The Cost of Renting Premises Consists of a Plurality of Parameters

Multiple Choice

The cost of renting premises consists of a plurality of parameters. A real estate company attempts to identify the most significant factors and proposes a multiple regression model based on a sample of n = 18 observations. ​ y = Monthly rent ($) ​ x₁ = Surface area (m²) ​ x₂ = Historic building (1 = yes, 0 = no) ​ x₃ = Prestige of a district (1 to 5 scale) ​ x₄ = Parking facilities (1 = yes, 0 = no) ​ x₅ = Availability of infrastructure (1 to 5 scale) Suppose that SSRegr = 846,325 and SSTo = 3,900,000. Calculate the values of R² and adjusted R². Explain the difference between them. ​

A) Adjusted R² is significantly smaller than R², because R² itself is rather small.
B) Adjusted R² is significantly smaller than R², because the number of predictors is large as compared to the number of observations.
C) Adjusted R² is significantly larger than R², because R² itself is rather small.
D) Adjusted R² is significantly greater than R², because the number of predictors is large as compared to the number of observations.
E) The difference between adjusted R² and R² is not significant, because R² is substantial and there are only a few predictors.