I am puzzled at the use of regression. I have a categorical variable
ClassePop33000 which factors a Population variable into 3 levels. I want to
investigate whether that categorical variable has some relation with my
dependent variable, so I go :
lm(Cout.ton ~ ClassePop33000, data=ech2)
Call:
lm(formula = Cout.ton ~ ClassePop33000, data = ech2)
Residuals:
Min 1Q Median 3Q Max
-182.24 -62.91 -22.76 66.38 277.39
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 231.66 11.50 20.141 < 2e-16 ***
ClassePop33000[T.[3000,25000)] -72.91 16.70 -4.366 2.19e-05 ***
ClassePop33000[T.[25000,10000000)] -95.17 19.92 -4.777 3.82e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 97.6 on 170 degrees of freedom
Multiple R-Squared: 0.1502, Adjusted R-squared: 0.1402
F-statistic: 15.02 on 2 and 170 DF, p-value: 9.818e-07
Now I discovered one could omit the intercept and therefore have
coefficients for the N levels of the categorical variable. So I went :
lm(Cout.ton ~ ClassePop33000 + 0, data=ech2)
Call:
lm(formula = Cout.ton ~ ClassePop33000 + 0, data = ech2)
Residuals:
Min 1Q Median 3Q Max
-182.24 -62.91 -22.76 66.38 277.39
Coefficients:
Estimate Std. Error t value Pr(>|t|)
ClassePop33000[1,3000) 231.66 11.50 20.141 < 2e-16 ***
ClassePop33000[3000,25000) 158.75 12.11 13.114 < 2e-16 ***
ClassePop33000[25000,10000000) 136.49 16.27 8.391 1.8e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 97.6 on 170 degrees of freedom
Multiple R-Squared: 0.7922, Adjusted R-squared: 0.7885
F-statistic: 216 on 3 and 170 DF, p-value: < 2.2e-16
I tried the very pedagogical examples at
http://www.stat.umn.edu/geyer/5102/examp/dummy.html and plotting the
regression lines with abline gives me the exact same lines whether I use
with or without intercept. Now why do R squared differ then ? At least the
p-values are of the same order of magnitude, but I don't understand the
drastic difference in R squared. Pointers to stats 101 anyone ?
TIA
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