In an experiment conducted at the National Institute of Environmental Health Sciences, the absorption (or uptake) of a chemical by a rat on one of two different diets, I or II, was known to be affected by the weight (or size) of the rat. A completely randomized design utilizing four rats on each diet was employed in the experiment, and the initial weight of each rat was recorded so that the diets could be compared after the researchers adjusted for the effect of initial weight. The data for the experiment are given in the following table.

a. Using the initial weight as a covariate, state the ANACOVA regression model for comparing the two diets (set Z = -1 if diet I is used and Z = 1 if diet II is used).
b. Use the computer results given next to determine the adjusted mean responses for each diet, controlling for initial weight.
c. Use the ANACOVA regression model defined in part (a) to test whether the two diets differ significantly.
d. Test whether the two diets differ significantly, completely ignoring the covariate. How do the two testing procedures compare?
e. Determine a 95% confidence interval for the true difference in the adjusted mean responses.

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Initial weight (X) Diet (Z) Response (Y) Il 14 13 4 615 1514 Regression of Response (Y) on Initial Weight (X) and Diet (Z) ANALYSIS OF VARIANCE Sum of Mean Source Model Error Corrected Total DFI Squares | Square | FValue | Pr>F 2 5.00000 2.50000 5 100000 0.20000 7 6.00000 12:50 0.0113 Root MSE Dependent Mean Coeff Var 0.44721 14.50000 3.08423 R-Square Adj R-Sq 0.8333 07667 PARAMETER ESTIMATES Parameter Standard Variable DF Estimate Error t ValuePr>It Type I SS Intercept 0,41833 31.08 $0001 387 0.0117 1 0.50000 0.15811 316 0.0250 1682 00000 3.00000 2 00000 13.00000 0500000.12910