Find the prediction or the fitted values for an lm model

Hi,

  I would like to fit my data with a 4th order polynomial. Now I have only
5 data point, I should have a polynomial that exactly pass the five point

  Then I would like to compute the "fitted" or "predict" value with a
relatively large x dataset. How can I do it?

  BTW, I thought the model "prodfn" should pass by (0,0), but I just
wonder why the const is unequal to zero

x1<-c(0,3,4,5,8)
y1<-c(0,1,4,7,8)
prodfn<-lm(y1 ~ poly(x1, 4))

x<-seq(0,8,0.01)

temp<-predict(prodfn,data.frame(x=x))   # This line does not work..
You need to call the variable x1 because that is the name you used in the 
original data:

plot(x, predict(prodfn,data.frame(x1=x)), type = "l")
points(x1, y1)

prodfn
Call:
lm(formula = y1 ~ poly(x1, 4))

Coefficients:
(Intercept)  poly(x1, 4)1  poly(x1, 4)2  poly(x1, 4)3  poly(x1, 4)4
  4.000e+00     6.517e+00    -4.918e-16    -2.744e+00    -8.882e-16

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Find the prediction or the fitted values for an lm model

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