Imagine a regression line that relates average systolic blood pressure to a pers
ID: 3228101 • Letter: I
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 40 years old is 102, while for those 60 years old the average is 114.
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 50 years old?
(Round the answer to one decimal place.)
Explanation / Answer
Let X: Age and Y: Systollic Blood Pressure (SBP)
We have given SBP = 102 when Age = 40 years and SBP = 114 when age = 60, let us present this information in table format and create below table
Now we have to find SSxy, SSx, Slope(b), Xbar, Ybar and intercept(a) using above table
SSxy = sum(XY) - sum(X)*sum(Y) / n = 10920 - 100x216/2 = 10920 - 10800 = 120
SSx = sum(X2) - sum(X)2 / n = 5200 - 1002 / 2 = 5200 - 5000 = 200
Slope(b) = SSxy / SSx = 120 / 200 = 0.6
a) Thus the slope of the regression line is 0.60
Xbar = sum(X) / n = 100 / 2 = 50
Ybar = sum(Y) / n = 216 / 2 = 108
Intercept(a) = Ybar - slope*Xbar = 108 - 0.60 x 50 = 108 - 30 = 78
b) Thus the intercept of the regression line is 78.00
therefore, the regression line equation is
Yhat = a + b * Xhat
SBP = 78 + 0.6 * Age-------------- (1)
c) What is SBP when age = 50 years
Substitute age = 50 in equation (1), we get
SBP = 78 + 0.6 * 50 = 78 + 30 = 108
Thus the estimated average systolic blood pressure for people who are 50 years old is 108
Age(X) SBP(Y) X2 Y2 XY 40 102 1600 10404 4080 60 114 3600 12996 6840 Total 100 216 5200 23400 10920