4. A researcher is investigating variables that might be associated with the aca

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4. A researcher is investigating variables that might be associated with the academic performance of high school students. She examined 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 S per pupil The average number of dollars per pupil spent on education by the state 96 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-[b + A($ per pupil) + A0% taking) + a, where the deviations a were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Sum of squares df Model Error 45915.0 13835.1 48 Variable Constant S per pupil %taking Coefficient 514.652 0.00639 1.49221 Standard error 10.30 0.0025 0.1419 Another researcher, using the same data, ran the simple linear regression model SATM-A, + (S per pupil) + a. The following results were obtained from statistical software. Sum of squares df Source Model Error 14022.7 45727.449 Standard error Variable Constant560.374 sperpup 0.012 169 Coefficient 16.80 0.0031 The first researcher concluded that because the coefficient for the variable S per pupil was positive in her results, spending additional money on students would have a positive effect on SATM scores. This researcher therefore recommended more money be spent Page 3

Explanation / Answer

4. A researcher is investigating variables that might be associated with the academic performance of high school students. She examined 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 S per pupil The average number of dollars per pupil spent on education by the state 96 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-[b + A($ per pupil) + A0% taking) + a, where the deviations a were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Sum of squares df Model Error 45915.0 13835.1 48 Variable Constant S per pupil %taking Coefficient 514.652 0.00639 1.49221 Standard error 10.30 0.0025 0.1419 Another researcher, using the same data, ran the simple linear regression model SATM-A, + (S per pupil) + a. The following results were obtained from statistical software. Sum of squares df Source Model Error 14022.7 45727.449 Standard error Variable Constant560.374 sperpup 0.012 169 Coefficient 16.80 0.0031 The first researcher concluded that because the coefficient for the variable S per pupil was positive in her results, spending additional money on students would have a positive effect on SATM scores. This researcher therefore recommended more money be spent Page 3

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