Question: Physical activity of obese young adults. In a study published in the International Journal of Obesity (January 2007), pediatric researchers measured overall physical activity for two groups of young adults: 13 obese adults and 15 normal weight adults. The researchers recorded the total number of registered movements (counts) of each young adult over a period of time. Baseline physical activity was then computed as the number of counts per minute (cpm). Four years later, the physical activity measurements were taken again, called physical activity at follow-up.
(a) For the 13 obese young adults, the researchers reported a correlation of r = .50 between baseline and follow-up physical activity, with an associated p-value of .07. Give a practical interpretation of this correlation coefficient and p-value.
(b) Refer to part a. Construct a possible scatterplot for the 13 data points that would yield a value of r = .50.
(c) Refer to part a. Compute and interpret the coefficient of determination, r2, relating baseline and follow-up physical activity for obese young adults in a simple linear regression.
(d) For the 15 normal weight young adults, the researchers reported a correlation of r = -.12 between baseline and follow-up physical activity, with an associated p-value of .66. Give a practical interpretation of this correlation coefficient and p-value
(e) Refer to part d. Construct a possible scatterplot for the 15 data points that would yield a value of r = -.12.
(f) Refer to part d. Compute and interpret the coefficient of determination, r2, relating baseline and follow-up physical activity for normal weight young adults in a simple linear regression.