1. 58.4% of the variation in Percent Body Fat can be ac- counted for by the multiple regression model using Height, Age, and Weight as predictors.
2. For a given Height and Weight, an increase of one year in Age is associated with an increase of 0.137% in Body Fat on average.
3. The multiple regression coefficient is interpreted for given values of the other variables. That is, for peo- ple of the same Weight and Age, an increase of one inch of Height is associated with, on average, a decrease of 1.274% in Body Fat. The same cannot be said when looking at people of all Weights and Ages.
Demographics. Following is a data set on various measures of the 50 United States. The Murder rate is per 100,000, HS Graduation rate is in %, Income is per capita income in dollars, Illiteracy rate is per 1000, and Life Expectancy is in years. Find a regression model for Life Expectancy with three predictor variables by trying all four of the possible models.
a) Which model appears to do the best?
b) Would you leave all three predictors in this model?
c) Does this model mean that by changing the levels of the predictors in this equation, we could affect life expectancy in that state? Explain.
d) Be sure to check the conditions for multiple regression. What do you conclude?