Question

The homeownership rate in the U.S. was 60.6% in 2009. In order to determine if homeownership is linked with income, 2009 state-level data on the homeownership rate (Ownership in %) and median household income (Income in $) were collected. A portion of the data is shown in the accompanying table.

State	Ownership	Income
Alabama	65.8	35,500
Alaska	61.9	57,124
⋮	⋮	⋮
Wyoming	67.5	47,990

a-1. Estimate the model Ownership = β₀ + β₁Income + ε. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) [If you are using R to obtain the output, then first enter the following command at the prompt: options(scipen=10). This will ensure that the output is not in scientific notation.]

y^ = ____ + ____ Income

a-2. Interpret the model.

• For a $1000 increase in income, homeownership rate is predicted to decrease by 0.01%.

• For a $1000 increase in income, homeownership rate is predicted to decrease by 0.1%.

• For a $1000 increase in income, homeownership rate is predicted to decrease by 0.001%.

• For a $1000 increase in income, homeownership rate is predicted to decrease by 0.0001%.

b. What is the standard error of the estimate?

????

c. Interpret the coefficient of determination.

• 0.55% of the sample variation in y is explained by the estimated regression equation.

• 6.18% of the sample variation in x is explained by the estimated regression equation.

• 4.27% of the sample variation in x is explained by the estimated regression equation.

• 2.48% of the sample variation in y is explained by the estimated regression equation.

Data:

State	Ownership	Income
Alabama	65.8	35500
Alaska	61.9	57124
Arizona	62.2	41259
Arkansas	60.1	32058
California	52.5	51654
Colorado	62.9	51450
Connecticut	65.6	60371
Delaware	69.9	47634
District of Columbia	41.1	48661
Florida	63.9	41151
Georgia	60.4	38860
Hawaii	54.7	51169
Idaho	68.3	42298
Illinois	63.2	48390
Indiana	64.7	39825
Iowa	66.0	46241
Kansas	60.6	40237
Kentucky	63.7	38184
Louisiana	64.8	40953
Maine	67.0	43022
Maryland	64.7	59706
Massachusetts	60.2	54893
Michigan	67.2	41514
Minnesota	67.1	51610
Mississippi	65.9	30598
Missouri	65.4	44289
Montana	62.9	35957
Nebraska	63.9	45115
Nevada	57.0	46954
New Hampshire	70.7	59651
New Jersey	61.3	60297
New Mexico	62.0	39062
New York	49.5	45736
North Carolina	62.6	37426
North Dakota	59.8	45595
Ohio	62.9	41399
Oklahoma	62.8	41398
Oregon	62.0	44618
Pennsylvania	65.5	43692
Rhode Island	57.4	47154
South Carolina	66.3	36621
South Dakota	62.8	41346
Tennessee	63.2	36037
Texas	59.2	42995
Utah	68.4	54011
Vermont	67.9	47838
Virginia	64.5	56021
Washington	60.6	55912
West Virginia	70.0	36010
Wisconsin	64.2	46757
Wyoming	67.5	47990

Answer 1

Here I attach the R code # save the data as 'q' in a csv file

q
q=read.csv(file.choose())
fit=lm(q$Ownership~q$Income)
fit
summary(fit)

The fitted model becomes

Ownership = 65.1741 - 0.0000515 * Income

FOR a unit increase in income then the ownership is decreased by -0.0000155 unit

b) The standard error of the estimates is shown here

c) R squared value is 0.005516

0.55% of the sample variation in y is explained by the estimated regression equation.