In considering the analysis of covariance (ANCOVA) model for response Y , Factor A, and covariate x, partial output for the following four models was obtained: Response: y Df Sum Sq Mean Sq x 1 101.541 101.541 Residuals 12 21.387 1.782 Response: y Df Sum Sq Mean Sq A 2 6.529 3.2643 Residuals 11 116.400 10.5818 Model 1 Model 2 Response: y Df Sum Sq Mean Sq A 2 6.529 3.264 x 1 115.135 115.135 A:x 2 0.542 0.271 Residuals 8 0.723 0.090 Response: y Df Sum Sq Mean Sq A 2 6.529 3.264 x 1 115.135 115.135 Residuals 10 1.265 0.126 Model 3 Model 4 (a) If Yij represents the response for the jth observation in the ith group, express each of the models above. i. Model 1: Yij = ii. Model 2: Yij = iii. Model 3: Yij = iv. Model 4: Yij = (b) Using your notation above, state the hypotheses for the test of a Factor A effect. (c) Carry out the test above using = .05. Report the test statistic and conclusion