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..

(a) Estimate a linear regression model for each theory and report your results.
(b) Use an F test to choose one theory over another.

(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

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 3 years ago

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