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I ran a multiple regression analysis and got significant results for lFreq, Len variables, and interaction lFreq x Len. Now I need to report these results and I am a bit confused whether F(7, 924) = 9.876 and R^2= 0.06961 stand for all variables? It seems to me that each variable should have its own F and R^2 values... How should I calculate them?

Call:
lm(formula = duration ~ lFreq * Len * group, data = df.eyes)

 Residuals:
  Min        1Q    Median        3Q       Max 
-0.079878 -0.010185 -0.001281  0.009893  0.192742 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.2547662  0.0110199  23.119   <2e-16 ***
lFreq            -0.0038043  0.0012332  -3.085   0.0021 ** 
Len              -0.0034335  0.0014160  -2.425   0.0155 *  
group2            0.0186209  0.0156136   1.193   0.2333    
lFreq:Len         0.0003494  0.0001617   2.160   0.0310 *  
lFreq:group2     -0.0005048  0.0017458  -0.289   0.7725    
Len:group2       -0.0035563  0.0020054  -1.773   0.0765 .  
lFreq:Len:group2  0.0001673  0.0002290   0.731   0.4652    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01765 on 924 degrees of freedom
Multiple R-squared:  0.06961,   Adjusted R-squared:  0.06256 
F-statistic: 9.876 on 7 and 924 DF,  p-value: 6.388e-12
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The F test and R-squared values are for the entire model--inclusive of all the variables. The significance testing of each individual variable in the model is carried out via the t-test in each variable's row of output.

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  • 1
    $\begingroup$ Correct. In fact, there is an easy relation between $R^2$ and this $F$-statistic that tests the significance of the regression model: $R^2=kF/(kF+n-k-1)$, where $k=7$ is the number of regressors in the model and $n=931$ is the number of data points. $\endgroup$ – StijnDeVuyst Aug 22 '15 at 17:47

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