A realtor wants to predict and compare the prices of homes in three neighboring locations. She considers the following linear models:
Model A: Price = β₀ + β₁ Size + β₂ Age + ε
Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε
Model C: Price = β₀ + β₁ Size + β₂ Age + β₃ Loc1 + β₄ Loc2 + ε
where,
Price = the price of a home (in $1,000s)
Size = the square footage (in sq. feet)
Loc1 = a dummy variable taking on 1 for Location 1, and 0 otherwise
Loc2 = a dummy variable taking on 1 for Location 2, and 0 otherwise
After collecting data on 52 sales and applying regression, her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Suppose that at the 10% significance level, you do not reject the null hypothesis, H₀: β₂ = 0, when testing the significance of Age in Model C. Would you delete Age from Model C?

Question

A realtor wants to predict and compare the prices of homes in three neighboring locations. She considers the following linear models:
Model A: Price = β₀ + β₁ Size + β₂ Age + ε
Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε
Model C: Price = β₀ + β₁ Size + β₂ Age + β₃ Loc1 + β₄ Loc2 + ε
where,
Price = the price of a home (in $1,000s)
Size = the square footage (in sq. feet)
Loc1 = a dummy variable taking on 1 for Location 1, and 0 otherwise
Loc2 = a dummy variable taking on 1 for Location 2, and 0 otherwise
After collecting data on 52 sales and applying regression, her findings were summarized in the following table.

Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Suppose that at the 10% significance level, you do not reject the null hypothesis, H₀: β₂ = 0, when testing the significance of Age in Model C. Would you delete Age from Model C?

Quizplus · Accepted Answer

The Answer of A realtor wants to predict and compare the prices of homes in three neighboring locations. She considers the following linear models: Model A: Price = β₀ + β₁ Size + β₂ Age + ε Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε Model C: Price = β₀ + β₁ Size + β₂ Age + β₃ Loc1 + β₄ Loc2 + ε where, Price = the price of a home (in $1,000s) Size = the square footage (in sq. feet) Loc1 = a dummy variable taking on 1 for Location 1, and 0 otherwise Loc2 = a dummy variable taking on 1 for Location 2, and 0 otherwise After collecting data on 52 sales and applying regression, her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Suppose that at the 10% significance level, you do not reject the null hypothesis, H₀: β₂ = 0, when testing the significance of Age in Model C. Would you delete Age from Model C?

A Realtor Wants to Predict and Compare the Prices of Homes