Question: Emergency room (ER) overcrowding is a common problem in U.S. hospitals and inappropriate ER usage is an expensive, inefficient use of health care resources. In 2006 Massachusetts enacted a health care initiative that included near-universal health care insurance coverage. However, recent studies indicate that ER overcrowding in Massachusetts has gotten worse, not better. Information from the 50 US states plus the District of Columbia (DC) was studied to identify the factors associated with the rate of ER visits. Data on ER visits per year per 1,000 inhabitants, health insurance coverage (%), poverty rate (%), unemployment rate (%), non-citizenship status (%), hospital expenses per inpatient day, teen birth rate per 1,000 for ages 15-19, adults who are overweight/obese (%) and who smoke (%) were collected for each of these 51 areas. The data are given in a file on the class website under the filename ERVisits.xls. The only responses below that need to be submitted as homework are underlined .

1. Investigate the variables individually . Using Stata prepare histograms for each of the variables individually. Summarize your observations from all these histograms in 2-3 sentences . Note that the response variable "ervisits" has a single large value associated with DC. Print out a histogram of this response variable. Do not transform any of these variables.
2. Run a multiple linear regression using the ER visit rate per year as the response variable (Y) and all the other variables as predictor variables. Print out the regression results table from this multiple regression analysis and summarize your observations in 2-3 sentences.
3. Conduct a backward regression analysis. Using the multiple regression analysis result above (that included all 8 predictor variables) identify the "least significant" predictor variable (smallest | t |- statistic and largest P-value), delete that variable and rerun the multiple regression analysis with the remaining 7 predictor variables. Using the previous multiple regression analysis (that included 7 predictor variables) identify the "least significant" predictor variable, delete that variable and rerun the multiple regression analysis with the remaining 6 predictor variables. Continue this step-down process until all the remaining predictor variables are significant (P < 0.05). This is your final model. Print out the regression results table corresponding to each step above and summarize your observations in 2-3 sentences, commenting on what happened to the "uninsured rate" and the implications for the Massachusetts health care insurance initiative of 2006." [Checkpoint: your final model has 5 predictor variables and an R2 of 70.45%]
4. Interpret the results of your final regression model. Write down the formula of the final multiple regression model .

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