How to test for the difference between two regression coefficients in R?

To test for the difference between two regression coefficients, we can follow the below steps −

• First of all, creating data frame.
• Then creating a regression model.
• After that testing the difference between regression coefficients using LienarHypothesis function of car package.

Create the data frame

Let's create a data frame as shown below −

 Live Demo

x1<-rnorm(20)
x2<-rnorm(20,5,1)
y1<-rnorm(20)
df<-data.frame(x1,x2,y1)
df

On executing, the above script generates the below output(this output will vary on your system due to randomization) −

       x1          x2           y1
1   -0.20412848  4.556105   0.45908013
2    0.30523549  5.569055  -0.03171895
3    0.04370042  5.699348  -0.36329671
4   -1.17038676  3.946887  -0.36719554
5    0.44386866  5.421256 -1.22089962
6    0.73872256 4.206500  -0.54798050
7   -1.25760889 4.302561   0.86247603
8   -1.91528711 4.956543   1.46603539
9   -1.53261347 4.281640   1.13248696
10   0.18349241 5.587560   1.84692077
11  -0.87403060 5.563882   1.01042402
12   0.11175919 6.364895   0.12010507
13   1.25899545 4.760614  -0.33105484
14  -0.17737332 3.466253   0.70906765
15  -0.69325729 4.905586  -1.02842953
16   0.32417246 5.873589  -0.28118196
17  -0.46810874 5.690111  -0.03787195
18   1.26463339 4.674473  -0.80026871
19  -1.11437137 6.029646  1.77880908
20  -0.51711414 6.120406  -1.87254637

Creating regression model

Use lm function to create the regression model with x1 and x2 as independent variable and y1 as dependent variable −

 Live Demo

x1<-rnorm(20)
x2<-rnorm(20,5,1)
y1<-rnorm(20)
df<-data.frame(x1,x2,y1)
Model_1<-lm(y1~x1+x2,data=df)
summary(Model_1)

Output

Call:
lm(formula = y1 ~ x1 + x2)
Residuals:
   Min    1Q    Median    3Q    Max
-2.0904 -0.2602 0.1675 0.3739 1.9845

Coefficients:
         Estimate Std. Error t value    Pr(>|t|)
(Intercept) 0.20785 1.40412    0.148    0.8841
x1       -0.54075   0.24709    -2.188   0.0429 *
x2       -0.04406   0.27069 -  0.163    0.8726
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9463 on 17 degrees of freedom
Multiple R-squared: 0.225, Adjusted R-squared: 0.1338
F-statistic: 2.467 on 2 and 17 DF, p-value: 0.1146

Testing for the difference between coefficient of x1 and x2

Using LinearHypothesis function of car package to test the difference between coefficient of x1 and x2 −

 Live Demo

x1<-rnorm(20)
x2<-rnorm(20,5,1)
y1<-rnorm(20)
df<-data.frame(x1,x2,y1)
Model_1<-lm(y1~x1+x2,data=df)
summary(Model_1)
library(car)
linearHypothesis(Model_1,"x1 = x2")

Output

Linear hypothesis test
Hypothesis:
x1 - x2 = 0

Model 1: restricted model
Model 2: y1 ~ x1 + x2

Res.Df RSS Df Sum of Sq F Pr(>F)
1 18 16.719
2 17 15.222 1 1.4974 1.6723 0.2132