2. A randomized trial was mnduct.ed to investigate the relationship betwrwn a continuous y and four treatments A, B, C, and D. The sample size was n 21K), with olk;ervations in each of the four treatment grouTB. y the x I vector of Values, ordered so that the first 50 are for treatment group A, thc next 50 for B, then C, and finally D. Verify that this situation can rncxieled twing the regression model y X + e, where X is thc 200 x 4 (block) design matrix given by 1 1 1 1 o 1 o o o o 1 o o o o 1 where each (boldface) entry is a mlumn vector of length 50. After data collection, a researcher finds that the estimated rK*nxsion coefficients are (37.5, I I .5, I -O, 27.7), With standard errors 2.75, 3.89, 3.89, 3.89, and standard deviation 19.45, and that 0.02 0.02 0112 0.02 0.02 0.04 0.02 0.02 0.02 0.02 0.02 -0.02 0.02 0.02 0.04 (a) Interpret each of the four regrewsion parameters in 43 in terms of the expected responses of the groups. (b) What is an approximate 95% confidence interval for the mean difference in response twtween treatment, B and A (namely, the different-I'