Consider the data below. Suppose that in the aerobic exercise group we also measured the number of hours of aerobic exercise per week; the mean is 5.2 hours with a standard deviation of 2.1 hours. The sample correlation is -0.42. a) Estimate the equation of the regression line that best describes the relationship between number of hours of exercise per week and HDL cholesterol level (Assume that the dependent variable is HDL level). b) Estimate the HDL level for a person who exercises 7 hours per week. c) Estimate the HDL level for a person who does not exercise.Exercise GroupNMeanStandard DeviationWeight Training 2049.710.2Aerobic Exercise 2043.111.1Stretching/Yoga2057.012.5

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Asked Dec 3, 2019
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Consider the data below. Suppose that in the aerobic exercise group we also measured the number of hours of aerobic exercise per week; the mean is 5.2 hours with a standard deviation of 2.1 hours. The sample correlation is -0.42. a) Estimate the equation of the regression line that best describes the relationship between number of hours of exercise per week and HDL cholesterol level (Assume that the dependent variable is HDL level). b) Estimate the HDL level for a person who exercises 7 hours per week. c) Estimate the HDL level for a person who does not exercise.

Exercise Group N Mean Standard Deviation
Weight Training  20 49.7 10.2
Aerobic Exercise  20 43.1 11.1
Stretching/Yoga 20 57.0 12.5
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Expert Answer

Step 1

It is given that the sample correlation is –0.42.

Step 2

a.

 

The slope of the regression equation is obtained as follows:

Standard deviation of HDL
Slope Corrlation x
Standard deviation of number of houres of exerice
11.1
=-0.42 x
2.1
=-2.22
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Standard deviation of HDL Slope Corrlation x Standard deviation of number of houres of exerice 11.1 =-0.42 x 2.1 =-2.22

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Step 3

The intercept is obtained as follows:

...
Intercept Mean of HDL - Slope x (Mean number of hours of exercise)
-43.1-(2.22)(5.2)
- 43.1 +11.544
=54.644
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Intercept Mean of HDL - Slope x (Mean number of hours of exercise) -43.1-(2.22)(5.2) - 43.1 +11.544 =54.644

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