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    Correlation and regression analysis

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    City planners believe that larger cities are populated by older residents. To investigate the relationship, data on population and median age in ten large cities were collected.

    City Population (in millions) Median Age

    Chicago, IL 2.833 31.5
    Dallas, TX 1.233 30.5
    Houston, TX 2.144 30.9
    Los Angeles, CA 3.849 31.6
    New York, NY 8.214 34.2
    Philadelphia, PA 1.448 34.2
    Phoenix, AZ 1.513 30.7
    San Antonio, TX 1.297 31.7
    San Diego, CA 1.257 32.5
    San Jose, CA 0.930 32.6

    Plot this data on a scatter diagram with median age as the dependent variable.
    Find the correlation coefficient
    A regression analysis was performed and the resulting regression equation is Median age= 31.4+0.272 population. Interpret the meaning of the slope.
    Estimate the median age for a city of 2.5 million people.
    Here is a portion of the regression software output. What does it tell you?

    Predictor coef se coef t p
    Constant 31.3672 0.6158 50.94 0.000
    Population 0.2722 0.1901 1.43 0.190

    Test at the .10 significance level whether there is a significant relationship between these two variables.

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    Solution Summary

    Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.