Simple Linear Regression - Prediction

$One\; use\; of\; a\; least\; squares\; regression\; equation\; is\; the\; prediction\; of\; Y\; for\; a\; given\; X.\; Prediction\; is\; often\; used\; when\; direct\; measurement\; or\; observation\; of\; Y\; is\; expensive\; or\; impossible,\; while\; X\; is\; readily\; and\; cheaply\; observed.\; Given\; an$appropriate least squares equation, the predicted Y^* for a given X^* is

Yhat^* = bhat₀ + bhat₁ X^*

and the variance of the prediction is

The predictive ability of a least squares regression equation thus depends upon how well the original equation fits the data, s_y.x, how large the sample used to fit was, n, and how far the given X^* is from xbar relative to the Xs used in fitting the equation.