習(xí)題：
　　Exercise:
　　You test a regression model with three regressors:
　　Y = 1.2%+0.38X1+1.23X2+0.17X3 R2 = 0.520.
　　The number of observations is 384. Then you perform a restricted regression which imposes the joint null hypothesis that the true coefficients on X2 and X3 are zero. The restricted OLS regression is given by
　　Y = 0.9%+0.44X1 R2 = 0.490.
　　What is the homoskedasticity-only F-statistic?
　　A     1.7
　　B     3.4
　　C     11.9
　　D     23.3
　　解析：
　　Answer: C
　　Explanation: As the unrestricted regression has three regressors and the restricted regression hypothesizes two of the coefficients are zero, we have unrestricted k = 3 and number of restriction q = 2.
 
　　知識(shí)點(diǎn)：
　　Hypothesis Testing of Multiple Linear Regression
　　A joint hypothesis tests two or more coefficients at the same time. For example, we could develop a null hypothesis for a linear regression model with three independent variables that sets two of these coefficients equal to zero: H0: b1 = b2 = 0 versus the alternative hypothesis that at least one of them is not equal to zero.
　　l  Homoskedasticity-only F statistic
　　The F-statistic is used to test joint hypothesis about regression coefficients. If the error term is homoskedastic, the F-statistic can be written in terms of the improvement in the fit of the regression as measured either by the sum of squared residuals or by the regression R2.
　　The homoskedasticity-only F-statistic is computed using a simple formula based on the sum of squared residuals from two regressions. In the restricted regression, the null hypothesis is forced to be true in which those coefficients are set to zero. In the unrestricted regression, the alternative hypothesis is allowed to be true.
　　The homoskedasticity-only F-statistic is given by:

 
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