prediction vs fitted values

Question

After trying to do som e cross validation i got some models that fitted the data fairly good but predicted them horribly (eg. fitted = [10001.543,10034.324,104023.23..], true value = [10001,543,10034,104023] and predicted = [10.22,9.44,11.323...])

For you who is a bit more experienced than i am, How can it be possible that when predicting the same data a model i based on can be so differ so much? what is the difference when the model predics something vs when it fits?

I am using poisson regression on data for you who wonder

Data1 <- data.frame(var1,var2,var3,var4,var5,var6)
data_file <- Data1[50:200,]
data_file2 <- Data1[1:50,]

model1 <- glm(var1~var2+var3+offset(log(var4)),data=data_file,family="poisson"

So what i was about to do was a K-fold cross validation so i split the data up in two variables.

pred <- predict(model1,data_file2)
pred
data_file2[,1]
model1$fitted.values

the last 3 lines gave the following results:

[10.22,9.44,11.323...]

[10001,543,10034,104023]

[10001.543,10034.324,104023.23..],

Answer 1

Regression methods aim to model your data in a relatively simple way. This is achieved by assuming the data is distributed by some parameterized known distribution, and then fitting these parameters. The model doesn't have to generate the exact same values for each data sample (which causes bad generalization. e.g. predicting bad values for new data).

Consider the problem of fitting some polynomial of degree $d$ to your data. As you increase $d$, the polynomial is more likely to fit your training data exactly . But will it generalize well? consider this example (taken from here): The middle polynomials ($d=2$) seems most promising, but the third option predicts a closer values for each training example. Still, we would consider the second polynomial as "better" in this case.

In your case, it seems like the model is underfitting your data. This is illustrated in the left polynomial above ($d=1$). You should verify that you are training it correctly, use different model parameters or try a different model.