Given a new valuexn+1for the explanatory variable, we wish to predictyn+1. It can beassumed thatyn+1=α+βxn+1+n+1
Consider the following model:yi=α+βxi+i;i= 1,2,···,n(4)wherexiis fixed in repeated sampling, and the random disturbance termisatisfies the usualassumptions ofE(i) = 0V(i) =σ2∀iE(ij) = 0∀i6=j(5)Let ˆi, ˆαandˆβdenote the OLS residuals and the parameter estimators, respectively. The re-gression model of (4) is fitted to the data: (x1,y1),···, (xn,yn), giving least squares estimates ˆα1 andˆβ. Given a new valuexn+1for the […]