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    Multiple Regression Analysis

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    1. Maria Gomez, a research analyst in the state department of health, has undertaken a study of the possible consequences of overbuilding hospital facilities. One aspect of the study has been to calculate the effect of available hospital beds on length of patient stays. She has gathered data from 50 areas in the US; including mean duration of hospital stays per patient (measured in days), percent covered by private health insurance programs (i.e., non-HMO), percent covered by HMO health insurance programs, and median income level of the area. She runs a series of regression analyzes. Answer the questions following each of these regression runs. [Note: "b" = regular regression coefficient and "beta' = standardized regression coefficient]

    Y= Mean duration of hospital stays per patient (in days)
    X1 = Percent patients over 65 years of age
    X2 = Percent covered by private health insurance (non HMO)
    X3 = Percent covered by HMO health insurance
    X4 = Median annual family income of the area
    X5 = Number of hospital beds available per 1,000 population

    R = .721
    R Squared = .520

    Independent Variable b beta t
    X1 .50 .36 2.38
    X2 .23 .21 1.53
    X3 -.15 -.25 -2.14
    X4 .01 .10 0.01
    X5 2.0 .42 3.17

    [Assume percentages are coded without decimals, i.e., 33 percent is coded as 33]
    [Assume dollars are coded in hundreds. i.e., a median income of $8,000 is coded as 80]

    a. What variable has the biggest impact on Y?
    b. Which variables have statistical significance at p<.05?
    c. How much variation in Y is explained by these variables?
    d. What is the effect on patient stays if you increase hospital beds by one per 1,000 population?
    e. Write a paragraph summarizing the findings of this regression as might do in a report. Remember the main purpose of the research was to investigate the influence of available hospital beds on duration of patient stays.

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    Solution Summary

    The solution gives the step by step procedure for the calculation of multiple regression analysis of health data.