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Given:

Yield Temp CO2 0 57 3.6 305 1 73 3.5 325 2 96 3.7 345 3 100 3.8 353 4 99 4.0 360 5 104 4.1 369

For regression on Yield on CO2 and Temperature, I got F- test values as

F-value for CO2: 9.458903707185229e-05

F-value for Temp: 10572.049689441008.

But these seem wrong. Any helps? I am confused a) whether I should have two f-values or one f value against f-critical. b) F-test is Analysis of Variance test, right? It compares two means have the same variance, right? Am I missing anything?

Kaleab Woldemariam
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1 Answers1

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I can't reproduce either $F$ statistic for your data -- assuming that they are the complete data. These are Stata results. An $F$ test here is not about comparing two means: see any regression text. For a regression any $F$ that is $\ll 1$ or $\gg 1$ needs a careful check to see why it occurs given that data, but -- to the point -- the results you cite make no sense for these data.

If it's your own calculation, then it seems you made some mistake. If you are using some software we can't distinguish without more detail between citing the wrong thing and outrageously bad programming. 

. regress Yield Temp

      Source |       SS           df       MS      Number of obs   =         6
-------------+----------------------------------   F(1, 4)         =      6.06
       Model |  1066.48581         1  1066.48581   Prob > F        =    0.0696
    Residual |  704.347527         4  176.086882   R-squared       =    0.6023
-------------+----------------------------------   Adj R-squared   =    0.5028
       Total |  1770.83333         5  354.166667   Root MSE        =     13.27

------------------------------------------------------------------------------
       Yield |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        Temp |   63.04349   25.61688     2.46   0.070    -8.080367    134.1673
       _cons |  -150.3479   97.06848    -1.55   0.196    -419.8532    119.1574
------------------------------------------------------------------------------

. regress Yield CO2

      Source |       SS           df       MS      Number of obs   =         6
-------------+----------------------------------   F(1, 4)         =     79.77
       Model |  1686.28096         1  1686.28096   Prob > F        =    0.0009
    Residual |  84.5523765         4  21.1380941   R-squared       =    0.9523
-------------+----------------------------------   Adj R-squared   =    0.9403
       Total |  1770.83333         5  354.166667   Root MSE        =    4.5976

------------------------------------------------------------------------------
       Yield |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         CO2 |   .7709888   .0863209     8.93   0.001     .5313235    1.010654
       _cons |   -176.154   29.65315    -5.94   0.004    -258.4843   -93.82365
------------------------------------------------------------------------------

This is, naturally, a very small sample.

Nick Cox
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  • I am still confused. Yes, that is all the sample size. The added knowledge I got from your answer is that F-test in case of regression is different from comparing means. The values I got are calculated by dividing the variances of the two samples, which you seem to suggest wrong as my teacher does. You could as well refer me how to do that F-stat in hand or python or SPSS? – Kaleab Woldemariam Apr 16 '20 at 15:23
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    You didn't give any information except the data and your $F$ results. use Now I don't know what you mean by two samples. You have one sample. Sorry, I don't use python or SPSS to advise but how to do regression in either should be very well documented. – Nick Cox Apr 16 '20 at 15:38
  • Since you don't have two samples, it's hard to see what you divided.

    You apparently are taking a class on regression; you should consult the teacher and the textbook.

     – Peter Flom Apr 18 '20 at 13:51