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10.1 Understanding a linear regression model. Consider a linear regression model for the decrease in blood...

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.

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

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

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

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

(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?

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Answer #1

(a) The slope of the population regression line is 0.8.

(b) For every one increase in the number of servings of fruits and vegetables in a calorie-controlled diet, there is a decrease in blood pressure by 0.8.

(c) μy = 2.8 + 0.8x

Put x = 7

μy = 2.8 + 0.8*7

μy = 8.4

(d) The distribution of y for this subpopulation is the normal distribution.

(e) 8.4 2*3.2 = 2, 14.8

95% of the observed responses, y, would fall between 2 and 14.8 when x = 7.

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