To determine if the amount a family spends on their home depends on their income, a...

To determine if the amount a family spends on their home depends on their income, a social researcher collects the Median Household Income (in $1,000) and Median Home Prices (in $1,000) for 34 U.S. cities. The data appear in the HomePrice worksheet of the Simple Regression work sheet below..

a) Draw a scatter plot of the data. Does there appear to be a linear association between Household Income and Home Price?

b) Fit the simple linear regression model using Home Price as the dependent or Y variable and Household Income as the dependent or X variable. Is the model significant at  = 0.05?

c) What percentage of the variation in Home Price has been explained by the linear relationship with Household Income?

d) Provide the equation of the fit line. Interpret the parameter estimates in the context of the problem.

e) Use a hypothesis test to determine if the increase in house price is less than $4,000 for a $1,000 in household income, i.e., test the hypothesis null hypothesis Beta1 >or= to 4.0 versus the alternative Beta1 < 4.0 using alpha 0.05.

g) Provide a point prediction and a 95% confidence interval for the median house price for cities with a median household income of 100.

City	Income	Home
Alexandria, VA	59.976	290
Bernards Twp., NJ	112.435	279.9
Brentwood, TN	107.866	338.25
Bridgewater, NJ	93.484	316
Cary, NC	77.091	207
Centreville, VA	77.243	250
Chantilly, VA	94.864	320
Chesapeake, VA	53.758	150
Collierville, TN	85.716	230
Columbia, MD	77.033	199
Coral Springs, FL	62.632	218.5
Dranesville, VA	109.502	290
Dunwoody, GA	86.971	315
Ellicott City, MD	83.583	248
Franconia, VA	84.537	290
Gaithersburg, MD	64.944	220
Hoover, AL	64.431	170.45
Hunter Mill, VA	93.987	290
Lower Makefield Twp., PA	102.997	205
Manalapan Twp., NJ	91.245	410
Marlboro Twp., NJ	108.759	379.975
Matoaca, VA	65.149	135
Newtown, CT	97.723	358.5
North Andover, MA	79.169	342.5
Oakton, VA	90.824	341
Olney, MD	100.716	287.45
Peachtree City, GA	79.805	214.5
Ramapo, NY	64.954	330.875
Randolph Twp., NJ	104.121	444.5
Reston, VA	85.264	240
Roswell, GA	76.53	226.45
Sugarland Run, VA	103.35	278.25
Sully, VA	92.942	290
Wellington, FL	76.076	230

Expert Solution

orchestra answered 2 years ago

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