You can use the following methods to extract p-values from the in R:

Method 1: Extract Overall P-Value of Regression Model

#define function to extract overall p-value of model
overall_p <- function(my_model) {
    f <- summary(my_model)$fstatistic
    p <- pf(f[1],f[2],f[3],lower.tail=F)
    attributes(p) <- NULL
    return(p)
}

#extract overall p-value of model
overall_p(model)

Method 2: Extract Individual P-Values for Regression Coefficients

summary(model)$coefficients[,4]

The following example shows how to use these methods in practice.

Example: Extract P-Values from lm() in R

Suppose we fit the following model in R:

#create data frame
df <- data.frame(rating=c(67, 75, 79, 85, 90, 96, 97),
                 points=c(8, 12, 16, 15, 22, 28, 24),
                 assists=c(4, 6, 6, 5, 3, 8, 7),
                 rebounds=c(1, 4, 3, 3, 2, 6, 7))

#fit multiple linear regression model
model <- lm(rating ~ points + assists + rebounds, data=df)

We can use the summary() function to view the entire summary of the regression model:

#view model summary
summary(model)

Call:
lm(formula = rating ~ points + assists + rebounds, data = df)

Residuals:
      1       2       3       4       5       6       7 
-1.5902 -1.7181  0.2413  4.8597 -1.0201 -0.6082 -0.1644 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  66.4355     6.6932   9.926  0.00218 **
points        1.2152     0.2788   4.359  0.02232 * 
assists      -2.5968     1.6263  -1.597  0.20860   
rebounds      2.8202     1.6118   1.750  0.17847   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.193 on 3 degrees of freedom
Multiple R-squared:  0.9589,	Adjusted R-squared:  0.9179 
F-statistic: 23.35 on 3 and 3 DF,  p-value: 0.01396

At the very bottom of the output we can see that the overall p-value for the regression model is 0.01396.

If we would like to only extract this p-value from the model, we can define a custom function to do so:

#define function to extract overall p-value of model
overall_p <- function(my_model) {
    f <- summary(my_model)$fstatistic
    p <- pf(f[1],f[2],f[3],lower.tail=F)
    attributes(p) <- NULL
    return(p)
}

#extract overall p-value of model
overall_p(model)

[1] 0.01395572

Notice that the function returns the same p-value as the model output from above.

To extract the p-values for the individual regression coefficients in the model, we can use the following syntax:

#extract p-values for individual regression coefficients in model
summary(model)$coefficients[,4] 

(Intercept)      points     assists    rebounds 
0.002175313 0.022315418 0.208600183 0.178471275