1. 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.
2. 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?
1. Ho: β1=β3=0
Ha: at least one of them is not equal to 0.
Test statistic F=(0.87-0.84)/2/((1-0.87)/(28-1-7))= 2.308
P value=FDIST(2.308, 2, 20)= 0.12535 (FDIST is a function in excel)
Since 0.12535>0.10, we could not reject Ho.
Based on the test, we could not conclude that variables X1 and X3 ...
The significance level dependent variables are examined. Prediction of market capitalization are determined.