TABLE 17-8
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 Table 17-8,which of the following is a correct statement?
A)The mean percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of percentage of students attending class increases by 1%.
B)The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%.
C)The mean percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of the percentage of students attending class increases by 1% holding constant the effects of all the remaining independent variables.
D)The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1% holding constant the effects of all the remaining independent variables.

Question

TABLE 17-8
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 Table 17-8,which of the following is a correct statement?
A)The mean percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of percentage of students attending class increases by 1%. 
B)The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%. 
C)The mean percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of the percentage of students attending class increases by 1% holding constant the effects of all the remaining independent variables. 
D)The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1% holding constant the effects of all the remaining independent variables.

Quizplus · Accepted Answer

According to the regression output, the coefficient for X₁ (% Attendance) is 0.085 and it is statistically significant at the 0.05 level. This means that for a 1% increase in the daily mean of the percentage of students attending class, the mean percentage of students passing the proficiency test is estimated to go up by 0.085 (or 8.50%) holding constant the effects of all the remaining independent variables. Therefore, option C is the correct statement. Option A and B are incorrect because they have reversed the cause and effect relationship between the dependent and independent variables. Option D is incorrect because it implies a causal relationship between X₁ (% Attendance) and Y (% Passing) which cannot be established from the regression output alone.

TABLE 17-8 the Superintendent of a School District Wanted to Predict the Predict