Imagine a regression line that relates average systolic blood pressure to a pers

Question

Imagine a regression line that relates average systolic blood pressure to a person's age. For this setting let the average systolic blood pressure play the role of response variable. The average blood pressure for people 24 years old is 104, while for those 60 years old the average is 118 Recall from high school that the slope is "rise" over "run". Since this is a two point line your model will fit perfectly (r = 1) (a) What is the slope of the regression line? (Round the answer to two decimal places.) (b) What is the intercept of the regression line? (Round the answer to two decimal places.) (c) What is the estimated average systolic blood pressure for people who are 34 years old? (Round the answer to one decimal place.)

Explanation / Answer

Let the line is:

y = a + bx

Given

x = 24, y = 104

104 = a + 24b

and

x = 60, y = 118

118 = a + 60b

Subtract the two equations:

14 = 36b

b = 2.57

And thus, a = - 36.2

a) Slope = b = 2.57

b) Intercept = - 36.2

c) When x = 34

y = - 36.2 + 2.57 * 34

y = 51.2

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