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 H0: µY.x = β0 + β1x for some values β0, β1 (the true regression function is linear) versus Ha: H0 is not true (the true regression function is not linear) Suppose observations are made at x1, x2, ..., xc. Let Y11, Y12, ..., Y1n1 denote the nc observations when x = xc; ...; Yc1, Yc2, ..., Ycnc denote the nc observations when x = xc. With n = Σni (the total number of observations), SSE has n - 2 df. We break SSE into two pieces, SSPE (pure error) and SSLF (lack of fit), as follows:

The test statistic is F = MSLF/MSPE, and the corresponding P-value is the area under the right of f. The following data comes from the article "Changes in Growth Hormone tatus Related to Body Weight of Growing Cattle" (Growth, 1977: 241-247), with x 5 body weight and y 5 metabolic clearance rate/body weight.

a. Test H0 versus Ha at level .05 using the lack-of-fit test just described.
b. Does a scatterplot of the data suggest that the relationship between x and y is linear? How does this compare with the result of part (a)?

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SSLF-SSE SSPE x 110 110110 230 230 230 360 y235 198 173 174 149 124 115 x 360 360 360 505 505 505 505 y 130 102 95 122 112 98 96