Yi = Bo + B1X11 + 32x11 +... + Bkxki + E holds and that the standard regression assumptions are valid, let bo, by be the least squares estimates of the model coefficients, Bi, where j = based on the x1,x2,..., xk (i = 1,...,n) data points. Then, given a ne vation of a data point, X1,1+1, X2,11+1, ... , XK,n+1 the best linear unbiased f of Yn+1 is ; = bo + byxli + b2x1i + ... + bkxki i = n + 1 It is very risky to obtain forecasts that are based on X values outsi range of the data used to estimate the model coefficients because we have data evidence to support the linear model at those points. In addition to the predicted value of Y for a particular set of x; terms, interested in a confidence interval or a prediction interval associated with th As we discussed in Section 11.6, the confidence interval includes the expecte with probability 1 - a. In contrast, the prediction interval includes individu values-expected values of Y plus the random error term. To obtain these need to compute estimates of the standard deviations for the expected va for the individual points. These computations are similar in form to those us regression, but the estimator equations are much more complicated. The sta tions for predicted values, S, are a function of the standard error of the est standard deviation of the predictor variables; the correlations between the p ables; and the square of the distance between the mean of the independent X15 the X terms for the prediction. This standard deviation is similar to the star tion for simple regression predictions in Chapter 11. However, the equations regression are very complex and are not presented hereinstead, we compu using Minitab. The standard deviations for the prediction interval, the conf val, and the corresponding intervals are computed by most good statistics pa does not have the capability to compute the standard deviation of the predict Example 12.10 Forecast of Savings and Loan Margin (Regression Model Forecasts) You have been asked to forecast the savings and loan profit margin for a ye the percentage net revenue is 4.50 and there are 9,000 offices, using the s loan regression model. Data are stored in the file Savings and Loan