The homeownership rate in the U.S. was 62.6% in 2009. In order to determine if h
ID: 3131411 • Letter: T
Question
The homeownership rate in the U.S. was 62.6% in 2009. In order to determine if homeownership is linked with income, 2009 state level data on homeownership rate (Ownership) and median household income (Income) were collected. The data is shown below. State Income Ownership Alabama $36,780 68.2% Alaska $58,404 63.3% Arizona $42,539 64.1% Arkansas $33,338 62.5% California $52,934 53.8% Colorado $52,730 64.5% Connecticut $61,651 67.0% Delaware $48,914 71.8% District of Columbia $49,941 42.2% Florida $42,431 65.9% Georgia $40,140 62.4% Hawaii $52,449 56.1% Idaho $43,578 70.3% Illinois $49,670 64.9% Indiana $41,105 66.8% Iowa $47,521 67.8% Kansas $41,517 62.6% Kentucky $39,464 65.9% Louisiana $42,233 66.8% Maine $44,302 69.0% Maryland $60,986 66.1% Massachusetts $56,173 61.6% Michigan $42,794 69.3% Minnesota $52,890 68.7% Mississippi $31,878 68.6% Missouri $45,569 67.3% Montana $37,237 65.1% Nebraska $46,395 65.7% Nevada $48,234 58.5% New Hampshire $60,931 72.2% New Jersey $61,577 62.6% New Mexico $40,342 64.0% New York $47,016 50.9% North Carolina $38,706 64.7% North Dakota $46,875 61.5% Ohio $42,679 64.8% Oklahoma $42,678 64.7% Oregon $45,898 63.8% Pennsylvania $44,972 67.4% Rhode Island $48,434 59.0% South Carolina $37,901 68.6% South Dakota $42,626 64.7% Tennessee $37,317 65.5% Texas $44,275 61.0% Utah $55,291 70.0% Vermont $49,118 69.8% Virginia $57,301 66.0% Washington $57,192 62.0% West Virginia $37,290 72.5% Wisconsin $48,037 66.0% Wyoming $49,270 69.3% PictureClick here for the Excel Data File a-1. Estimate the model: Ownership = 0 + 1Income + . (Negative values should be indicated by minus sign. Round your answers to 4 decimal places.) y-hat = + Income a-2. Interpret the model. For a $1,000 increase in income, homeownership rate is predicted to decrease by 0.10%. For a $1,000 increase in income, homeownership rate is predicted to increase by 0.10%. For a $1,000 increase in income, homeownership rate is predicted to decrease by 0.20%. For a $1,000 increase in income, homeownership rate is predicted to increase by 0.20%. b-1. What is the standard error of the estimate? (Round your answer to 2 decimal places.) se b-2. Does this model seem promising? Yes, since se / y-bar is more than 0.10. Yes, since se / y-bar is less than 0.10. No, since se / y-bar is more than 0.10. No, since se / y-bar is less than 0.10. c. Interpret the coefficient of determination. 1.66% of the sample variation in y is explained by the estimated regression equation. 1.66% of the sample variation in x is explained by the estimated regression equation. 2.66% of the sample variation in x is explained by the estimated regression equation. 0.66% of the sample variation in y is explained by the estimated regression equation. rev: 03_14_2013_QC_27911, 03_22_2013_QC_27911, 09_01_2013_QC_34001, 09_27_2013_QC_34001, 04_12_2014_QC_47852
Explanation / Answer
a-1.
Estimate the model: Ownership = 0 + 1Income + . (Negative values should be indicated by minus sign. Round your answers to 4 decimal places.)
y-hat = 68.9773 + (0.00009247) Income
a-2. Interpret the model.
A. For a $1,000 increase in income, homeownership rate is predicted to decrease by 0.10%.
B. For a $1,000 increase in income, homeownership rate is predicted to increase by 0.10%.
C. For a $1,000 increase in income, homeownership rate is predicted to decrease by 0.20%.
D. For a $1,000 increase in income, homeownership rate is predicted to increase by 0.20%.
b-1.
What is the standard error of the estimate? (Round your answer to 2 decimal places.)
se
= 5.38
b-2.
se/ybar =5.38/64.66=0.08
Does this model seem promising?
A. Yes, since se / y-bar is more than 0.10.
B. Yes, since se / y-bar is less than 0.10.
C. No, since se / y-bar is more than 0.10.
D. No, since se / y-bar is less than 0.10.
c. Interpret the coefficient of determination.
A. 1.66% of the sample variation in y is explained by the estimated
regression equation.
B. 1.66% of the sample variation in x is explained by the estimated regression equation.
C. 2.66% of the sample variation in x is explained by the estimated regression equation.
D. 0.66% of the sample variation in y is explained by the estimated regression equation.
Regression Analysis
r²
0.0166
n
51
r
-0.129
k
1
Std. Error
5.383
Dep. Var.
Ownership
ANOVA table
Source
SS
df
MS
F
p-value
Regression
24.02724445
1
24.02724445
0.83
.3670
Residual
1,420.01197124
49
28.97983615
Total
1,444.03921569
50
Regression output
confidence interval
variables
coefficients
std. error
t (df=49)
p-value
95% lower
95% upper
Intercept
68.9773
4.7980
14.376
3.31E-19
59.3354
78.6193
Income
-0.00009247
0.00010156
-0.911
.3670
-0.00029656
0.00011161
a-1.
Estimate the model: Ownership = 0 + 1Income + . (Negative values should be indicated by minus sign. Round your answers to 4 decimal places.)
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