In addition to the size variables, we also have information on several binary variables. The variable URBAN is used to indicate the facility's location. It is one if the facility is located in an urban environment and zero otherwise. The variable MCERT indicates whether the facility is Medicare certified. Most, but not all, nursing homes are certified to provide Medicarefunded care. There are three organizational structures for nursing homes. They are government (state, counties, municipalities), for-profit businesses, and tax-exempt organizations. Periodically, facilities may change ownership and, less frequently, ownership type. We create two binary variables PRO and TAXEXEMPT to denote for-profit business and tax-exempt organizations, respectively. Some nursing homes opt not to purchase private insurance coverage for their employees. Instead, such facilities directly provide insurance and pension benefits to their employees; this is referred to as " self-fundingof insurance." We use binary variable SELFFUNDINS to denote it.

You decide to examine the relationship between LOGTPY(y) and the explanatory variables. Use cost-report year 2001 data, and do the following analysis:

a. There are three levels of organizational structures, but we only use two binary variables (PRO and TAXEXEMPT). Explain why.

b. Run a one-way analysis of variance using TAXEXEMPT as the factor. Decide whether tax-exempt is an important factor in determining LOGTPY. State your null hypothesis, alternative hypothesis, and all components of the decision-making rule. Use a 5\% level of significance.

c. Run a one-way analysis of variance using MCERT as the factor. Decide whether location is an important factor in determining LOGTPY.
c(i). Provide a point estimate of LOGTPY for a nursing facility that is not Medicare certified.
c(ii). Provide a \(95 \%\) confidence interval for your point estimate in part c(i).

d. Run a regression model using the binary variables, URBAN, PRO, TAXEXEMPT, SELFFUNDINS, and MCERT. Find \(R^{2}\). Which variables are statistically significant?

e. Run a regression model using all explanatory variables, LOGNUMBED, LOGSQRFOOT, URBAN, PRO, TAXEXEMPT, SELFFUNDINS, and MCERT. Find \(R^{2}\). Which variables are statistically significant?
e(i). Calculate the partial correlation between LOGTPY and LOGSQRFOOT. Compare this to the correlation between LOGTPY and LOGSQRFOOT. Explain why the partial correlation is small.
e(ii). Compare the low level of the \(t\)-ratios (for testing the importance of individual regression coefficients) and the high level of the \(F\)-ratio (for testing model adequacy). Describe the seeming inconsistency, and provide an explanation for this inconsistency.