Alexander Sirotkin [at Yahoo]
2003-Dec-06 16:10 UTC
[R] Difference between summary.lm() and summary.aov()
I have a simple linear model (fitted with lm()) with 2 independant variables : one categorical and one integer. When I run summary.lm() on this model, I get a standard linear regression summary (in which one categorical variable has to be converted into many indicator variables) which looks like : Estimate Std. Error t value Pr(>|t|) (Intercept) -3595.3 2767.1 -1.299 0.2005 physicianB 802.0 2289.5 0.350 0.7277 physicianC 4906.8 2419.8 2.028 0.0485 * severity 7554.4 906.3 8.336 1.12e-10 *** and when I run summary.aov() I get similar ANOVA table : Df Sum Sq Mean Sq F value Pr(>F) physician 2 294559803 147279901 3.3557 0.04381 * severity 1 3049694210 3049694210 69.4864 1.124e-10 *** Residuals 45 1975007569 43889057 What is absolutely unclear to me is how F-value and Pr(>F) for the categorical "physician" variable of the summary.aov() is calculated from the t-value of the summary.lm() table. I looked at the summary.aov() source code but still could not figure it. Thanks a lot. __________________________________ New Yahoo! Photos - easier uploading and sharing.
Spencer Graves
2003-Dec-06 17:17 UTC
[R] Difference between summary.lm() and summary.aov()
The square of a Student's t with "df" degrees of freedom is an F distribution with 1 and "df" degrees of freedom. hope this helps. spencer graves Alexander Sirotkin [at Yahoo] wrote:>I have a simple linear model (fitted with lm()) with 2 >independant >variables : one categorical and one integer. > >When I run summary.lm() on this model, I get a >standard linear >regression summary (in which one categorical variable >has to be >converted into many indicator variables) which looks >like : > > Estimate Std. Error t value Pr(>|t|) >(Intercept) -3595.3 2767.1 -1.299 0.2005 >physicianB 802.0 2289.5 0.350 0.7277 >physicianC 4906.8 2419.8 2.028 0.0485 * >severity 7554.4 906.3 8.336 1.12e-10 *** > >and when I run summary.aov() I get similar ANOVA table >: > > Df Sum Sq Mean Sq F value Pr(>F) >physician 2 294559803 147279901 3.3557 0.04381 >* >severity 1 3049694210 3049694210 69.4864 1.124e-10 >*** >Residuals 45 1975007569 43889057 > >What is absolutely unclear to me is how F-value and >Pr(>F) for the >categorical "physician" variable of the summary.aov() >is calculated >from the t-value of the summary.lm() table. > >I looked at the summary.aov() source code but still >could not figure >it. > >Thanks a lot. > >__________________________________ > >New Yahoo! Photos - easier uploading and sharing. > >______________________________________________ >R-help at stat.math.ethz.ch mailing list >https://www.stat.math.ethz.ch/mailman/listinfo/r-help > >
Dear Spencer and Alexander, In this case, physician is apparently a factor with three levels, so summary.aov() gives you a sequential ANOVA, equivalent to what you'd get from anova(). There no simple relationship between the F-statistic for physician, which has 2 df in the numerator, and the two t's. (By the way, I doubt whether a sequential ANOVA is what's wanted here.) Regards, John At 09:17 AM 12/6/2003 -0800, Spencer Graves wrote:> The square of a Student's t with "df" degrees of freedom is an F > distribution with 1 and "df" degrees of freedom. > hope this helps. spencer graves > >Alexander Sirotkin [at Yahoo] wrote: > >>I have a simple linear model (fitted with lm()) with 2 >>independant >>variables : one categorical and one integer. >> >>When I run summary.lm() on this model, I get a >>standard linear >>regression summary (in which one categorical variable >>has to be >>converted into many indicator variables) which looks >>like : >> >> Estimate Std. Error t value Pr(>|t|) >>(Intercept) -3595.3 2767.1 -1.299 0.2005 >>physicianB 802.0 2289.5 0.350 0.7277 >>physicianC 4906.8 2419.8 2.028 0.0485 * >>severity 7554.4 906.3 8.336 1.12e-10 *** >> >>and when I run summary.aov() I get similar ANOVA table >>: >> Df Sum Sq Mean Sq F value Pr(>F) >>physician 2 294559803 147279901 3.3557 0.04381 >>* >>severity 1 3049694210 3049694210 69.4864 1.124e-10 >>*** >>Residuals 45 1975007569 43889057 >> >>What is absolutely unclear to me is how F-value and >>Pr(>F) for the >>categorical "physician" variable of the summary.aov() >>is calculated >>from the t-value of the summary.lm() table. >> >>I looked at the summary.aov() source code but still >>could not figure >>it. >> >>Thanks a lot. >> >>__________________________________ >> >>New Yahoo! Photos - easier uploading and sharing. >> >>______________________________________________ >>R-help at stat.math.ethz.ch mailing list >>https://www.stat.math.ethz.ch/mailman/listinfo/r-help >> > >______________________________________________ >R-help at stat.math.ethz.ch mailing list >https://www.stat.math.ethz.ch/mailman/listinfo/r-help----------------------------------------------------- John Fox Department of Sociology McMaster University Hamilton, Ontario, Canada L8S 4M4 email: jfox at mcmaster.ca phone: 905-525-9140x23604 web: www.socsci.mcmaster.ca/jfox