Question

Using the data in the Excel file Home Market Value, develop a multiple linear regression model for esti- mating 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.

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 $120,700.00

Answer 1

To predict house market values using multiple linear regression, input age and size as independent variables into statistical software, yielding an equation incorporating these factors. Use the equation to calculate predicted values for specific house ages and sizes after validating the model's fit and assumptions.

Step-by-step explanation:

To develop a multiple linear regression model for estimating the market value of a house based on its age and size, we will use the provided Excel data. Using statistical software or Excel's data analysis tool, we can input the age and square feet as independent variables and the market value as the dependent variable. This will give us an equation of the form:

Market Value = a + (b1 × Age) + (b2 × Square Feet)

where 'a' is the intercept, 'b1' is the coefficient for the age of the house, and 'b2' is the coefficient for the size of the house in square feet. With the regression equation, we can then make predictions about the market value based on the age and size of a house. To 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, we'd replace the corresponding values of Age and Square Feet in our equation and calculate the results.

Note that before making predictions, it's important to check the model for its goodness of fit, typically using the R-squared value, and to validate the assumptions of linear regression, such as linearity, independence, homoscedasticity, and normality of residuals.