This exercise considers nursing home data provided by the Wisconsin Department of Health and Family Services (DHFS).

Part 1: Use cost-report year 2000 data, and do the following analysis.

a. Correlations a(i). Calculate the correlation between TPY and LOGTPY. Comment on your result.

a(ii). Calculate the correlation among TPY, NUMBED, and SQRFOOT. Do these variables appear highly correlated?

a(iii). Calculate the correlation between TPY and NUMBED/10. Comment on your result.

b. Scatter plots. Plot TPY versus NUMBED and TPY versus SQRFOOT. Comment on the plots.

c. Basic linear regression.

c(i). Fit a basic linear regression model using TPY as the outcome variable and NUMBED as the explanatory variable. Summarize the fit by quoting the coefficient of determination, \(R^{2}\), and the \(t\)-statistic for NUMBED.

c(ii). Repeat c(i), using SQRFOOT instead of NUMBED. In terms of \(R^{2}\), which model fits better?
c(iii). Repeat c(i), using LOGTPY for the outcome variable and LOG(NUMBED) as the explanatory variable.
c(iv). Repeat c(iii) using LOGTPY for the outcome variable and LOG(SQRFOOT) as the explanatory variable.
Part 2: Fit the model in Part 1.c(1) using 2001 data. Are the patterns stable over time?