Question

Please asnwer c (iii) and d only. Thank you in advance.

5.16. In an experiment to study the effect of temperature (x) on the yield of a chemical reaction (y), 30 experimental runs were conducted. The level of temperature was carefully controlled at each of five levels, coded as x = -2, -1, 0, 1, 2. Two catalysts were used. For each catalyst three runs were taken at each level of temperature, and the yield was measured. The model y=Bo+Bix + B2x +B3z +e, E~N(0, a2) was considered, where z 0 for catalyst 1 and z 1 for catalyst 2 a. Carefully interpret the parameter B3 in this model. b. The model was fit to the data and the output is summarized below. The residual sum of squares is 25.05, and Standard Error Parameter Estimate 0.33 29.83 Bo 0.13 0.95 0.41 0.11 0.36 -0.32 B3 Is there any evidence of a difference in the two catalysts? Find a 95% confidence interval for B2. c. We also know that 0.114 0 0.023 -0.067 0 0 0 0.017 0 (X'X)- -0.023 0 0.012 -0.067 0 0.133 0 i. Explain why B1 and B3 are independent random variables. ii. Find a 95% confidence interval for the expected yield when the standard temperature (x = 0) and catalyst 2 are used. iii. Find a 95% prediction interval for the yield of a new experiment run under standard temperature (x 0) and with catalyst 2. d. It was thought that the effects of temperature differ for the two catalysts. Accordingly, the model =Bo+B1xPrx+B3z+ B4zx +Bszx E 2 was fit to the data, leading to a residual sum of squares of 19.70. Is there any evidence that the effects of temperature differ for the two catalysts?

Answer 1

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