[R] Multiple regression (with interactions) by hand

[Christoph Scherber]

Dear all,

I´ve played around with the "airquality" dataset, trying to solve the matrix equations of a simple
multiple regression by hand; however, my matrix multiplications don´t lead to the estimates returned
by coef(). What have I done wrong here?

##
m1=lm(Ozone~Solar.R*Wind,airquality)

# remove NA´s:
airquality2=airquality[complete.cases(airquality$Ozone)&
complete.cases(airquality$Solar.R)&
complete.cases(airquality$Wind),]

# create the model matrix by hand:
X=cbind("(Intercept)"=1,Solar.R=airquality2$Solar.R,Wind=airquality2$Wind,"Solar.R:Wind"=airquality2$Solar.R*airquality2$Wind)
# is the same as:
model.matrix(m1)

# create the response vector by hand:
Y=airquality2$Ozone
# is the same as:
m1$model$Ozone

# Now solve for the parameter estimates:
library(MASS)
ginv(t(X)%*%X)%*%t(X)%*%Y

# is not the same as:
coef(m1)

##
Now why is my result (line ginv(...)) not the same as the one returned by coef(m1)?

Thanks very much for your help!

Best regards,
Christoph

[using R 3.0.1 on Windows 7 32-Bit]





-- 
PD Dr Christoph Scherber
Georg-August University Goettingen
Department of Crop Science
Agroecology
Grisebachstrasse 6
D-37077 Goettingen
Germany
phone 0049 (0)551 39 8807
fax 0049 (0)551 39 8806
http://www.gwdg.de/~cscherb1