The primary objective of the Study on the Efficacy of Nosocomial Infection Control (SENIC Project) was to determine whether infection surveillance and control programs have reduced the rates of nosocomial (hospital-acquired) infection in United States hospitals. This data set consists of a random sample of 113 hospitals from a study done between 1975-1976. Each line of the data set has an identification number and provides information on 11 other variables for a single hospital.

Use this data set to answer questions 1,2 , and 3 . The data can be found on the course website in SPSS and Excel formats.

1. For predicting the length of stay, it has been decided to include age and infection risk as predictor variables. It is believed that a 3 predictor model is appropriate. The candidates for the third predictor are culturing ratio, average daily census, number of nurses, and available facilities.

1. For each, calculate the coefficient of partial determination given that age and infection risk are already in the model. Using this result, determine which predictor should be added to the model.
2. Conduct a partial \(F\) test to determine if the variable added is significant at \(\alpha=0.05\). State the null hypothesis, alternative, decision rule, and conclusion.

2. It is desired to predict length of stay \((Y)\) based on a potential pool of predictors which includes all variables except identification number, medical school affiliation, and region. It is believed that a multiple regression model with \(\log _{10} Y\) as the response is appropriate.

1. Obtain the best model using forward stepwise, forward selection, and backward elimination procedures. Are the models different?
2. Obtain the three best models according to \(R_{a d j}^{2}\) and Mallow's \(C_{P}\) criterion. Are the models different?
3. State the final model and explain why it should be chosen over the rest.

3. Infection risk is to be predicted using length of stay and medical school affiliation.

1. Obtain a sample regression equation without interaction.
2. Estimate the effect of medical school affiliation on infection risk using a 98 percent confidence interval. Give a brief interpretation of the interval.
3. It has been suggested that medical school affiliation may interact with the length of stay. Add the appropriate interaction term, fit the revised regression model, then test whether the interaction term is significant at \(\alpha=0.1\). State the null hypothesis, alternative, decision rule, and conclusion.

4. Suppose you are the senior statistical analyst for a consulting firm. You conduct a hypothesis test and obtain a \(p\) -value. Upon reporting the result to your client, he asks, "what is a \(p\) -value?" How do you answer this question knowing that your client has little or no experience with statistics.

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Solution: The downloadable solution consists of 13 pages, 990 words and 16 charts.
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