A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x₁), the number of bathrooms (x₂), and its square footage (x₃). She estimates the following model as Rent = β₀ + β₁Bedroom + β₂Bath + β₃Sqft + ε. The following ANOVA table shows a portion of the regression results. The coefficient of determination indicates that ________. A) 19.08% of the variation in Rent is explained by the sample regression equation B) 19.08% of the variation in square footage is explained by the sample regression equation C) 80.92% of the variation in Rent is explained by the sample regression equation D) 80.92% of the variation in square footage is explained by the sample regression equation

Question

Quizplus · Accepted Answer

The coefficient of determination, also known as R-squared, measures the proportion of variation in the dependent variable (Rent) that is explained by the independent variables (Bedroom, Bath, Sqft) in the regression model. In this case, the ANOVA table shows that the R-squared value is 0.8092 or 80.92%. This means that the model explains 80.92% of the variation in Rent. Therefore, the correct answer is C. Option A and B are incorrect because they both refer to square footage, which is just one of the independent variables in the model and not the dependent variable. Option D is also incorrect for the same reason.

A Real Estate Analyst Believes That the Three Main Factors