Cost-of-living indices are often used to measure the desirability of living in a particular geographical area. The data in the following table give a composite index and six component indices for several urban areas in the United States.
a. Build a linear model to predict the composite index based on the component indices. Evaluate the model in terms of overall goodness-of-fit. Evaluate the results for each regression parameter: Are the signs appropriate? Are the values different from zero?
b. Can you improve the model in (a) by removing or transforming one or more of the explanatory variables from the regression? If so, compare the advantages and disadvantages of the resulting regression to the one in (a).

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Urban area Birmingham, AL Cullman County, AL Decatur-Hartselle, AL Gasden, AL Huntsville, AL Marshall County, AL Mobile, AL Montgomery, AL Anchorage, AK Fairbanks, AK Juneau, AK Composite index 98.4 95.0 94.7 93.2 95.6 91.2 96.0 100.8 123.0 128.7 140.0 Grocery items 97.7 98.9 95.8 101.5 94.1 101.5 100.5 98.5 120.1 118.4 122.6 Housing Utilities Transportation 94.8 95.5 88.1 97.4 87.4 102.2 79.1 87.0 85.1 101.9 84.6 82.0 94.9 132.3 134.0 164.2 102.6 98.7 89.8 101.8 88.6 97.6 105.2 102.0 88.0 166.7 157.2 87.3 102.6 99.3 112.0 119.6 117.2 Health care 98.3 87.1 96.3 87.4 99.3 83.1 91.1 94.1 170.1 168.1 165.5 Miscellaneous goods and services 101.5 98.9 99.3 101.7 104.6 92.9 102.6 108.3 119.3 115.3 125.2