# Statistics, prediction

1. May 10, 2009

### MaxManus

1. The problem statement, all variables and given/known data
Given a simple linear model y = B1 + B2*x + e and the least square estimators, we can estimate E(y) for any value of x = x0 as Y0 = b1 + b2*x0

Describe the difference between predicting y0 and estimating E(y0)
2. Relevant equations

3. The attempt at a solution

I am not sure what the difference is.

Prediction:
Y= b1 + b2*x0

f = y0 - Y0 = (B1 +B2*x0 + e0) - (b1 + b2*x0)

E(f) = 0

and var(f) = sigma2*(1 + 1/N + (x0 - $$\bar{x}$$)2/sum(xi - $$\bar{}x$$)2

where $$\bar{}x$$ is the average.

the prediction interval is Y0 +- tc*se(f)

where se is the standard error of the forcast.

Can anyone help me with estimating E(y0)?