# Why there are two p-values for the F value, one from Summary and others from ANOVA?

Consider the 'estandar' output of R that I copied from Anova from R output interpretation and added other variables.

Why there are two p-values? One from Summary F-statistic: 9.24 on 1 and 118 DF, p-value: 0.0001851 and others from ANOVA 6.241e-07***,0.08837,0.47480?

Residuals:
Min       1Q   Median       3Q      Max
-2.74004 -0.33827  0.04062  0.44064  1.22737

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  2.11405    0.32089   6.588  1.3e-09 ***
V2           0.03883    0.01277   3.040  0.00292 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6231 on 118 degrees of freedom
Multiple R-squared: 0.07262,    Adjusted R-squared: 0.06476
F-statistic:  9.24 on 1 and 118 DF,  p-value: 0.0001851

> anova(fit)
Analysis of Variance Table

Response: V1
Df Sum Sq Mean Sq F value   Pr(>F)
V2          1  3.588  3.5878  9.2402
6.241e-07***
V3          1  4       4       5.0889
0.08837
V4          1  3       3       5.7637
0.47480
....(here are more variables)
Residuals 118 45.818  0.3883
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


## 1 Answer

So one p-value gives information whether your overall model is significant or not and other gives about the variables used whether variables used in model are significant or not.

These are for each variable V1, V2 and V3:

6.241e-07***,0.08837,0.47480


And, this one is for your overall model F statistics.

F-statistic:  9.24 on 1 and 118 DF,  p-value: 0.0001851

• And the p-values are actually the same for linear regression with one predictor: x <- 1:5; y <- x^2; fit <- lm(y ~ x); summary(fit); anova(fit) – Roland Feb 13 at 8:41