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Discuss the definition of linear regression

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What is linear regression? Can you give an example?

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https://brainmass.com/statistics/descriptive-statistics/discuss-the-definition-of-linear-regression-595859

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Answer: linear regression is a tool to check the relationship between two variables. We use the word "linear" because we try to fit the data with a linear line. Hence, linear regression is used to the find the linear model ...

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The solution discusses the definition of linear regression and gives real examples.

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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.

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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