Dear John,
Here's the summary for your model:
----- snip -----
> summary(model)
Call:
lm(formula = income ~ education * gender, data = data)
Residuals:
1 2 3 4 5 6
-4.286e+00 -5.000e+00 6.429e+00 -1.080e-14 -2.143e+00 5.000e+00
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -16.6667 22.0389 -0.756 0.528
education 4.1667 1.5430 2.700 0.114
genderMale -4.7619 34.1067 -0.140 0.902
education:genderMale 0.4762 2.3328 0.204 0.857
Residual standard error: 7.559 on 2 degrees of freedom
Multiple R-squared: 0.8823, Adjusted R-squared: 0.7057
F-statistic: 4.997 on 3 and 2 DF, p-value: 0.1713
----- snip -----
The factor gender, with two levels ("Female" and "Male") produces one
dummy regressor, genderMale, coded 1 for "Male" and 0 for "Female". The
difference in education slopes between the genders is then captured by
the education:genderMale interaction coefficient, so the t-test for the
difference is directly in the summary output.
You can also get essentially the same test from
car::linearyHypothesis(), as David Winsemius suggested to you:
> linearHypothesis(model, "education:genderMale = 0")
Linear hypothesis test:
education:genderMale = 0
Model 1: restricted model
Model 2: income ~ education * gender
Res.Df RSS Df Sum of Sq F Pr(>F)
1 3 116.67
2 2 114.29 1 2.381 0.0417 0.8571
Your attempt to use linearHypothesis() failed because there is no
genderFemale coefficients in the model. Apparently, the AI you consulted
wasn't very I.
Frankly, all this is very basic information about how linear (and
similar) statistical models are implemented in R, covered in the book
associated with car package and many other places.
I hope this helps,
John
--
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://www.john-fox.ca/
--
On 2025-01-18 9:59 p.m., Sparks, John wrote:
Caution: External email.
Hello R-Helpers,
I was looking into how to test whether the beta coefficient from a
regression would be the same for two different groups contained in the
dataset for the regression.
When I put that question into google, AI returned a very nice looking
answer (and a couple of variations on it).
library(car)
data <- data.frame(income = c(30, 45, 50, 25, 60, 55),
education = c(12, 16, 14, 10, 18, 16),
gender = c("Male", "Female", "Male", "Female",
"Male", "Female"))
model <- lm(income ~ education * gender, data = data)
# Test if the beta for "education" is significantly different between
genders
test <- linearHypothesis(model, "genderMale - genderFemale = 0")
print(test)
This, however, produces an error that I can't find a way to resolve.
Can this test actually be done in this manner, or is this a case of AI
run amok.
Guidance would be appreciated.
--John Sparks
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