Dear all
I have observations done in 4 different classes and the between classes
*variance* is too high that I decided to run a model without pooling the
*variance*. I used the following code first :
model<-lm(y~x+factor(class))
and got the following output:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 52.41405 17.38161 3.015 0.00658 **
x 0.27679 0.07387 3.747 0.00119 **
factor(class)2 92.68083 32.26645 2.872 0.00912 **
factor(class)3 197.82029 33.24916 5.950 6.63e-06 ***
factor(class)4 105.61266 55.18373 1.914 0.06937 .
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 43.07 on 21 degrees of freedom
Multiple R-squared: 0.9206, Adjusted R-squared: 0.9055
F-statistic: 60.91 on 4 and 21 DF, p-value: 2.976e-11
My understanding of this output is that class 1 is used as a baseline
(constant) and each other class's p values means for example the dependent
value in class 2 is significantly different from that of class 1.
Now I ran the model again, but without using a constant i.e
model<-lm(y~x+factor(class)-1)
and got the following output:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x 0.27679 0.07387 3.747 0.00119 **
factor(class)1 52.41405 17.38161 3.015 0.00658 **
factor(class)2 145.09488 39.42651 3.680 0.00139 **
factor(class)3 250.23434 40.61189 6.162 4.11e-06 ***
factor(class)4 158.02672 64.09549 2.465 0.02238 *
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 43.07 on 21 degrees of freedom
Multiple R-squared: 0.9801, Adjusted R-squared: 0.9754
F-statistic: 207.1 on 5 and 21 DF, p-value: < 2.2e-16
Can somebody please tell me how to interpret this one now? what do the
classes' P values mean ? Do they merely show if they significantly
contribute to the model or whether they are significantly different from
the overall mean or not? Does it mean if one class had a p value > 0.05 it
would mean the observations from that class are not significantly
contributing to the model?
Thanks in advance
David
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