The California Standardized Testing and Reporting (STAR) dataset contains data o
ID: 3349870 • Letter: T
Question
The California Standardized Testing and Reporting (STAR) dataset contains data on test performance, school characteristics and student demographic backgrounds. The data used here are from all 420 K-6 and K-8 districts in California with data available for 1998 and 1999. Test scores are the average of the reading and math scores on the Stanford 9 standardized test administered to 5th grade students. TESTSCR: AVG TEST SCORE (= (READ_SCR+MATH_SCR)/2 ); STR: STUDENT TEACHER RATIO (ENRL_TOT/TEACHERS);
Are estimated coefficients (both intercept and slope) significant at 10% 5% and 1% significance level? What does it mean: a coefficient is significant at 5%? Bob’s class size is 20. Predict Bob’s average test score using the regression equation. If Bob was in a class of 15 how would the prediction of his average test change? Fill out the missing parts of the table
698.933
source ss df ms model 7794.11004 1 7794.1100 residual 144315.484 418 345.252353 total 152109.594 419 363.03005Explanation / Answer
Are estimated coefficients (both intercept and slope) significant at 10% 5% and 1% significance level?
For slope,
t = Coeff / Std. err. = -2.279808 / 0.4798256 = -4.751326
Degree of freedom for residual = 418
For df = 418 P( t < -4.751326) is 0.0000014
p-value = p>|t| = 2 * 0.0000014 = 0.0000028
As, 0.0000028 is less than 0.1, 0.05 and 0.01, we coclude that the estimated slope coefficient is significant at 10% 5% and 1% significance level.
For intercept,
t = Coeff / Std. err. = 698.933/ 9.467491 = 73.82452
Degree of freedom for residual = 418
For df = 418 P( t > 73.82452) is 0
p-value = p>|t| = 2 * 0 = 0
As, 0 is less than 0.1, 0.05 and 0.01, we coclude that the estimated intercept coefficient is significant at 10% 5% and 1% significance level.
What does it mean: a coefficient is significant at 5%?
It means that the model is a significant fit of the data at 5% significance level.
Bob’s class size is 20. Predict Bob’s average test score using the regression equation.
The regression equation is,
TESTSCR = 698.933 - 2.279808 * STR
For STR = 20,
TESTSCR = 698.933 - 2.279808 * 20 = 653.3368
If Bob was in a class of 15 how would the prediction of his average test change?
For STR = 15,
TESTSCR = 698.933 - 2.279808 * 15 = 664.7359
So, the average test score increases from 653.3368 to 664.7359, if the class size reduces from 20 to 15.
t and p>|t| are already calculated in 1st part,
95% con interval is calculated as,
t value for 95% con interval and df = 418 = 1.966
95% con interval for slope is,
(-2.279808 - 0.4798256 * 1.96, -2.279808 + 0.4798256 * 1.96
(-3.220266, -1.33935)
95% con interval for intercept is,
(698.933 - 9.467491 * 1.96, 698.933 + 9.467491 * 1.96)
(680.3767, 717.4893)
testscr coef std err t p>|t| 95% con interval str -2.279808 0.4798256 -4.751326 0.0000028 (-3.220266, -1.33935) _cons 698.933 9.467491 73.82452 0 (680.3767, 717.4893)Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.