You are given the accompanying response data on concentration of a chemical as a function of time. The six sets of observations Y1 to Y6 represent different environmental conditions.
Time (h) Y1 Y2 Y3 Y4 Y5 Y6
6 .38 .20 .34 .43 .10 .26
12 .74 .34 .69 .82 .16 .48
24 .84 .51 .74 .87 .18 .51
48 .70 .41 .62 .69 .19 .44
72 .43 .29 .43 .60 .15 .33
(a) Use cubic polynomial models to relate Y = concentration to X = time, where each environment is allowed to have its own intercept and response curve. Is the cubic term significant for any of the environments? [For the purposes of testing homogeneity in Part (c), retain the minimum-degree polynomial model that describes all responses.]
(b) Your knowledge of the process tells you that Y must be zero when X = 0. Test the composite null hypothesis that the six intercepts are zero using the model in Part (a) as the full model. What model do you adopt based on this test?
(c) Use the model determined from the test in Part (b) and test the homogeneity of the six response curves. State the conclusion of the test and give the model you have adopted at this stage.