6. Seven observations of a response variable Y, two treatments A and B, and a covariate X are given as follows. A 1 2 2 2 B 2 2 2 X -1 0 2 3 4 Y -1.0 0.8 -0.9 1.7 2.0 2.3 1.8 (a) State the regression model equivalent to covariance model. Fit this full model and report the least squares estimates of the regression coefficients and SSE. It is given that 7 15 -3 -15 - 6 35 3 18 6 (b) State the reduced regression models for testing for interaction effects. Fit the reduced regression models and report the least squares estimates of the regression coefficients and SSE. It is given that 7 4 -17 -74 -23 35 5 18 3 84 14 21 (c) Test for interaction effects; use a - .05. State the alternatives, decision rule, and conclusion. What is the p-value of the test? (d) Consider an ANCOVA model without interaction effects, test for A and B main effects, respectively; use a= .05. State the alternatives, decision rule, and conclusion. It is given that 7 4 31 28 35 0 84 4 49 7 4 68 -18 -77 35 -2 21 42 98