Question

Applying Simple Linear Regression to Your favorite Data.

Many dependent variables in business serve as the subjects of regression modeling efforts. We list such variables here:

Rate of return of a stock

Annual unemployment rate

Grade point average of an accounting student

Gross domestic product of a country

Salary cap space available for your favorite NFL team

Choose one of these dependent variables, or choose some other dependent variable, for which you want to construct a prediction model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List three potentially important variables, x_1, x_{2 ,and} x₃, that you think might be (individually) strongly related to your dependent variable. Next, obtain 25 data values, each of which consist of a measure of your dependent variable � and the corresponding values of x_1, x_{2 ,and} x₃

1. Use the least squares formulas given in our chapter to fit three straight-line models-one for each independent variable- for predicting y.

2. Interpret the sign of the estimated slope coefficient " β1 ' in each case, and test the utility of each model by testing H₀ : β1  = 0 against H_a: β1 " ≠ 0. What assumptions must be satisfied to ensure the validity of these tests?

3. Calculate the coefficient of determination, r², for each model. Which of the independent variables predicts y best for the 25 sampled sets of data? Is this variable necessarily best in general (i.e., for the entire population)? Explain.

Answer 1