River Hills Hospital is interested in determining the effectiveness of a new drug for reducing the time required for complete recovery from knee surgery. Complete recovery is measured by a series of strength tests that compare the treated knee with the untreated knee. The drug was given in varying amounts to 18 patients over a 6-month period. For each patient the number of drug units, X, and the days for complete recovery, Y, are given by the following (x, y) data:
15, 532 121, 652 114, 482 111, 662 19, 462 14, 562 17, 532 121, 572 117, 492 114, 662 19, 542 17, 562 19, 532 121, 522 113, 492 114, 562 19, 592 14, 562
a. Compute the covariance.
b. Compute the correlation coefficient.
c. Briefly discuss the relationship between the number of drug units and the recovery time. What dosage might we recommend based on this initial analysis?