How to Extract Regression Coefficients from lm() Function in R

You can use the following methods to extract regression coefficients from the lm() function in R:

Method 1: Extract Regression Coefficients Only

model$coefficients

Method 2: Extract Regression Coefficients with Standard Error, T-Statistic, & P-values

summary(model)$coefficients

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

Example: Extract Regression Coefficients from lm() in R

Suppose we fit the following multiple linear regression 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

To view the regression coefficients only, we can use model$coefficients as follows:

#view only regression coefficients of model
model$coefficients

(Intercept)      points     assists    rebounds 
  66.435519    1.215203   -2.596789    2.820224

We can use these coefficients to write the following fitted regression equation:

Rating = 66.43551 + 1.21520(points) – 2.59678(assists) + 2.82022(rebounds)

To view the regression coefficients along with their standard errors, t-statistics, and p-values, we can use summary(model)$coefficients as follows:

#view regression coefficients with standard errors, t-statistics, and p-values
summary(model)$coefficients

             Estimate Std. Error   t value    Pr(>|t|)
(Intercept) 66.435519  6.6931808  9.925852 0.002175313
points       1.215203  0.2787838  4.358942 0.022315418
assists     -2.596789  1.6262899 -1.596757 0.208600183
rebounds     2.820224  1.6117911  1.749745 0.178471275

We can also access specific values in this output.

For example, we can use the following code to access the p-value for the points variable:

#view p-value for points variable
summary(model)$coefficients["points", "Pr(>|t|)"]

[1] 0.02231542

Or we could use the following code to access the p-value for each of the regression coefficients:

#view p-value for all variables
summary(model)$coefficients[, "Pr(>|t|)"]

(Intercept)      points     assists    rebounds 
0.002175313 0.022315418 0.208600183 0.178471275

The p-values are shown for each regression coefficient in the model.

You can use similar syntax to access any of the values in the regression output.