Experience with a certain type of plastic indicates that a relation exists between the hardness (measured in Brinell units) of items molded from the plastic (Y) and the elapsed time since ter¬mination of the molding process (X). It is proposed to study this relation by means of regression analysis. A participant in the discussion objects, pointing out that the hardening of the plastic "is the result of a natural chemical process that doesn't leave anything to chance, so the relation must be mathematical and regression analysis is not appropriate." Evaluate this objection.
Refer to Problem. Four different elapsed times since termination of the molding process (treatments) are to be studied to see how they affect the hardness of a plastic. Sixteen batches (experimental units) are available for the study. Each treatment is to be assigned to four exper¬imental units selected at random. Use a table of random digits or a random number generator to make an appropriate randomization of assignments.
| i: |
1 |
2 |
3 |
.... |
14 |
15 |
16 |
| x1 |
16 |
16 |
16 |
.... |
40 |
40 |
40 |
| y1 |
199 |
205 |
196 |
.... |
248 |
253 |
246 |
Plastic hardness. Sixteen batches of the plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours, and Y is hardness in Brinell units. Assume that first-order regression model (1.1) is appropriate.
a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here?
b. Obtain a point estimate of the mean hardness when X = 40 hours.
c. Obtain a point estimate of the change in mean hardness when X increases by 1 hour.
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