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I ask because they say "Inferences about the significance of any individual \(\hat{\gamma}\) can be drawn based on tstatistics for the individual portfolio regressions and joint tests can be performed with F-statistics on combinations."

This "F-statistic on combinations" business made me post this thread.

Source:

TITLE: An Approach to Statistical Inference in Cross-Sectional Models with Security AbnormalReturns As Dependent Variable

AUTHORS: Sefcik & Thompson

DATABASE: JSTOR

YEAR: 1986.

from this information (along with sample size, estimated b1, estimated b2, etc) can I construct an F statistic testing Ho : b1 = b2 = 0 ?

where R is the reduced model and C the complete model. In the denominator it is supposed to be n, not N (my bad). g and k are number of parameter estimates in the reduced model and the complete model, respectively. Using STATA; just write

test _b[X1] = _b[X2] = 0

and STATA will give you the result. This statistica follows an F distribution with k-g numerator degrees of freedom and n-k+1 denominator degrees of freedom.

Edit: It is supposed to be a summation sign at the beginning of the denominator as well...

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Let me re-phrase my problem. Using S&T's portfolio OLS, I have the following:

(i) The SAME coefficient estimates.

(ii) DIFFERENT standard errors.

Using your method, as well as the SSR/TSS method, will give me an \(R^2\) and F-statistic the SAME as the OLS model.

This is very problematic for me because I know with some OLS heteroscedasticity robust SEs, the F changes as well ... But I'm not sure how to get my F to change when ONLY my SEs are changing.\)

http://www.talkstats.com/showthread.php/27013-Testing-arbitrary-contrasts-based-on-summary-statistics?p=89184#post89184

But like I mentioned earlier, I am not sure how to make this work in the case of continuous predictors. A lot what is detailed in the link works nicely because it takes advantage of the fact that the design matrix is so simple for ANOVA.