Consider a linear regression of response variable Y Y1 Yn

Consider a linear regression of response variable Y = (Y1,. . ,Yn) on a predictor variable X = (X1,. . Xn) The least-squares estimates of intercept and slope, alpha and Beta, are the values minimizing the function: d(alpha,Beta) = Sigma n to i = 1 {Yi - (alpha + BetaXi)}2 Further, predicted values are y(x) = alpha + Beta x. Find y(X bar), where X bar is the average of the Xis.

Solution

yhat(xbr)=E(alpha+betax)

yhat(xbar)=alpha+beta xbar