Consider the regression model Yi = b0 + b1X1i + b2X2i + ui . Use approach 2 from Section 7.3 to transform the regression so that you can use a t-statistic to test a. b1 = b2. b. b1 + 2b2 = 0. c. b1 + b2 = 1. (Hint: You must redefine the dependent variable in the regression.)
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Consider the regression model Yi = b0 + b1X1i + b2X2i + ui
. Use approach 2
from Section 7.3 to transform the regression so that you can use a t-statistic to test
a. b1 = b2.
b. b1 + 2b2 = 0.
c. b1 + b2 = 1. (Hint: You must redefine the dependent variable in the
regression.)
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- 10. Residual analysis Consider a regression of y on several independent variables, and the resulting predicted values of the dependent variable. The residual for the ith observation Consider a data set for a large sample of professional basketball players. Each observation contains the salary, as well as various performance statistics such as points, rebounds, and assists for each player. Suppose a regression of salary on all performance statistics is run, and the residuals are obtained. The player with the lowest (most negative) resid represents which of the following? (Assume the regression reasonably predicts salaries in most cases.) The most fairly paid player relative to her on-court performance The most overpaid player relative to her on-court performance The highest-paid player, regardless of her on-court performance The most underpaid player relative to her on-court performanceConsider a linear causal model Ya+BX+yW+u, with cov(X, W) > 0. Suppose we do not observe the variable W and have to omit it from the regression, then O OLS is expected to be larger than 3 in large samples. BOLS is expected to be equal to 3 in large samples. OLS is expected to be smaller than 3 in large samples. Since we do not know whether X and u are correlated and the sign of y, there is not enough information to compare OLS and B.Consider the following regression model where Suppose and are highly (but not perfectly) correlated. Then, a. b. C. d. e. OLS estimators are biased. OLS estimators are not consistent. OLS estimators will have large standard errors. One of,, or the constant should be dropped. cannot be interpreted as the population intercept.
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