Refer to Example 9.5. For the four levels of P, a linear trend can be represented as a contrast with coefficients ( - 3, - 1,1,3) and a quadratic trend as a contrast with coefficients (1, - 1, - 1,1)....

Refer to Example 9.5. For the four levels of P, a linear trend can be represented as a contrast with coefficients ( - 3, - 1,1,3) and a quadratic trend as a contrast with coefficients (1, - 1, - 1,1). Are these contrasts significant? If so, how do you interpret the trends? (The sample means for each cell are given in Table 9.14 and the MSE in Table 9.13.)

Example 9.5

This experiment concerns the search for some optimum levels of two fertilizer ingredients, nitrogen (N) and phosphorus (P). We know that there is likely to be an interaction between these two factors. The data are shown in Table 9.12. Notice that the levels of N and P are actually quantities of fertilizer per unit of area. That is, N and P are quantitative factors.