# Question

Thirty volunteers participated in the following experiment. The subjects took their own pulse rates (which is easiest to do by holding the thumb and forefinger of one hand on the pair of arteries on the side of the neck). They were then asked to flip a coin. If their coin came up heads, they ran in place for 1 minute. Then all subjects took their own pulse rates again. The difference in the before and after pulse rates was recorded, as were other data on subject characteristics. Fit a regression model to “explain’’ the pulse rate differences using the other variables as independent variables. The variables were

PULSE = difference between the before and after pulse rates

RUN = dummy variable, 1 = did not run in place, 0 = ran in place

SMOKE = dummy variable, 1 = does not smoke, 0 = smokes

HEIGHT = height in inches

WEIGHT = weight in pounds

PHYS1 = dummy variable, 1 = a lot of physical exercise, 0 = otherwise

PHYS2 = dummy variable, 1 = moderate physical exercise, 0 = otherwise

a. Perform an appropriate test to determine whether the entire set of independent variables explains a significant amount of the variability of PULSE. Draw a conclusion based on α = .01.

b. Does multicollinearity seem to be a problem here? What is your evidence? What effect does multicollinearity have on your ability to make predictions using regression?

c. Based on the full regression model ( six dependent variables), compute a point estimate of the average increase in PULSE for individuals who engaged in a lot of physical activity compared to those who engaged in little physical activity. Can we be 95% certain that the actual average increase is greater than 0?

PULSE = difference between the before and after pulse rates

RUN = dummy variable, 1 = did not run in place, 0 = ran in place

SMOKE = dummy variable, 1 = does not smoke, 0 = smokes

HEIGHT = height in inches

WEIGHT = weight in pounds

PHYS1 = dummy variable, 1 = a lot of physical exercise, 0 = otherwise

PHYS2 = dummy variable, 1 = moderate physical exercise, 0 = otherwise

a. Perform an appropriate test to determine whether the entire set of independent variables explains a significant amount of the variability of PULSE. Draw a conclusion based on α = .01.

b. Does multicollinearity seem to be a problem here? What is your evidence? What effect does multicollinearity have on your ability to make predictions using regression?

c. Based on the full regression model ( six dependent variables), compute a point estimate of the average increase in PULSE for individuals who engaged in a lot of physical activity compared to those who engaged in little physical activity. Can we be 95% certain that the actual average increase is greater than 0?

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