A certain drug is suspected of lowering blood pressure as a side effect. A clinical trial is conducted to investigate this suspicion. Thirty-two patients are randomized into drug and placebo groups (16 per group). Their initial and posttreatment systolic blood pressures (SBPs, measured in mm Hg) and their body sizes as measured by the quetelet index (QUET) are recorded.
The researchers conducted a multiple linear regression analysis to investigate whether the mean changes in SBP differ between the placebo and drug groups, controlling for initial SBP and QUET. The dependent variable is posttreatment SBP. One model under consideration involves three predictors: DRUG status, initial SBP, and QUET as main effects only (together with an intercept term). Suppose that a computer program that calculates unweighted least-squares estimates of the regression coefficients (e.g., the REG procedure in SAS) is used to fit this model.
a. Are the unweighted least-squares estimates of the regression coefficients identical to the ML estimates of these same coefficients for the above model? Explain briefly.
b. Assuming that the estimation procedure is ML, how would one carry out a Wald test for the effect of the DRUG status variable, controlling for initial SBP and QUET? (Specify the null hypothesis being tested, the form of the test statistic, and its large-sample distribution under the null hypothesis.)
c. Is the Wald test procedure described in part (b) equivalent to a partial f test obtained from unweighted least-squares estimation? Explain briefly.
d. How would one carry out an LR test for the effect of the DRUG status variable, controlling for initial SBP and QUET? (Specify the null hypothesis being tested, the form of the test statistic, and its large-sample distribution under the null hypothesis.)
e. Should one expect to obtain the same P-value for the LR test described in pan (d) as for the Wald test described in part (c)? Explain briefly.
f. Assuming ML estimation, state the formula for a large-sample 95% confidence interval for the effect of the DRUG status variable, controlling for initial SBP and QUET