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 ni observations at xi contribute ni –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.
1
(So c = 4, n1 5 n2 = 3, n3 = n4 = 4.)
a. Test H0 versus Ha 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.)
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