Answer Happy

Q. 5 IMPORTANT: For this question only use R as a calculator, for matrix multipli- cation etc. or for calculation of probabilities or quantiles. Do NOT use lm, aov or related functions. Consider the following dataset arising from a study to examine how two factors (A and B) affect a response variable Y. AHHH H L L L L B H H L L H H - L Y 18 15 16 12 10 14 8 5 a) Construct the design matrix for the full two-factor model we would fit for this dataset using a sum-to-zero coding of the factors. [4] b) Calculate the least squares estimates of the parameter vector ß in the linear model corresponding to the full two-factor model. c) Find the mean square for error in this model and hence give the standard errors of the estimates found in (b). [4] d) Construct a 95% confidence interval for the true mean response when both factors are at the Low (L) level based on the fitted full model. [4] e) Conduct a likelihood ratio test to examine if the effect of one factor on the response differs depending on the level of the other factor. [4]