It seems to me that your question is more about the econometrics than about R. Any introductory econometric textbook or compendium on econometrics will cover this as it is a basic. See, for example, Greene 2006 or Wooldridge 2002.
Say X is your data matrix, that contains columns for each of the individual variables (x), columns with their interactions, and one column of 1s for the intercept. Let y be your dependent variable. Then, OLS estimates are computed by X'X inverse X'y Or in R solve(t(X)%*%X)%*%t(X)%*%y Best, Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Something Something Sent: Saturday, February 13, 2010 5:04 PM To: Bert Gunter Cc: r-help@r-project.org Subject: Re: [R] lm function in R I tried.. mod = lm(Y ~ X1*X2*X3, na.action = na.exclude) formula(mod) This produced.... Y ~ X1 * X2 * X3 When I typed just mod I got: Call: lm(formula = Y ~ X1 * X2 * X3, na.action = na.exclude) Coefficients: (Intercept) X11 X21 X31 X11:X21 X11:X31 X21:X31 X11:X21:X31 177.9245 0.2005 2.4482 3.1216 0.8127 -26.6166 -3.0398 29.6049 I am trying to figure out how R computed all these coefficients. On Sat, Feb 13, 2010 at 1:30 PM, Bert Gunter <gunter.ber...@gene.com> wrote: > ?formula > > > Bert Gunter > Genentech Nonclinical Statistics > > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] > On > Behalf Of Something Something > Sent: Saturday, February 13, 2010 1:24 PM > To: Daniel Nordlund > Cc: r-help@r-project.org > Subject: Re: [R] lm function in R > > Thanks Dan. Yes that was very helpful. I didn't see the change from '*' > to > '+'. > > Seems like when I put * it means - interaction & when I put + it's not an > interaction. > > Is it correct to assume then that... > > When I put + R evaluates the following equation: > Y-Hat = b0 + b1X1 + b2X2 + . . . bkXk + 7 7 7 + bkXk > > > But when I put * R evaluates the following equation; > Y-Hat = b0 + b1X1 + b2x2 + ... + bkXk + b12 X12+ b13 X13 +........ + c > > Is this correct? If it is then can someone point me to any sources that > will explain how the coefficients (such as b0... bk, b12.. , b123..) are > calculated. I guess, one source is the R source code :) but is there any > other documentation anywhere? > > Please let me know. Thanks. > > > > On Fri, Feb 12, 2010 at 5:54 PM, Daniel Nordlund > <djnordl...@verizon.net>wrote: > > > > -----Original Message----- > > > From: r-help-boun...@r-project.org [mailto: > r-help-boun...@r-project.org] > > > On Behalf Of Something Something > > > Sent: Friday, February 12, 2010 5:28 PM > > > To: Phil Spector; r-help@r-project.org > > > Subject: Re: [R] lm function in R > > > > > > Thanks for the replies everyone. Greatly appreciate it. Some > progress, > > > but > > > now I am getting the following values when I don't use "as.factor" > > > > > > 13.14167 25.11667 28.34167 49.14167 40.39167 66.86667 > > > > > > Is that what you guys get? > > > > > > If you look at Phil's response below, no, that is not what he got. The > > difference is that you are specifying an interaction, whereas Phil did > not > > (because the equation you initially specified did not include an > > interaction. Use Y ~ X1 + X2 instead of Y ~ X1*X2 for your formula. > > > > > > > > > > > On Fri, Feb 12, 2010 at 5:00 PM, Phil Spector > > > <spec...@stat.berkeley.edu>wrote: > > > > > > > By converting the two variables to factors, you are fitting > > > > an entirely different model. Leave out the as.factor stuff > > > > and it will work exactly as you want it to. > > > > > > > > dat > > > >> > > > > V1 V2 V3 V4 > > > > 1 s1 14 4 1 > > > > 2 s2 23 4 2 > > > > 3 s3 30 7 2 > > > > 4 s4 50 7 4 > > > > 5 s5 39 10 3 > > > > 6 s6 67 10 6 > > > > > > > >> names(dat) = c('id','y','x1','x2') > > > >> z = lm(y~x1+x2,dat) > > > >> predict(z) > > > >> > > > > 1 2 3 4 5 6 15.16667 > 24.66667 > > > > 27.66667 46.66667 40.16667 68.66667 > > > > > > > > > > > > - Phil Spector > > > > Statistical Computing > Facility > > > > Department of Statistics > > > > UC Berkeley > > > > spec...@stat.berkeley.edu > > > > > > > > > > > > > > > > On Fri, 12 Feb 2010, Something Something wrote: > > > > > > > > Hello, > > > >> > > > >> I am trying to learn how to perform Multiple Regression Analysis in > R. > > > I > > > >> decided to take a simple example given in this PDF: > > > >> http://www.utdallas.edu/~herve/abdi-prc-pretty.pdf > > > >> > > > >> I created a small CSV called, students.csv that contains the > following > > > >> data: > > > >> > > > >> s1 14 4 1 > > > >> s2 23 4 2 > > > >> s3 30 7 2 > > > >> s4 50 7 4 > > > >> s5 39 10 3 > > > >> s6 67 10 6 > > > >> > > > >> Col headers: Student id, Memory span(Y), age(X1), speech rate(X2) > > > >> > > > >> Now the expected results are: > > > >> > > > >> yHat[0]:15.166666666666668 > > > >> yHat[1]:24.666666666666668 > > > >> yHat[2]:27.666666666666664 > > > >> yHat[3]:46.666666666666664 > > > >> yHat[4]:40.166666666666664 > > > >> yHat[5]:68.66666666666667 > > > >> > > > >> This is based on the following equation (given in the PDF): Y = > 1.67 > > + > > > X1 > > > >> + > > > >> 9.50 X2 > > > >> > > > >> I ran the following commands in R: > > > >> > > > >> data = read.table("students.csv", head=F, as.is=T, na.string=".", > > > >> row.nam=NULL) > > > >> X1 = as.factor(data[[3]]) > > > >> X2 = as.factor(data[[4]]) > > > >> Y = data[[2]] > > > >> mod = lm(Y ~ X1*X2, na.action = na.exclude) > > > >> Y.hat = fitted(mod) > > > >> Y.hat > > > >> > > > >> This gives me the following output: > > > >> > > > >> Y.hat > > > >>> > > > >> 1 2 3 4 5 6 > > > >> 14 23 30 50 39 67 > > > >> > > > >> Obviously I am doing something wrong. Please help. Thanks. > > > >> > > > > Hope this is helpful, > > > > Dan > > > > Daniel Nordlund > > Bothell, WA USA > > > > > > ______________________________________________ > > R-help@r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > > http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > > > [[alternative HTML version deleted]] > > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
