[R] linearHypothesis

Johan Lassen joh@n|@@@en @end|ng |rom gm@||@com
Thu Sep 17 15:07:46 CEST 2020

Dear R-users,

I am using the R-function "linearHypothesis" to test if the sum of all
parameters, but the intercept, in a multiple linear regression is different
from zero.
I wonder if it is statistically valid to use the  linearHypothesis-function
for this?
Below is a reproducible example in R. A multiple regression: y =

It seems to me that the linearHypothesis function does the calculation as
an F-test on the extra residuals when going from the starting model to a
'subset' model, although all variables in the 'subset' model differ from
the variables in the starting model.
I normally think of a subset model as a model built on the same input data
as the starting model but one variable.

Hence, is this a valid calculation?

Thanks in advance,Johan

# R-code:
y <-

data <-

model <- lm(y~t0+t1+t2+t3+t4+0,data=data)


# Reproduce the result from linearHypothesis:
# beta1+beta2+beta3+beta4=0 -> beta4=-(beta1+beta2+beta3) ->
# y=beta0+beta1*t1+beta2*t2+beta3*t3-(beta1+beta2+beta3)*t4
# y = beta0'+beta1'*(t1-t4)+beta2'*(t2-t4)+beta3'*(t3-t4)

data$t1 <- data$t1-data$t4
data$t2 <- data$t2-data$t4
data$t3 <- data$t3-data$t4

model_reduced <- lm(y~t0+t1+t2+t3+0,data=data)


Johan Lassen

"In the cities people live in time -
in the mountains people live in space" (Budistisk munk).

	[[alternative HTML version deleted]]

More information about the R-help mailing list