Exercise 14 presented data on body weight x and metabolic clearance rate/body weight y....

Exercise 14 presented data on body weight x and metabolic clearance rate/body weight y. Consider the following intrinsically linear functions for specifying the relationship between the two variables: (a) ln(y) versus x, (b) ln(y) versus ln(x), (c) y versus ln(x), (d) y versus 1/x, and (e) ln(y) versus 1/x. Use any appropriate diagnostic plots and analyses to decide which of these functions you would select to specify a probabilistic model. Explain your reasoning.

Reference exercise 14

If there is at least one x value at which more than one observation has been made, there is a formal test procedure for testing for some valuesβ₀,β₁ (the true regression function is linear) versus

H _a: H₀ is not true (the true regression function is not linear)

The n_i observations at xi contribute n_i –1 df to SSPE, so the number of degrees of freedom for SSPE is , and the degrees of freedom for SSLF

Test statistic:

Rejection region:

The following data comes from the article “Changes in Growth Hormone Status Related to Body Weight of Growing Cattle” (Growth, 1977: 241–247), with x = body weight and y = metabolic clearance rate/body weight.

(So c = 4, n1 5 n2 = 3, n3 = n4 = 4.)

a. Test H₀ versus H_a at level .05 using the lack-of-fit test just described.

b. Does a scatter plot of the data suggest that the relationship between x and y is linear? How does this compare with the result of part (a)? (A nonlinear regression function was used in the article.)