Using the data in the Excel file Home Market Value, develop a multiple linear re
ID: 3047321 • Letter: U
Question
Using the data in the Excel file Home Market Value, develop a multiple linear regression model for estimating the market value as a function of both the age and size of the house. Predict the value of a house that is 30 years old and has 1,800 square feet, and one that is 5 years old and has 2,800 square feet.
1. Identify the dependent variable (Y)
2. Identify the independent variables (Xs)
3. Check for multicollinearity among the Xs: Data>Data Analysis>Correlation -> take
action as needed
4. Run Regression: Data>Data Analysis>Regression, including residuals, standardized
residuals, and residual plots
5. Evaluate residuals for obvious non-random patterns and outliers -> take action as
needed
6. Check p-values for X coefficients -> take action as needed
7. Check the significance of the overall model based upon the ANOVA
significance F (p-value) – take action as needed
8. Interpret the adjusted R Square value
9. Write out the prediction equation to include the y=f(x) regression coefficient
and perform any predictions as required. Please note that the regression coefficient
is the slope of the line of the regression equation.
10. Tell the story. Explain the meaning of the analysis using everyday words.
Home Market Value House Age Square Feet Market Value 33 1,812 $90,000.00 32 1,914 $104,400.00 32 1,842 $93,300.00 33 1,812 $91,000.00 32 1,836 $101,900.00 33 2,028 $108,500.00 32 1,732 $87,600.00 33 1,850 $96,000.00 32 1,791 $89,200.00 33 1,666 $88,400.00 32 1,852 $100,800.00 32 1,620 $96,700.00 32 1,692 $87,500.00 32 2,372 $114,000.00 32 2,372 $113,200.00 33 1,666 $87,500.00 32 2,123 $116,100.00 32 1,620 $94,700.00 32 1,731 $86,400.00 32 1,666 $87,100.00 28 1,520 $83,400.00 27 1,484 $79,800.00 28 1,588 $81,500.00 28 1,598 $87,100.00 28 1,484 $82,600.00 28 1,484 $78,800.00 28 1,520 $87,600.00 27 1,701 $94,200.00 28 1,484 $82,000.00 28 1,468 $88,100.00 28 1,520 $88,100.00 27 1,520 $88,600.00 27 1,484 $76,600.00 28 1,520 $84,400.00 27 1,668 $90,900.00 28 1,588 $81,000.00 28 1,784 $91,300.00 27 1,484 $81,300.00 27 1,520 $100,700.00 28 1,520 $87,200.00 27 1,684 $96,700.00 27 1,581 $120,700.00Explanation / Answer
Market Value =
Age(-825.16) + size(40.91)+47331.38
is a multiple linear regression model for estimating the market value as a function of both the age and size of the house.
Market value of a house that is 30 years old and has 1,800 square feet = 30*(-825.16) + 1800*(40.91)+47331.38 = 96214.58
and one that is 5 years old and has 2,800 square feet have a market value of 5*(-825.16) + 2800*(40.91)+47331.38 = 157753.6
Market Value =
Age(-825.16) + size(40.91)+47331.38
is a multiple linear regression model for estimating the market value as a function of both the age and size of the house.
Market value of a house that is 30 years old and has 1,800 square feet = 30*(-825.16) + 1800*(40.91)+47331.38 = 96214.58
and one that is 5 years old and has 2,800 square feet have a market value of 5*(-825.16) + 2800*(40.91)+47331.38 = 157753.6
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