July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short CourseBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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12.9 The Prediction of a Particular Value of Y given X
We now turn to the task of predicting a specific Y value from a given level of X. In particular, for X = Xo, let us predict or forecast the value of the random variable Yo = β0 + β1Xo + εo. If the true population regression line were known, the predictor of Yo would be E(Yo|Xo)= β0 + β1Xo, a point on the population regression line corresponding to Xo. Since E(Yo|Xo) 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 Yo, then the forecast error is the random variable 
its mean is 
that is, 
is an unbiased estimator for Yo since 
. Moreover, it can be demonstrated that the estimated standard deviation of the forecast error is
If we next assume ...
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