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    Getting F statistic from multiple t-statistics?




    If I have

    Y = a + b1*X1 + b2*X2 + b3*X3 + error,

    and I have calculated sample t-statistics for b1 and b2, from this information (along with sample size) can I construct an F statistic testing Ho : b1 = b2 = 0 ?
    Last edited by derksheng; 07-24-2012 at 12:01 AM.

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    Re: Getting F statistic from multiple t-statistics?

    I know how to do it in the case where X1, X2, and X3 are all categorical predictors (i.e., if this were a two-way ANOVA where X3 = X1*X2, or a one-way ANOVA on a 4-level factor), but I am not sure how to work it out with continuous predictors... I will think about it a little more though.
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    Re: Getting F statistic from multiple t-statistics?

    My question is, why would you not look at the software printout (unless this is a homework problem where you can't)? Any software that will print out a t statistic will a f test.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Getting F statistic from multiple t-statistics?

    Because I'm trying to apply Portfolio OLS by Sefcik & Thompson (1986). This is quite esoteric and no package has it automated (and I'm newb at econometrics).

    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.

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    Re: Getting F statistic from multiple t-statistics?

    Quote Originally Posted by Jake View Post
    I know how to do it in the case where X1, X2, and X3 are all categorical predictors
    this sounds really interesting! care to share how?
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    Re: Getting F statistic from multiple t-statistics?

    Quote Originally Posted by derksheng View Post
    from this information (along with sample size, estimated b1, estimated b2, etc) can I construct an F statistic testing Ho : b1 = b2 = 0 ?
    Using the following equation will test what you asked for



    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...
    Last edited by Englund; 07-23-2012 at 03:45 PM.

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    Re: Getting F statistic from multiple t-statistics?

    Nice Englud, I see what you did there. FYI you might be interested in this forum's [math] tags. Thanks for your help.

    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.

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    Re: Getting F statistic from multiple t-statistics?


    In case you are interested in the ANOVA case I posted some details here:
    http://www.talkstats.com/showthread....9184#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.
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