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With this output, I know that intercept is when both factors are 0. I understand that factor(V1)1 means V1=1 and factor(V2)1 means V2=1. To get the slope for just V1 being = 1 I would add 5.1122 +(-0.4044). However, I am wondering how to interpret the p-values in this output. If just V1 = 1, does that mean the p-value is 2.39e-12 + 0.376? If so, every model I run is only significant when all factors = 0... 

> lm.comfortgender=lm(V13~factor(V1)+factor(V2),data=comfort.txt)
> summary(lm.comfortgender)

Call:
lm(formula = V13 ~ factor(V1) + factor(V2), data = comfort.txt)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5676 -1.0411  0.1701  1.4324  2.0590 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   5.1122     0.5244   9.748 2.39e-12 ***
factor(V1)1  -0.4044     0.4516  -0.895    0.376    
factor(V2)1   0.2332     0.5105   0.457    0.650    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.487 on 42 degrees of freedom
Multiple R-squared:  0.02793,   Adjusted R-squared:  -0.01836 
F-statistic: 0.6033 on 2 and 42 DF,  p-value: 0.5517
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  • This is more of a Cross-Validated question and you should probably consult a statistics textbook here. The p-value you are referencing is that of the intercept. It has nothing to do with the significance of the "model" - actually there is no measure for that unless you want to consider R-squared (for which yours is extremely low). It's also the case that your F-stat is low which means your model is poorly specified (or the probability of your coefficients being jointly zero is high). – Jason Nov 13 '15 at 01:07

1 Answers1

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The p-values given as output in the R regression models test the null hypothesis that the mean of the distribution of that particular coefficient is zero, under the assumption that the distribution is normal and the standard deviation is the square root of the variance. Refer to this other answer for further clarifications.

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