Question

A researcher, using data on class size (CS) and average test scores (ATS) from 100 third grade classes, estimate the OLS regression ATS = 520.4 - 5.82 times CS, R^2 = 0.8, SER = 11.5
a) Suppose a classroom has 20 students. What is the regression's prediction for that classroom's average test score?

(b) Last year a classroom had 19 students, and this year it has 21 students. What is the regression'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?

(d) What is the sample standard deviation of the test scores across the 100 classrooms?

Answer 1

Answer:

Step-by-step explanation:

Given that a researcher, using data on class size (CS) and average test scores (ATS) from 100 third grade classes, estimate the OLS regression

ATS = 520.4 - 5.82 times CS,

R^2 = 0.8,

SER = 11.5

a) If class size =20

ATS = $520.4-5.82(20)\\= 520.4 - 116.4\\=404$

b) When CS increases from 19 to 21 i.e. 2 units ATS increases by 2(slope)

= 11.64 units

c) Here n=100, mean CS = 21.4

So Sample average test score = $520.4-5.82(21.4)\\= 359.852$

d) Sample std deviation = std dev/sqrt of 100

=1.15