Q. 1 Suppose that a we have a continuous response variable Y and a single categorical variable X with values 1,...,p. It is of interest to test if the levels of the response vary among categories of the predictor. Define the indicator variables. Ej = { ŏ 1 0 if X = j otherwise for j = 1,..., p and consider fitting the linear model Y1E12 E2 ++pEp+€ a) State the assumptions of this model and give an interpretation for the parameters. b) Let X be the design matrix for this model. Give the form of X*X and its inverse and then use the results for multiple regression to obtain the least squares estimates for Y1,...,Yp. c) Give the variance of ; and the correlation between ; and fk when jk. d) State the null hypotheses that are being tested in the usual t-tests that are produced as part of the regression output and also the F test from the ANOVA for this model. Comment on whether these are appropriate tests.