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A Follow-Up on F-Test in Multi-Linear Regression

  1. May 11, 2017 #1

    WWGD

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    Hi All,
    Say we want to linearly regress Y (dependent) against ## X_1, X_2,..., X_n ## (Independent) , all numerical variables to get a model ## Y=a_1X_1+...+a_n X_n ## .

    Then we test ## H_0 ## for whether :

    ##H_0: 0= a_1= a_2 =...=a_n ##

    ## H_1 : a_i \neq 0 ## for some ## i=1,2,..,n ##

    ( This is a generalization on the test for equality of 2 means to equality of means, to zero )

    Could someone remind me what one does when one rejects ## H_0 ## in terms of deciding, figuring
    out which of the ## a_i' ##s is non-zero , other than considering the t-intervals for each of the ##a_i ## 'sand checking whether the intervals (a,b) contain 0, i.e., whether a<0<b ?

    EDIT IIRC, we then do a pairwise comparison of means and then consider the intervals?
     
    Last edited: May 11, 2017
  2. jcsd
  3. May 11, 2017 #2

    MarneMath

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    The F-test doesn't really allow for finding out which coefficients are zero. It's a test for overall regression. To look at the main effects and see which are interesting and which are not, you'll have to do a multiple comparison test of some sort, depending on your goal. At the very least, you should probably apply Bonferroni correction (although that's a debatable path).
     
  4. May 11, 2017 #3

    WWGD

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    I ( think I ) understand; the F-test only tells you ( If you reject ## H_0 ##) whether there is at least one non-zero coefficient in the regression ## Y=a_1X_1+..+a_n X_n ## , but does not say which. I understand afterwards you do pairwise comparisons.
     
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