How to find the standardized coefficients of a linear regression model in R?

The standardized coefficients in regression are also called beta coefficients and they are obtained by standardizing the dependent and independent variables. Standardization of the dependent and independent variables means that converting the values of these variables in a way that the mean and the standard deviation becomes 0 and 1 respectively. We can find the standardized coefficients of a linear regression model by using scale function while creating the model.

Example

Consider the below data frame −

 Live Demo

> set.seed(99)
> x<-rnorm(10,1.5)
> y<-rnorm(10,2)
> df1<-data.frame(x,y)
> df1

Output

      x       y
1 1.7139625 1.2542310
2 1.9796581 2.9215504
3 1.5878287  2.7500544
4 1.9438585 -0.5085540
5 1.1371621 -1.0409341
6 1.6226740  2.0002658
7 0.6361548  1.6059810
8 1.9896243  0.2549723
9 1.1358831  2.4986315
10 0.2057580 2.2709538

Creating the regression model −

> Model1<-lm(y~x,data=df1)
> summary(Model1)

Output

Call:
lm(formula = y ~ x, data = df1)
Residuals:
   Min    1Q       Median 3Q    Max
 -2.5458 -0.7047 0.1862 0.9178 1.7566
Coefficients:
      Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.9635 1.2055 1.629    0.142
   x    -0.4034    0.7988  -0.505   0.627
Residual standard error: 1.453 on 8 degrees of freedom
Multiple R-squared: 0.0309, Adjusted R-squared: -0.09024
F-statistic: 0.2551 on 1 and 8 DF, p-value: 0.6272

Creating the regression model for standardized coefficients −

> Model1_standardized_coefficients<-lm(scale(y)~scale(x),data=df1)
> summary(Model1_standardized_coefficients)

Output

Call:
lm(formula = scale(y) ~ scale(x), data = df1)
Residuals:
   Min 1Q Median 3Q Max
-1.8288 -0.5063 0.1338 0.6593 1.2619
Coefficients:
      Estimate Std.    Error t value Pr(>|t|)
(Intercept) -3.701e-18 3.302e-01  0.000    1.000
scale(x)    -1.758e-01 3.480e-01  -0.505    0.627
Residual standard error: 1.044 on 8 degrees of freedom
Multiple R-squared: 0.0309, Adjusted R-squared: -0.09024
F-statistic: 0.2551 on 1 and 8 DF, p-value: 0.6272

Let’s have a look at another example −

Example

 Live Demo

> y<-rnorm(10,2.5)
> x1<-rnorm(10,0.2)
> x2<-rnorm(10,0.5)
> x3<-rnorm(10,1.5)
> df2<-data.frame(x1,x2,x3,y)
> df2

Output

         x1       x2       x3       y
1 1.573053947 0.6329786 -0.07655243 3.598922
2 0.650256559 -1.1792643 2.12408260 3.252513
3 0.053706144 0.2215204 1.83022068 2.440583
4 0.328097240 -1.0524110 1.10187774 2.155431
5 -2.094720947 -0.8796993 0.41860307 2.722668
6 -1.166568921 -0.8570566 1.42307794 3.051786
7 0.002520447 -0.4211372 0.97446338 3.183643
8 0.268085782 -0.3668177 1.89128965 1.954121
9 0.290503410 2.1566444 0.81954674 1.132564
10 0.522759967 0.3449203 0.75130307 3.900052

> Model2_standardized_coefficients<-
lm(scale(y)~scale(x1)+scale(x2)+scale(x3),data=df2)
> summary(Model2_standardized_coefficients)

Output

Call:
lm(formula = scale(y) ~ scale(x1) + scale(x2) + scale(x3), data = df2)
Residuals:
   Min    1Q    Median    3Q    Max
-1.4389 -0.5336 0.1917 0.3699 1.2726
Coefficients:
         Estimate    Std. Error t value Pr(>|t|)
(Intercept) -8.577e-17    2.970e-01    0.000    1.000
scale(x1) 3.896e-01    3.415e-01     1.141       0.297
scale(x2) -6.845e-01    3.682e-01    -1.859    0.112
scale(x3) -4.808e-01    3.409e-01    -1.410    0.208
Residual standard error: 0.9392 on 6 degrees of freedom
Multiple R-squared: 0.4119, Adjusted R-squared: 0.1179
F-statistic: 1.401 on 3 and 6 DF, p-value: 0.331