A researcher is investigating variables that might be associated with the academic performance of high school students. He examined data from 1990 for each of the 50 states plus Washington, D.C. The data included information on the following variables: SATM The average SAT Math score of all high school seniors in the state who took the exam S Per Pupil spent on education by the state % Taking state that took the exam The average number of dollars per pupil The percentage of high school seniors in the As part of his investigation, he ran the following multiple regression model: SATM = L, + 0($ Per Pupil) + % Taking) + where the deviations O, were assumed to be independent and Normally distributed with mean 0 and standard deviation [. This model was fit to the data using the method of least squares. The following results were obtained from statistical software: Source Sum of Squares df Model Error 45915.0 2 13835.1 48 Variable Coefficient Standard Error 514.652 Constant S Per Pupil 0.00639 % Taking -1.49221| 10.30 0.0025 0.1419 10. What is the value of the MSE? C) 13835.10 A)10.30 B) 288.23 D) 22957.50

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3:04
Back
A researcher is investigating variables that might be associated
with the academic performance of high school students. He
examined data from 1990 for each of the 50 states plus
Washington, D.C. The data included information on the
following variables:
SATM
The average SAT Math score of all high
school seniors in the state who
took the exam
The average number of dollars per pupil
S Per Pupil
spent on education by the state
% Taking
The percentage of high school seniors in the
state that took the exam
As part of his investigation, he ran the following multiple
regression model:
SATM = L + 0,($ Per Pupil) + (% Taking) + D
where the deviations were assumed to be independent and
Normally distributed with mean 0 and standard deviation .
This model was fit to the data using the method of least squares.
The following results were obtained from statistical software:
Source Sum of Squares df
Model
Error
45915.0 2
13835.1 48
Variable
Coefficient Standard Erron
Constant
514.652
10.30
S Per Pupil
% Taking
0.00639
-1.49221
0.0025
0.1419
10. What is the value of the MSET
A) 10.30
B) 288.23
C) 13835.10
D) 22957.50
11. What proportion of the variation in the variable SATM is explained by the explanatory
variables S Per Pupil and % Taking?
A) 0.232
B) 0.301
C)
0.768
D)
0.960
12. Suppose we wish to test the hypotheses H,: 0, = 0, =0 versus H: at least one of the is
not 0, using the ANOVA F test. What is the value of the F statistic?
A) 3.32
B) 24.0
C)
79.65
D)
159.3
13. What is an approximate 95% confidence interval for 0, the coefficient of the variable
S Per Pupil?
A) 0.00639 + 0.0025
B) 0.00639 + 0.0042
C)
0.00639 +0.0050
D)
0.00639 +0.0067
Use the following additional information to answer questions 14
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Transcribed Image Text:3:04 Back A researcher is investigating variables that might be associated with the academic performance of high school students. He examined data from 1990 for each of the 50 states plus Washington, D.C. The data included information on the following variables: SATM The average SAT Math score of all high school seniors in the state who took the exam The average number of dollars per pupil S Per Pupil spent on education by the state % Taking The percentage of high school seniors in the state that took the exam As part of his investigation, he ran the following multiple regression model: SATM = L + 0,($ Per Pupil) + (% Taking) + D where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software: Source Sum of Squares df Model Error 45915.0 2 13835.1 48 Variable Coefficient Standard Erron Constant 514.652 10.30 S Per Pupil % Taking 0.00639 -1.49221 0.0025 0.1419 10. What is the value of the MSET A) 10.30 B) 288.23 C) 13835.10 D) 22957.50 11. What proportion of the variation in the variable SATM is explained by the explanatory variables S Per Pupil and % Taking? A) 0.232 B) 0.301 C) 0.768 D) 0.960 12. Suppose we wish to test the hypotheses H,: 0, = 0, =0 versus H: at least one of the is not 0, using the ANOVA F test. What is the value of the F statistic? A) 3.32 B) 24.0 C) 79.65 D) 159.3 13. What is an approximate 95% confidence interval for 0, the coefficient of the variable S Per Pupil? A) 0.00639 + 0.0025 B) 0.00639 + 0.0042 C) 0.00639 +0.0050 D) 0.00639 +0.0067 Use the following additional information to answer questions 14 3 89 o00 o00 Dashboard Calendar To Do Notifications Inbox
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