Question

5.1.) Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimate the simple linear regression: Test Score = 520.4-5.82 x CS, n= 100, R2 = 0.08. (20.4) (2.21) (a) A classroom has 22 students. What is the model's prediction for that classroom's average test score? (b) Last year a classroom had 19 students, and this year it has 23 students. What is the model's prediction for the change in the classroom average test score? (c) The sample average class size across the 100 classrooms is 21.4. What is the sample average of the test scores across the 100 classrooms? (Hint: review the formulas for the OLS coefficients.) (d) Name one factor in the error term and discuss its correlation with class size and average test score. (e) Construct 95% and 90% confidence intervals for Bi. (f) Calculate the p-value for the two-sided test of the null hypotheis H. : B1 = 0. Do you reject the null hypothesis at the 95% level? At the 1% level? (g) Calculate the p-value for the hypotheses H : B1 = -5.6 v.s. H : B1 + -5.6. Without doing any additional calculations, determine whether -5.6 is contained in the 95% confidence interval for B1.

(h) Construct a 99% confidence interval for β0.

Answer 1

Solution : (5.1) Given Test score = 520.4-5582*CS – 0 n = 100 R2 = 0.08 (2014) (321) SER = 11.5 @ A class room has aa students, the model's prediction text score is: for the call rooms average - The general formula for average that score i8 : - Testscore = ß + CB *cs ) 1. The general for change in test score is; - * s closssize A test score = p (clagssize)." Residuals: • General formula for the sum of souared SSR = (n-2) SER? - © General formula for total sum of squares:

TES = SPR -09 1. I-R² for sample standard Deviation is: 1. General formala Sy = • Determine på. Å from the formula (1): fô =52014 B[class size) = Â =-5782 for average Test score is: The regression's prediction Given class size (CS) = 22, Test score = 520.4+ (-5.82 *cs) = 5204 + (-5-82*22) = 520.4 - 128.04 = (392.36] : Regrellion's prediction = 392.36

(6) Regretsin's prediction for change in class's average teat score is a > Given clars Size = (58) = 19 one year -23 next A Teltscore = Prclapsizes *o dass Size = -5.82 (19-23) =-5.82 (-4) = (23.28) :: Regreffime predictim = 23:28 6 sample average test score over 100 rooms is: - Giren class size = 91.4 Test score = fo + ( @s #cs) = 520.4+ (-5.82 ** 21.4) = 590.4-124.548 . = 395.852

& sample standard deviation for 100 class rooms: > SBR = (0-2) SER? =(200-2) (11.52 = (98) (132.25) =(1296005) and TS = SRR |-R² = 12960.5 10.08 = 12960.5 0.92 = 14087.5) and S30 100-) = 140875 = 514087.5/99 = 11.9289] [1093] - o-