A medical center is concerned about the length of stay, measured in days, of its patients who undergo joint-replacement procedures.
To this end, it has asked you to compare the length of stay of patients who received a ceramic implant (coded as 1 in the predictor variable Ceramic) to the length of stay of patients who received a conventional implant (coded as 0 in the predictor variable Ceramic).
After drawing a small random sample of the patients who received a joint replacement at this medical center, you ran the following regression model:
Length of Stay Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 4.34 0.25 17.35 0.00 3.85 4.83
Ceramic -0.81 0.26 -3.07 0.00 -1.33 -0.29
1.
Use the regression results from the table shown above to write out the estimated equation.
2.
What does the number 4.34 in the Coefficients column measure?
3.
What does the number -0.81 in the Coefficients column measure?
4.
Was there a difference in predicted length of stay between the two groups in the small random sample of the patients who received a joint replacement at this medical center?
That is, was the estimated coefficient of Ceramic different from zero numerically?
Explain your answer.
5.
At a 5% level of statistical significance, do you infer that there was a difference in length of stay between the two groups in the population of all patients who received a joint replacement at this medical center?
That is, was the estimated coefficient of Ceramic different from zero statistically?
Explain your answer.
6.
Compute the predicted length of stay if 60% of patients receive a ceramic implant.
7.
Compute the change in predicted length of stay when the percentage of patients receiving a ceramic implant increases from 60% to 100%.
