# Linear regression

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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

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##### Solution Summary

Interprets linear multiple regression output.

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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.

Y=-11.1091 + 2.0179 X1 + 0.1812 X2 - 0.3143 X3

Where

Y= mean price of housing unit

X1= Median income

X2= Average monthly rent of new units

X3= Vacancy rate

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

Y= mean price of housing unit

Intercept coefficient= -11.1091.

This is a constant in the intercept equation. This means that its value remains at -11.1091 for any combination of X1, X2 and X3.

The coefficient of X1(= Median income) is 2.0179

Thus for every unit rise in X1 (median income ) the mean price of housing unit (Y) ...

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