10.1 Understanding a linear regression model. Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with μy = 2.8 + 0.8x and standard deviation σ = 3.2. The explanatory variable x is the number of servings of fruits and vegetables in a calorie-controlled diet.

  1. (a) What is the slope of the population regression line?

  2. (b) Explain clearly what this slope says about the change in the mean of y for a change in x.

  3. (c) What is the subpopulation mean when x = 7 servings per day?

  4. (d) The decrease in blood pressure y will vary about this subpopulation mean. What is the distribution of y for this subpopulation?

  5. (e) Using the 68–95–99.7 rule (page 57), between what two values would approximately 95% of the observed responses, y, fall when x = 7?