In Problem 3, the independent variable of interest, copper ion concentration, is an interval-scaled variable.
a. Treating copper ion concentration as a five-level categorical predictor (as in the randomized-blocks analysis) corresponds to including a collection of polynomial terms for copper ion concentration (e.g., X, X2,. . .) in the model. What is the highest order power of X allowed?
b. State, in terms of k levels of a predictor, a general principle based on the example in part (a).
c. State the expansion of the regression model given in Problem 3(b) that encompasses the polynomial terms discussed in part (a).
d. Use a computer program to fit the model stated in part (c). Center X by subtracting 0.330. (Why?) Provide estimated regression coefficients.
e. Provide a multiple partial F test comparing the model in parts (b) and (g) of Problem 3 to the one fitted here; the latter is equivalent to the model considered in part (d) of Problem 3.