A completely randomized experiment was conducted to investigate the potential difference in four treatments A, B, C, and D. The sample size was n = 200, with 50 observations in each of the four treatment groups. Let y be the 200 1 vector of response values, ordered so that the first 50 entries are for treatment group A, the next 50 for B, then C, and finally D. The regression model y = X? + e was fit, where X is the 200 4 design matrix given by

|||l|-||| DDHD DI'DD HOOD and where each entry is a column vector of length 50. The estimated regression coefcients were ,6" = [3.3. 5'], E2, 53) = (37.5. 11.5, 1.0, 47.7). with standard errors 2.75, 3.89. 3.89, 3.39 and residual standard deviation Er.a = 19.45. a. Interpret each of the four regression parameters. As in, \"the intercept, u, is the mean response when ...\". 1:). Compute a 95% condence interval for the mean response in treatment group B? Hint: If v is a 4 x 1 column vector, then the variance of V'Q is equal to agv'{X'X)_1v. In our example1 0.02 0.02 0.02 0.02 0.02 0.04 0.02 0.02 0.02 0.02 0.04 0.02 0.02 0.02 0.02 0.04 (X'xri = c. Compute a 95% condence interval for the mean difference in response between treatment groups B and A that is, the difference ,uB HA