TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing) ,daily mean of the percentage of students attending class (% Attendance) ,mean teacher salary in dollars (Salaries) ,and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination ( ) of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743.
The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models:
Model (I) : Model (II) : Model (III) :
-Referring to Table 15-4,which of the following models should be taken into consideration using the Mallows' C_p statistic?

Question

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing) ,daily mean of the percentage of students attending class (% Attendance) ,mean teacher salary in dollars (Salaries) ,and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (

) of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743.
The output from the best-subset regressions is given below:

Following is the residual plot for % Attendance:

Following is the output of several multiple regression models:
Model (I) :

Model (II) :

Model (III) :

-Referring to Table 15-4,which of the following models should be taken into consideration using the Mallows' C_p statistic?

Quizplus · Accepted Answer

We can determine the best model using Mallows' Cp statistic, which gives an estimate of the prediction error of each model. In this case, the best models are the ones with the lowest value of Cp. Model I has a Cp of 4.93, Model II has a Cp of 4.67, and Model III has a Cp of 5.05. Therefore, Model II, which includes all three predictors X₁, X₂, and X₃, should be considered. Additionally, Model I, which only includes X₁ and X₃, should also be considered as it has a relatively low Cp value.

TABLE 15-4 the Superintendent of a School District Wanted to Predict the Predict