Question

In: Statistics and Probability

Using the data below, we would like to understand why some cities have a higher proportion...

Using the data below, we would like to understand why some cities have a higher proportion of creative-class workers than others. Under one theory, the proportion may be explained only by the city’s income, while in another theory, income along with population and cost-of-living are thought to explain the proportion..

  1. (a) Estimate a linear regression model for each theory and report your results.

  2. (b) Use an F test to choose one theory over another.

  3. (c) State the null hypothesis, the test statistic, and the specific distribution used (including the degrees of freedom) for your test in (b)

    Metro Area Population Income Cost-of-Living Index Creative Class (%)
    New Orleans-Metairie-Kenner, LA 1,024.68 46.459 99 29.6
    Rochester, NY 1,035.44 47.749 102 33.1
    Salt Lake City, UT 1,067.19 53.587 101 30.4
    Birmingham-Hoover, AL 1,089.88 44.534 93 30.6
    Buffalo-Niagara Falls, NY 1,137.52 42.831 127 29.7
    Oklahoma City, OK 1,173.63 42.036 92 31.6
    Hartford-West Hartford-East Hartford, CT 1,188.84 61.753 116 37.5
    Richmond, VA 1,196.41 53.416 106 31.1
    Louisville-Jefferson County, KY-IN 1,220.64 45.115 98 27.2
    Memphis, TN-MS-AR 1,268.33 42.092 97 26.7
    Jacksonville, FL 1,276.86 49.736 96 27.4
    Nashville-Davidson--Murfreesboro, TN 1,455.30 47.699 92 29.8
    Austin-Round Rock, TX 1,506.43 52.882 93 36.5
    Milwaukee-Waukesha-West Allis, WI 1,509.98 50.27 100 30.3
    Charlotte-Gastonia-Concord, NC-SC 1,582.63 50.367 92 30.9
    Providence-New Bedford-Fall River, RI-MA 1,612.99 51.797 126 30.1
    Virginia Beach-Norfolk-Newport News, VA-NC 1,647.40 52.976 105 29.3
    Indianapolis-Carmel, IN 1,669.37 50.841 98 29.4
    Columbus, OH 1,725.57 49.92 102 30.9
    Las Vegas-Paradise, NV 1,777.54 53.536 109 20.6
    San Jose-Sunnyvale-Santa Clara, CA 1,784.83 80.638 154 44.4
    San Antonio, TX 1,948.44 45.019 92 29.7
    Kansas City, MO-KS 1,966.79 52.359 94 32.1
    Orlando-Kissimmee, FL 1,984.86 48.934 107 27.3
    Sacramento--Arden-Arcade--Roseville, CA 2,067.12 56.953 122 34
    Cincinnati-Middletown, OH-KY-IN 2,105.01 50.306 93 30.3
    Cleveland-Elyria-Mentor, OH 2,114.16 45.925 101 30.4
    Portland-Vancouver-Beaverton, OR-WA 2,137.60 52.48 109 30.1
    Pittsburgh, PA 2,370.78 43.26 95 30.1
    Denver-Aurora, CO 2,408.62 54.994 102 34.5
    Baltimore-Towson, MD 2,658.41 61.01 121 33.9
    Tampa-St. Petersburg-Clearwater, FL 2,697.73 43.742 101 30.2
    St. Louis, MO-IL 2,793.99 49.765 100 30.1
    San Diego-Carlsbad-San Marcos, CA 2,941.45 59.591 131 32.8
    Minneapolis-St. Paul-Bloomington, MN-WI 3,175.04 62.223 99 35.2
    Seattle-Tacoma-Bellevue, WA 3,263.50 60.663 108 35
    Riverside-San Bernardino-Ontario, CA 4,026.14 53.243 121 24.2
    Phoenix-Mesa-Scottsdale, AZ 4,039.18 51.862 102 28.3
    San Francisco-Oakland-Fremont, CA 4,180.03 70.463 157 38.8
    Boston-Cambridge-Quincy, MA-NH 4,455.22 64.144 139 41.6
    Detroit-Warren-Livonia, MI 4,468.97 52.004 105 30.6
    Atlanta-Sandy Springs-Marietta, GA 5,134.87 55.552 98 33
    Washington-Arlington-Alexandria, DC-VA-MD-WV 5,288.67 78.978 133 43.7
    Miami-Fort Lauderdale-Miami Beach, FL 5,463.86 46.637 115 25.6
    Houston-Sugar Land-Baytown, TX 5,542.05 50.25 88 31.3
    Philadelphia-Camden-Wilmington, PA-NJ-DE-MD 5,826.74 55.593 116 34.9
    Dallas-Fort Worth-Arlington, TX 6,006.09 52.001 92 33
    Chicago-Naperville-Joliet, IL-IN-WI 9,506.86 57.008 106 32.3
    Los Angeles-Long Beach-Santa Ana, CA 12,950.13 55.516 131 32.9
    New York-Northern New Jersey-Long Island, NY-NJ-PA 18,818.54 59.281 148 35.6

Solutions

Expert Solution

Model 1

Proportion=f(Income)

a)Reg equation->Creative Class %=9.61129+0.4165Income

b) F stat=72.48856, Hence, the model is significant

c)H0:The coefficients of regression are equal to 0

Ha: Atleast one coefficient of regression is not equal to 0

test stat=72.48856, pvalue=0.000

Hence,reject H0 in favor of Ha and say the model is significant.

Model2

Proportion= f(Population, Income, Cost of Living)

Reg Eqn->y=10.12808+0.0000381Population+0.4326Income-0.38136Cost of living.

F test shows us that the model is significant.

Comparison:

The model 1 is found to be performing better because the Adj Rsq of model 1 is higher than the one in model 2

orchestra answered 1 year ago
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