Refer to the instrument calibration study example in Section 8.7. Suppose that three instruments (A, B, C) had been developed to identical specifications, that the regression functions relating gauge reading (Y) to actual pressure (X I) are second-order polynomials for each instrument, that the error variances are the same, and that the polynomial coefficients may differ from one instrument to the next. Let X 3 denote a second indicator variable, where X 3 = I if instrument C and 0 otherwise.

a. Expand regression model (8.58) to cover this situation.

b. State the alternatives. define the test statistic. and give the decision rule for each of the following tests when the level of significance is .0\: (1) test whether the second-orderre gression functions for the three instruments are identical, (2) test whether all three regression functions have the same intercept, (3) test whether both the linear and quadl1ltic effects are the same in all three regression functions.