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Analysis of Infection Risk in Hospitals: A Multiple Regression Approach Using Stepwise and Subset Regression Methods

An analysis of infection risk in hospitals using multiple regression methods for risk prediction.

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    Analysis of Infection Risk in Hospitals: A Multiple Regression Approach Using Stepwise and Subset Regression Methods For this assignment use the data set senic .xls x . This data set consists of a random sample of 113 hospitals. The objective is to study the infection risk and what factors influence it. The variables from the data set are: Variable Name Description Identification number 1 - 113 Length of stay Average length of stay in hospital (in days) Age Average age of patients (in years) Infection risk Average estimated probability of acquiring infection in hospital (in percent) Routing culturing ratio Ratio of number of cultures performed to number of patients without signs or symptoms of pneumonia, times 100 Routine chest X - ray ratio Ratio of number of X - rays performed to number of patients without signs or symptoms of pneumonia, times 100 Number of beds Average number of beds in hospital Medical school affiliation 0 = Yes, 1 = No Average daily census Average number of patients in hospital per day Number of nurses Average number of full - time licensed practical nurses Available facilities and services Percent of 35 potential facilities and services that are provided by the hospital The goal is to fit the best multiple regression model to the response (infection risk). Do an analysis using the first 108 observations. Use the stepwise regression method to see which model is the best. Repeat using subset regression. Do they agree? Are there any outliers in the data? Look for x - outliers, y - outliers, and high - influence points. Come up with one model that you think best describes the data and can be used for future predictions. Show the residual plot for this one. Does the model seem appropriate? Use this model to predict (using prediction interval) y for the last 5 observations of the data and see if the model is doing well.

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    Solution: First we tried to find whether there are any outliers in the data considering all variables and first 108 observations. There are few outliers as shown by the below tables with classification of outliers: Also the same can be seen from the below box plots: stay age culturing xray beds school census nurses facilities risk count 108 108 108 108 108 108 108 108 108 108 empirical rule mean - 1s 7.8135 48.660 5.436 61.950 64.18 0.51 44.87 34.92 28.045 2.981 mean + 1s 11.3330 57.627 25.569 100.732 432.73 1.21 329.57 307.62 57.927 5.670 percent in interval (68.26%) 75.9% 75.9% 78.7% 64.8% 79.6% 86.1% 75.9% 79.6% 72.2% 69.4% mean - 2s 6.0538 44.176 -4.630 42.558 -120.10 0.17 -97.48 -101.43 13.104 1.637 mean + 2s 13.0927 62.111 35.636 120.123 617.01 1.56 471.93 443.97 72.868 7.015 percent in interval (95.44%) 97.2% 93.5% 95.4% 95.4% 94.4% 86.1% 95.4% 94.4% 95.4% 93.5% mean - 3s 4.2940 39.692 -14.697 23.167 -304.38 -0.18 -239.84 -237.78 -1.837 0.292 mean + 3s 14.8525 66.595 45.702 139.514 801.28 1.90 614.28 580.31 87.809 8.359 percent in interval (99.73%) 99.1% 99.1% 97.2% 100.0% 98.1% 100.0% 100.0% 98.1% 100.0% 100.0% low extremes 0 0 0 0 0 0 0 0 0 0 low outliers 0 2 0 0 0 0 0 0 0 3 high outliers 2 3 4 1 6 0 5 6 0 3 high extremes 1 0 1 0 0 0 0 1 0 0 5 7 9 11 13 15 17 19 21 stay BoxPlot 30 35 40 45 50 55 60 65 70 75 age BoxPlot

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    0 10 20 30 40 50 60 70 culturing BoxPlot 0 20 40 60 80 100 120 140 160 180 xray BoxPlot 0 200 400 600 800 1000 beds BoxPlot 0 0.2 0.4 0.6 0.8 1 1.2 school BoxPlot

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