Linear Regression

A report on housing in metropolitan areas suggests a regression model
relating the mean price of a housing unit to several factors, such as
median income, average monthly rent of new units and vacancy rate.  A
sample of 25 cities was taken.

a) Write down the multiple regression equation.

b) Interpret the meaning of the intercept and regression coefficients.

c) Discuss the strength of the multiple regression model on the basis of
the computer output. Did the estimated regression equation provide a
good fit?

d) Discuss the significance of each of the regression coefficients.  

e) How would you improve the model given a chance and taking into
account tests for significance? What other independent variables you
might include in the model?

 

SUMMARY OUTPUT

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Regression Statistics

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Multiple R  0.9165

R Square  0.8399

Adjusted R Square  0.8171

Standard Error  6.4514

Observations  25

ANOVA

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  df  SS  MS  F  Significance F

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Regression  3  4586.2701  1528.7567  36.730  0.0001

Residual  21  874.0395  41.6209

Total  24  5460.3096

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Coefficients  Standard Error  T-Stat  P-value

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Intercept  -11.1091  32.7302  -0.339  0.7377

INCOME  2.0179  0.7323  2.756  0.0118

RENT  0.1812  0.0691  2.623  0.0159

VACANT  -0.3143  0.0599  -0.524  0.6056