Let's say I have a simple model like this:
yi ~ beta1*xi + errori
> dat <- data.frame(y=c(10,20,30,40),x=c(1,2,5,8))
> m <- lm(y~x,data=dat)
summary(m) gives me this information
Residuals:
1 2 3 4
-3 3 1 -1
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.0000 2.7988 3.216 0.0846 .
x 4.0000 0.5774 6.928 0.0202 *
If I plug in the values above to calculate y1
y1 = 9 + 4*1 - 3
y1 = 10
however, the predict function gives me a different value for y1:
> predict(m)
1 2 3 4
13 17 29 41
why do we ignore errori when predicting y values in regression?
yi ~ beta1*xi + errori
> dat <- data.frame(y=c(10,20,30,40),x=c(1,2,5,8))
> m <- lm(y~x,data=dat)
summary(m) gives me this information
Residuals:
1 2 3 4
-3 3 1 -1
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.0000 2.7988 3.216 0.0846 .
x 4.0000 0.5774 6.928 0.0202 *
If I plug in the values above to calculate y1
y1 = 9 + 4*1 - 3
y1 = 10
however, the predict function gives me a different value for y1:
> predict(m)
1 2 3 4
13 17 29 41
why do we ignore errori when predicting y values in regression?