Q: A real estate agent uses the regression equation $$\text{Price} = 179,739.41 + 63.07x_1 - 1,144.44x_2 + 8,000x_3 + 12,000x_4 + 5,000x_5 to $$estimate the price of a house. If a house has 2,100 square feet, is 15 years old, has 4 bedrooms, 3 bathrooms, and a 2-car garage, what is the estimated price?

$$179,739.41 + 63.07 \times 2,100 - 1,144.44 \times 15 + 8,000 \times 4 + 12,000 \times 3 + 5,000 \times 2$$

Question 1

Which of the following best describes the purpose of multiple regression analysis in business statistics?

Accepted Answer

To predict a dependent variable using two or more independent variables.

Question 2

In the context of the First City Real Estate example, which variable is the dependent variable in the multiple regression model?

Accepted Answer

Sales price

Question 3

Suppose the estimated regression equation for predicting house price is $$	ext{Price} = 50,000 + 60x_1 - 1,200x_2 + 10,000x_3$$, where $$x_1 is $$square feet, $$x_2 is $$age, and $$x_3 is $$number of bathrooms. What is the interpretation of the coefficient $$-1,200$$ for $$x_2$$?

Accepted Answer

For each additional year of age, the price decreases by $1,200, holding other variables constant.

Question 4

If the $$R^2$$ value for a multiple regression model is $$0.82$$, what does this indicate?

Accepted Answer

82% of the variation in the dependent variable is explained by the independent variables.

Question 5

Which of the following is the correct null hypothesis for testing the overall significance of a multiple regression model with five independent variables?

Accepted Answer

$$H_0$$: \$$beta_1$$ = \$$beta_2$$ = \$$beta_3$$ = \$$beta_4$$ = \$$beta_5 = 0$

Question 6

A real estate agent uses the regression equation $$	ext{Price} = 179,739.41 + 63.07x_1 - 1,144.44x_2 + 8,000x_3 + 12,000x_4 + 5,000x_5 to $$estimate the price of a house. If a house has 2,100 square feet, is 15 years old, has 4 bedrooms, 3 bathrooms, and a 2-car garage, what is the estimated price?

Accepted Answer

$$179,739.41 + 63.07 	imes 2,100 - 1,144.44 	imes 15 + 8,000 	imes 4 + 12,000 	imes 3 + 5,000 	imes 2$$

Question 7

What is the main reason for removing properties with missing data from the regression analysis in the First City Real Estate example?

Accepted Answer

Missing data can bias the regression results and reduce the accuracy of the model.

Question 8

Which of the following best describes the interpretation of a slope coefficient in a multiple regression model?

Accepted Answer

It is the average change in the dependent variable for a one-unit change in the independent variable, holding all other variables constant.

Question 9

In the context of model significance, what does a small p-value (e.g., less than 0.05) for the F-test indicate about the regression model?

Accepted Answer

The regression model explains a significant proportion of the variation in the dependent variable.

Question 10

A business analyst wants to use Excel to run a multiple regression analysis. According to the provided instructions, which step comes immediately after selecting 'Regression' from the Data Analysis menu?

Accepted Answer

Define y variable range (Price) and x variable range (include row with labels).

Question 11

If the regression output shows an adjusted $$R^2$$ value that is much lower than the $$R^2$$ value, what does this suggest about the model?

Accepted Answer

The model may include unnecessary independent variables that do not improve the fit.

Question 12

Which of the following is NOT a typical independent variable used in the First City Real Estate regression model?

Accepted Answer

Weekly average high temperature

Question 13

A regression model for predicting sales price includes the variable 'number of bedrooms.' If the coefficient for this variable is $$8,000$$, how should this be interpreted?

Accepted Answer

Each additional bedroom increases the predicted sales price by $8,000, holding other variables constant.

Question 14

Which of the following best describes the F-test in the context of multiple regression?

Accepted Answer

It tests whether at least one regression coefficient is different from zero.

Question 15

If a regression model has five independent variables and the null hypothesis $$H_0$$: \$$beta_1$$ = \$$beta_2$$ = \$$beta_3$$ = \$$beta_4$$ = \$$beta_5 = 0$ is rejected, what does this mean?

Accepted Answer

At least one independent variable significantly contributes to explaining the variation in the dependent variable.

Question 16

A real estate company wants to predict house prices using multiple regression. Which of the following is a valid reason for including 'garage size' as an independent variable?

Accepted Answer

Garage size may influence the value buyers place on a house, affecting its sales price.

Multiple Regression Analysis and Model Building

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