TABLE 14-15
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, X₁ = % Attendance, X₂= Salaries and X₃= Spending:

-Referring to Table 14-15, 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

TABLE 14-15
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, X₁ = % Attendance, X₂= Salaries and X₃= Spending:
 
-Referring to Table 14-15, 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 adjusted R-squared value of 0.573 indicates that 57.3% of the variation in % Passing can be explained by the three predictor variables, after adjusting for the number of predictors and sample size. Therefore, only option B is a correct statement. Option A mistakenly suggests that the R-squared value is for the total variation, while options C and D incorrectly imply that only one predictor variable is being considered.

TABLE 14-15 the Superintendent of a School District Wanted to Predict the Predict