Statistics help needed
1. A researcher collected datafrom 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?
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