Instruction 13.18
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y).
To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X 1 ), the amount of insulation in cm (X 2 ), the number of windows in the house (X 3 ) and the age of the furnace in years (X 4 ). Given below are the Microsoft Excel outputs of two regression models.

-Referring to Instruction 13.18,what can you say about Model 1?
A) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
B) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
C) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.
D) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.

Question

Instruction 13.18
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y).
To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X 1 ), the amount of insulation in cm (X 2 ), the number of windows in the house (X 3 ) and the age of the furnace in years (X 4 ). Given below are the Microsoft Excel outputs of two regression models.
  
-Referring to Instruction 13.18,what can you say about Model 1?
A) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs. 
B) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs. 
C) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs. 
D) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.

Quizplus · Accepted Answer

Instruction 13.18 likely refers to a statistical model's performance metrics. Choice A correctly describes a scenario where the model initially explains 80.8% of the variability (R-squared value), and after adjusting for the number of predictors in the model (to account for the degrees of freedom), the adjusted R-squared value is 75.7%, indicating a slight decrease in explained variability after adjustment. This is a common outcome when adjusting R-squared values for model complexity.

Instruction 13.18 One of the Most Common Questions of Prospective House Buyers