Confidence Intervals for Predicted Response

Each response variable has some true value, which we will never know.

From r replicas of an experiment (holding factor levels constant), we can estimate response variable's true value by statistical inference.

How far is our estimate from the true value?

Suppose our data satisfies three conditions:

• Independence of error components: Each experiment outcome is in no way related to the outcome of any other experiment

• Normal distribution of errors (e_{ij}) with zero mean

• Homogeneity of error variance: The variance of the errors e_i. for all i must be equal

Then t-distribution yields confidence interval for some significance level (\alpha).

• Computing confidence intervals...