How to Get F Statistics and p Value From lm in R

Renesh Bedre    2 minute read

get F statistics and p value from lm

In R, the summary() function provides detailed summary results of the fitted regression model obtained from the lm() function.

Sometimes, we are interested in only getting F statistics and p value from the fitted model instead of getting detailed summary statistics.

You can use the following syntax to get F statistics and p value from lm summary statistics,

# F statistic
summary(model)$fstatistic[1]

# p value
pf(summary(model)$fstatistic[1], summary(model)$fstatistic[2], summary(model)$fstatistic[3], lower.tail = FALSE)

The multiple regression example below illustrates how to get the F statistics and p value based on the fitted model.

Load blood pressure example dataset to fit the regression model,

df = read.csv("https://reneshbedre.github.io/assets/posts/reg/bp.csv")

# view first 5 rows
head(df)
   BP Age Weight  BSA Dur Pulse Stress
1 105  47   85.4 1.75 5.1    63     33
2 115  49   94.2 2.10 3.8    70     14
3 116  49   95.3 1.98 8.2    72     10
4 117  50   94.7 2.01 5.8    73     99
5 112  51   89.4 1.89 7.0    72     95
6 121  48   99.5 2.25 9.3    71     10

Fit the multiple regression model using the lm() function with BP as a dependent variable,

model <- lm(BP ~ ., data = df)

# summary statistics
summary(model)

# output
Call:
lm(formula = BP ~ ., data = df)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.93213 -0.11314  0.03064  0.21834  0.48454 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -12.870476   2.556650  -5.034 0.000229 ***
Age           0.703259   0.049606  14.177 2.76e-09 ***
Weight        0.969920   0.063108  15.369 1.02e-09 ***
BSA           3.776491   1.580151   2.390 0.032694 *  
Dur           0.068383   0.048441   1.412 0.181534    
Pulse        -0.084485   0.051609  -1.637 0.125594    
Stress        0.005572   0.003412   1.633 0.126491    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4072 on 13 degrees of freedom
Multiple R-squared:  0.9962,	Adjusted R-squared:  0.9944 
F-statistic: 560.6 on 6 and 13 DF,  p-value: 6.395e-15

The summary statistics provide values of F statistics (560.6) and p value (6.395e-15) along with other regression model statistics such as regression coefficients and residuals.

F statistics and p value are used to assess the significant relationship between the independent variables and dependent variable. The significant p value (p < 0.05) indicates statistically significant relationship and suggests independent variables reliably predict the dependent variable.

If you only want to get F statistics and p value from summary statistics, you can extract those values as below,

Extract F statistics,

summary(model)$fstatistic[1]
  value 
560.641

The summary() function does not explicitly return the p value. But p value can be calculated using F statistics and degrees of freedom.

pf(summary(model)$fstatistic[1], summary(model)$fstatistic[2], summary(model)$fstatistic[3], lower.tail = FALSE)
      value 
6.395226e-15

In the above code, summary(model)$fstatistic[2] and summary(model)$fstatistic[3] return the numerator and denominator degree of freedoms, respectively.

The lower.tail is set to FALSE for getting the right-sided probability of the F distribution

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