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

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
Updated on: 2021-08-13T11:46:01+05:30

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