When antibiotics are given to fight infections, they must be administered in such a way that the blood level of the antibiotic is high enough to kill the bacteria causing the infection. Because...

When antibiotics are given to fight infections, they must be administered in such a way that the blood level of the antibiotic is high enough to kill the bacteria causing the infection. Because antibiotics are usually given periodically, the blood levels change over time, rising after an injection, then falling back down until the next injection. The interval between injections of recently introduced antibiotics has been determined by extrapolating from studies of older antibiotics. To update the knowledge of dosing schedules, Vogelman and coworkers* studied the effect of different dosing intervals on the effectiveness of several newer antibiotics against a variety of bacteria in mice. One trial was the effectiveness of gentamicin against the bacterium Escherichia coli. As part of their assessment of the drug, they evaluated the effectiveness of gentamicin in killing E. coli as a function of the percentage of time the blood level of the drug remained above the effective level (the so-called mean inhibitory concentration M). Effectiveness was evaluated in terms of the number of bacterial colonies C that could be grown from the infected mice after treatment with a given dosing schedule (known as colony-forming units, CFU); the lower the value of C, the more efficacious the antibiotic. Table D-3, Appendix D, contains C and M values for two different dosing intervals: those with a code of 0 were obtained with dosing intervals of every 1 to 4 hours, whereas those with a code of 1 were obtained with dosing intervals of 6 to 12 hours. Analyze C as a function of M for the data obtained using 1- to 4-hour dosing intervals. Include the 95 percent confidence intervals for parameter estimates in your answer. Does this regression equation provide a significant fit to the data?

Table D-3