We now turn to the task of predicting a specific Y value from a given level of X. In particular, for X = X_{o}, let us predict or forecast the value of the random variable Y_{o} = β_{0} + β_{1}X_{o} + ε_{o}. If the true population regression line were known, the predictor of Y_{o} would be E(Y_{o}|X_{o})= β_{0} + β_{1}X_{o}, a point on the population regression line corresponding to X_{o}. Since E(Y_{o}|X_{o}) is unknown, and must be estimated from sample data, let us use the estimator , a point on the sample regression line. If is used to estimate Y_{o}, then the forecast error is the random variable its mean is that is, is an unbiased estimator for Y_{o} since . Moreover, it can be demonstrated that the estimated standard deviation of the forecast error is

If we next assume ...

Start Free Trial

No credit card required