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.

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Quizplus · Accepted Answer

The adjusted R-squared value is designed to account for the number of predictors in a model relative to the number of observations. It adjusts the R-squared value to penalize for adding predictors that do not improve the model significantly. In this scenario, with a relatively small sample size (n = 18) and several predictors, the adjusted R-squared is likely to be significantly smaller than the R-squared because it accounts for the potential overfitting of the model due to having many predictors compared to the number of observations.

The Cost of Renting Premises Consists of a Plurality of Parameters