Metabolic rate and body mass for caterpillars. Use the output provided in Example 28.10 (page 28-20) to answer the questions below.

(a) Find a 95% confidence interval for the slope parameter ß for caterpillars during Stage 4.

(b) If you were asked to report a confidence interval for the slope parameter ß for caterpillars during Stage 5, would you report the same interval that you calculated in part (a)? Explain why or why not.

(c) Are the values ß=2/3 and ß=3/4 contained in your confidence interval from part (a)?

(d) How does your confidence interval in part (a) compare with the confidence interval you computed in part (d) of Exercise 28.8?

(e) Use appropriate values from the output to test the claim that ß=2/3.

 (f) Use appropriate values from the output to test the claim that ß=3/4.

Exercise 28.8:

Metabolic rate and body mass for caterpillars. Does the general relationship between metabolic rate and body mass described in Example 28.10 hold for tobacco hornworm caterpillars? The Minitab output (see page 28-24) was obtained by regressing the response variable y =log(MR) on x₁ =log(BM) for the data.

(a) Use the regression equation from the Minitab output to estimate ∝ and ß in the general relationship MR =∝(BM) , which is the same as µ_y =log(∝) + ßx₁. The predicted model is  =a + bx₁, so that a estimates log(∝) and b estimates in the original model.

(b) Residual plots for the linear regression model µ_y = α+ ßx₁ are shown on page 28-25. Do you think that the conditions for inference are satisfied?

(c) Identify the percent of variation in y that is explained by using linear regression with the explanatory variable x₁.

(d) Even if you noticed some departures from the conditions for inference, the researchers were interested in making inferences because this model is well known in the field and has been used for a variety of different insects and animals. Find a 95% confidence interval for the slope parameter .

(e) Are the values ß=2/3 and ß=3/4 contained in your confidence interval?

(f) Use appropriate values from the Minitab output to test the claim that ß=2/3.

(g) Use appropriate values from the Minitab output to test the claim that ß=3/4.