Discuss the below:
Q1. A researcher collected data from 28 individuals. Seven independent variables were used to predict a dependent variable. The value of R2 for this model was .87. When the variable X_1 and X_3 were omitted from the model, R^2 was .84. Do the variables X1 and X3 contribute to the prediction of the dependent variable? Use a .10 significance level.
Q2. After a series of hurricanes struck Florida in 2004 and the price of oil exceeded $50 a barrel, the federal government negotiated with oil companies to lend them oil from the U.S. Strategic Petroleum Reserve. The market capitalization of major oil companies is mostly driven by their oil/ gas reserves. Suppose that an energy consultant collected data on 10 major oil companies to determine the relationship between an oil company's reserves, X (in units of billions of barrels), and market capitalization, Y (in units of billions of dollars).
a. The R^2 for the regression equation Y= -18.035 + 10.856X is 91.78%. Test that the variable oil reserves contributes to the prediction of market capitalization. Use a 1% significance level.
b. The R^2 for the regression equation Y= -9.045 + 7.857X + .150X2 is 92.29%. Test that the variable oil reserves and the square of this variable contribute to the prediction of market capitalization. Use a 1% significance level.
c. What is the adjusted value of R^2 for the model in parts a and b? Since the value of the adjusted R&2 does not increase in value for the model in part b, what conclusion can you make about the appropriateness of adding the quadratic term to the model?