R code to test the difference between coefficients of regressors from one regression

Question

I want to test whether coefficients in one linear regression are different from each other or whether at least one of them is significantly different from one certain value, say

Answer 1

The car package has a simple function to do that.

First, fit your model:

model <- lm(Sepal.Length ~ Sepal.Width + Petal.Length, data = iris)

Than you may test different linear hypothesis using the linearHypothesis function, for instance:

library(car)

# tests if the coefficient of Sepal.Width = Petal.Length
linearHypothesis(model, "Sepal.Width = Petal.Length")
Linear hypothesis test

Hypothesis:
Sepal.Width - Petal.Length = 0

Model 1: restricted model
Model 2: Sepal.Length ~ Sepal.Width + Petal.Length

  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1    148 16.744                              
2    147 16.329  1    0.4157 3.7423 0.05497 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Other examples:
# tests if the coefficient of Sepal.Width = 0
linearHypothesis(model, "Sepal.Width = 0")

# tests if the coefficient of Sepal.Width = 0.5
linearHypothesis(model, "Sepal.Width = 0.5")

# tests if both are equal to zero
linearHypothesis(model, c("Sepal.Width = 0", "Petal.Length = 0"))

Answer 2

You can compare the coefficients list from each respective model (say mod1 and mod2), as in:

diff=merge(mod1$coefficients, mod2$coefficients, by=0, all=TRUE)
diff[is.na(diff)]=0
diff$error=abs(diff$x-diff$y)
diff[order(diff$error, decreasing=TRUE),]

This produces a data frame sorted by the absolute value of the difference in coefficients, i.e.:

    Row.names            x            y        error
1 (Intercept) -0.264189182 -0.060450853 2.037383e-01
6          id  0.003402056  0.000000000 3.402056e-03
3           b -0.001804978 -0.003357193 1.552215e-03
2           a -0.049900767 -0.049417150 4.836163e-04
4           c  0.013749907  0.013819799 6.989203e-05
5           d -0.004097366 -0.004110830 1.346320e-05

If the slopes are not what you are after, you can access the other coefficients using the coef() function:

coef(summary(model))

To get Pr(>|z|), for example, use:

coef(summary(model))[,"Pr(>|z|)"]