In a study of weight gain, investigators randomly assigned 20 rats to two treatment groups: treatment 1 was a control; treatment 2 consisted of thiouracil. Weight, in grams, was measured at baseline (week 0) and at weeks 1, 2, 3, and 4. The objective of the homework is to compare the two treatments at a significance level of 0.05.

1.Assume that the mean weight changes linearly on time. Write out the regression model for mean weight over time.

2.Given the linearity assumption between time and outcome, test whether the rate of increase differs in the two groups using an unstructured covariance matrix. State the null and alternative hypotheses. Provide a result table and a conclusion.