SCENARIO 18-8
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.
Following is the multiple regression output with Y = % Passing as the dependent variable, X 1 =% Attendance, X 2 = Salaries and X 3 = Spending:

-Referring to Scenario 18-8,which of the following is a correct statement?
A)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class,mean teacher salary,and instructional spending per pupil.
B)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class,mean teacher salary,and instructional spending per pupil after adjusting for the number of predictors and sample size.
C)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class holding constant the effect of mean teacher salary,and instructional spending per pupil.
D)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class after adjusting for the effect of mean teacher salary,and instructional spending per pupil.

Question

SCENARIO 18-8
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.
Following is the multiple regression output with Y = % Passing as the dependent variable, X 1 =% Attendance, X 2 = Salaries and X 3 = Spending:

-Referring to Scenario 18-8,which of the following is a correct statement?
A)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class,mean teacher salary,and instructional spending per pupil. 
B)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class,mean teacher salary,and instructional spending per pupil after adjusting for the number of predictors and sample size. 
C)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class holding constant the effect of mean teacher salary,and instructional spending per pupil. 
D)60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class after adjusting for the effect of mean teacher salary,and instructional spending per pupil.

Quizplus · Accepted Answer

The correct statement is that "60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size." This is because the adjusted R-squared value, which takes into account the number of predictors and sample size, is presented in the output as 0.5477, which is equivalent to 54.77%. However, the unadjusted R-squared value is also presented as 0.6029 or 60.29%, which represents the total variation in the dependent variable that is accounted for by the independent variables. But the adjusted R-squared value is a better measure of the model's predictive power because it adjusts for the fact that adding more predictors to the model can increase the R-squared value even when they do not contribute much to the model's explanatory power. Therefore, option B is the correct statement.

SCENARIO 18-8 the Superintendent of a School District Wanted to Predict the Predict