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?