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In: Statistics and Probability

The homeownership rate in the U.S. was 64.1% in 2009. In order to determine if homeownership...

The homeownership rate in the U.S. was 64.1% 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	70.0	37770
Alaska	64.4	59394
Arizona	65.6	43529
Arkansas	64.4	34328
California	54.8	53924
Colorado	65.7	53720
Connecticut	68.1	62641
Delaware	73.3	49904
District of Columbia	43.0	50931
Florida	67.5	43421
Georgia	64.0	41130
Hawaii	57.1	53439
Idaho	71.9	44568
Illinois	66.2	50660
Indiana	68.4	42095
Iowa	69.2	48511
Kansas	64.1	42507
Kentucky	67.5	40454
Louisiana	68.4	43223
Maine	70.6	45292
Maryland	67.2	61976
Massachusetts	62.7	57163
Michigan	70.9	43784
Minnesota	70.0	53880
Mississippi	70.7	32868
Missouri	68.7	46559
Montana	66.8	38227
Nebraska	67.1	47385
Nevada	59.7	49224
New Hampshire	73.4	61921
New Jersey	63.7	62567
New Mexico	65.6	41332
New York	52.0	48006
North Carolina	66.4	39696
North Dakota	62.8	47865
Ohio	66.3	43669
Oklahoma	66.2	43668
Oregon	65.1	46888
Pennsylvania	68.9	45962
Rhode Island	60.2	49424
South Carolina	70.4	38891
South Dakota	66.2	43616
Tennessee	67.2	38307
Texas	62.4	45265
Utah	71.3	56281
Vermont	71.2	50108
Virginia	67.2	58291
Washington	63.1	58182
West Virginia	74.4	38280
Wisconsin	67.4	49027
Wyoming	70.7	50260

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.]

yˆy^ = + 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? (Round your answer to 2 decimal places.)

c. Interpret the coefficient of determination.

2.79% 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.

Expert Solution

I have used R code to build simple linear regression model.

(a-1) SIMPLE LINEAR REGRESSION R OUTPUT:

ESTIMATED SIMPLE LINEAR REGRESSION EQUATION:

The estimated simple linear regression equation is given by,

where

is the predicted dependent variable

is the intercept

is the slope coefficient of variable "Income"

is the independent variable "Income".

(a-2) MODEL INTERPRETATION:

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

(b) STANDARD ERROR OF ESTIMATE:

The standard error of estimate is .

(c) COEFFICIENT OF DETERMINATION:

The coefficient of determination . Thus % of the sample variation in y is explained by the estimated regression equation.

orchestra answered 2 years ago

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