A researcher is investigating variables that might be associated with the academic performance of high school students. She exam
ined data from 1990 for each of the 50 states plus Washington, DC. 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
$ per pupil The average number of dollars 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 her investigation, she ran the multiple regression model:
SATM = β0 + β1($ per pupil) + β2(% taking) + εi,
where the deviations εi were assumed to be independent and normally distributed with a mean of 0 and a standard deviation of σ. 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 45915.0 2
Error 13835.1 48
Variable Coefficient Standard error
Constant 514.652 10.30
$ per pupil 0.00639 0.0025
% taking –1.49221 0.1419
Suppose we wish to test the hypotheses H0: β1 = β2 = 0 versus Ha: at least one of the βj is not 0, using the ANOVA F test.
What is the value of the F statistic?
a) 79.65 b) 24.0 c) 159.3 d) 3.32
SATM The average SAT Math score of all high school seniors in the state who
took the exam
$ per pupil The average number of dollars 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 her investigation, she ran the multiple regression model:
SATM = β0 + β1($ per pupil) + β2(% taking) + εi,
where the deviations εi were assumed to be independent and normally distributed with a mean of 0 and a standard deviation of σ. 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 45915.0 2
Error 13835.1 48
Variable Coefficient Standard error
Constant 514.652 10.30
$ per pupil 0.00639 0.0025
% taking –1.49221 0.1419
Suppose we wish to test the hypotheses H0: β1 = β2 = 0 versus Ha: at least one of the βj is not 0, using the ANOVA F test.
What is the value of the F statistic?
a) 79.65 b) 24.0 c) 159.3 d) 3.32
1 answer:
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