatter diagram.
(6) Using your answer to part (b)(5), find an approximate 95% prediction interval for an individual with QUET = 3.4 (the sample mean value of QUET). Interpret your answer.
(7) Are any assumptions for straight-line regression clearly not satisfied in this example?
c. Repeat questions (1) through (4) in part (b) for the regression of QUET on AGE.
d. Repeat questions (1) through (4) in part (b) for the regression of SBP on AGE.
e. (1) Determine the least-squares estimates of the slope and intercept for the straight-line regression of SBP(Y) on SMK (X).
(2) Compare the value of β0 with the mean SBP for nonsmokers. Compare the values of β0 + β1 with the mean SBP for smokers. Explain the results of these comparisons.
(3) Test the null hypothesis that the true slope is 0; be sure to interpret the result.
(4) Is the test in part (e)(3) equivalent to the usual two-sample £test for the equality of two population means, assuming equal but unknown variances? Demonstrate your answer numerically.