Consider the data set in Exercise 14.12 and answer the following questions.
(a) Both factors, copper and time, are quantitative in nature. As a result, a regression model may be of interest. Describe what might be an appropriate model using x1Â = copper content and x2Â = time. Fit the model to the data, showing regression coefficients and a t-test on each.
(b) Fit the model
and compare it to the one you chose in (a). Which
is more appropriate? Use 
 as a criterion.
Exercise 14.12Â In an experiment conducted in the Civil Engineering Department at Virginia Tech, growth of a certain type of algae in water was observed as a function of time and the dosage of copper added to the water. The data are as follows. Response is in units of algae.
Copper | Â | Time in Days |
 | 5 | 12 | 18 |
 1 | 0.30 | 0.37 | 0.25 |
0.34 | 0.36 | 0.23 |
0.32 | 0.35 | 0.24 |
 2 | 0.24 | 0.30 | 0.27 |
0.23 | 0.32 | 0.25 |
0.22 | 0.31 | 0.25 |
 3 | 0.20 | 0.30 | 0.27 |
0.28 | 0.31 | 0.29 |
0.24 | 0.30 | 0.25 |
(a) Do an analysis of variance and show the analysisof- variance table.
(b) Comment concerning whether the data are sufficient to show a time effect on algae concentration.
(c) Do the same for copper content. Does the level of copper impact algae concentration?
(d) Comment on the results of the test for interaction. How is the effect of copper content influenced by time?