Casual Forecasting Methods: Regression Analysis

BFI (body fat index) measures the percentage of fat in the human body, and reflects the health condition of a person. Its difficult to do accurately though, typically requiring expensive MRI imaging. Insurance companies are interested in obtaining accurate body fat measures from applicants without having to spend on expensive MRIs. They think that body fat percent might have a connection with body height, weight, and age, such that the former can be accurately forecasted from the latter. Data is collected to test this premise and a multiple regression analysis is performed, with the following results:

R Sq: 0.584

Sig of F: 0.0001

Coeff p-value

Intercept 57.27 0.0001

Height (-) 1.27 0.0001

Weight 0.254 0.0690

Age 0.134 0.0001

1. What is the dependent variable?

2. Explain the R sq what does it mean?

3. Explain what the coeff of height means?

4. The coeff of height is (-) 1.27 in the regression model above, whereas a scatterplot of height against body fat percent shows no pattern or correlation. Explain why a regression model can show a significant relationship even when a significant correlation does not exist.

5. Would you accept and use this regression model, based on the verification guidelines provided in my forecasting chapter? Explain, why or why not?

6. Irrespective of your response to 5 above, what is the forecasted value of body fat

percent for the following values of height, weight and age: 5.8 ft; 130 lbs; 30 years.