Regression Statistics Multiple R 0.9069 R Square 0.8226 Adjusted R Square 0.8115 Standard Error 11.
Regression Statistics
Multiple R
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Regression Statistics Multiple R 0.9069 R Square 0.8226 Adjusted R Square 0.8115 Standard Error 11.
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0.9069
R Square
0.8226
Adjusted R Square
0.8115
Standard Error
11.2287
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
1
9355.71
9355.71
74.20
2.09742E-07
Residual
16
2017.36
126.08
Total
17
11373.09
Coefficients
Standard Error
t Stat
P-value
Intercept
-48.110
21.584
-2.228
0.0405
Income
2.332
0.270
8.614
2.1E-07
Dependent variable: average home price in $1000s
Independent variable: average household income in $1000s
Economists working for the federal government believed that the ability to pay for housing is an important determinant of housing prices. They collected data on average home prices and average household income from a sample of cities in the U.S. The regression results are presented above.
- How many cities were in the sample?
- Write the estimated regression equation.
- Is the intercept term significant at the 5 percent level?
- What does the intercept tell us about average home prices?
- Is the slope parameter significant at the 5 percent level?
- What does the slope parameter tell us about average home prices?
- Predict the average home price in a city where the average household income is $100,000.
- How well does the regression equation fit the sample data using
- the adjusted R square
- the ANOVA table
- What is the advantage of using the R square values to evaluate the equation’s goodness of fit?
- What is the advantage of using the F test to evaluate the equation’s goodness of fit?
- How comfortable would you be using this equation to predict housing prices in U.S. cities? Explain.
- Identify one other independent variable that might help explain average home prices in U.S. cities. Provide an explanation for including this variable. Do you expect this variable to have a positive or negative effect on home prices?
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