Using generic notation, let x = RSpd, y = CSpd and let n be the number of cases used in the regression (n = 1116 in the data we have used in this problem) and x and SXX defined from these n...

Using generic notation, let x = RSpd, y = CSpd and let n be the number of cases used in the regression (n = 1116 in the data we have used in this problem) and x and SXX defined from these n observations. Suppose we want to make predictions at m time points with values of wind speed

x*1, . . . , x*m that are different from the n cases used in constructing the prediction equation. Show that (1) the average of the m predictions is equal to the prediction taken at the average value x* of the m values of the predictor, and (2) using the first result, the standard error of the average of m predictions is

If m is very large, then the first term in the square root is negligible, and the standard error of average prediction is essentially the same as the standard error of a fitted value at