Suppose that a researcher using data on class size (CS) and average test scores from 100 thirdgrade classes, estimates the following OLS regression. Test̂Score = 520.4 − 5.82 × CS n = 100, R 2 = 0.08, SER = 11.5 a. A class has 22 students. What is the regression’s prediction for this classroom’s average test score?
b. Last year, a class had 19 students, and this year it has 23 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 test scores across the 100 classrooms?

This question is incomplete, the complete question is;

Suppose that a researcher using data on class size (CS) and average test scores from 100 third grade classes, estimates the following OLS regression. Test-Score = 520.4 - 5.82 × CS, n = 100, R² = 0.08, SER = 11.5

a. A class has 22 students. What is the regression's prediction for this classroom's average test score?

b. Last year, a class had 19 students, and this year it has 23 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 test scores across the 100 classrooms?

a)

the regression's prediction for this classroom's average test score is 392.36

b)

the regression's prediction for the change in the classroom average test score is -23.28

c)

the sample average of the test scores across the 100 classrooms is 395.852

d)

the sample standard deviation of test scores across the 100 classrooms is 11.92887

Step-by-step explanation:

Given the data in the question;

Test-Score = 520.4 - 5.82 × CS, n = 100, R² = 0.08, SER = 11.5 -----1

the general formula for the average test score is as follows;

Test score = ^β₀ + ( ^β₁ × CS ) -------- 2

the general for change in test score ;

ΔTest Score = β × ΔClass size  -------- 3

General formula for the sum of squared residuals SSR

SSR = ( n - 2 ) SER² ----- 4

General formula for total sum of squares TSS

TSS = SRR / 1 - R² -------- 5

General formula for sample standard deviation;

Sy = √(TSS / (n-1) )  ------ 6

now, from the given formula;

^β₀ = 520.4

aslo, β = ^β₁ =  - 5.82

so

a) A class has 22 students. What is the regression's prediction for this classroom's average test score?

given that class size CS is 22, to get  the regression's prediction for this classroom's average test score, we make use of formula 2 above;

Test score = ^β₀ + ( ^β₁ × CS )

so we substitute

Test score = 520.4 + ( -5.82  × 22 )

Test score = 520.4 + ( - 128.04 )

Test score = 520.4 - 128.04

Test score = 392.36

Therefore,  the regression's prediction for this classroom's average test score is 392.36

b) Last year, a class had 19 students, and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score.

we make use of formula 3 above

ΔTest Score = β × ΔClass size

we substitute

ΔTest Score = -5.82 × ( 23 - 19 )

ΔTest Score = -5.82 × 4

ΔTest Score = -23.28

Therefore,  the regression's prediction for the change in the classroom average test score is -23.28

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?

we make use of formula 2 above;

Test score = ^β₀ + ( ^β₁ × CS )

we substitute

Test score = 520.4 + ( -5.82 × 21.4 )

Test score = 520.4 + ( -124.548 )

Test score = 520.4 - 124.548

Test score = 395.852

Therefore, the sample average of the test scores across the 100 classrooms is 395.852

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

first we make use of formula 4 above; to calculate the sum of squared residuals SSR

SSR = ( n - 2 ) SER²

we substitute

SSR = ( 100 - 2 ) (11.5)²

SSR = 98 × 132.25

SSR = 12,960.5

Also, for total sum of squares TSS, we use formula 5

TSS = SRR / 1 - R²

we that R² = 0.08; from the given formula

so we substitute

TSS = 12,960.5 / 1 - 0.08

TSS = 12,960.5 / 0.92

TSS = 14087.5

so, the sample standard deviation will be;

from formula 6 above

Sy = √(TSS / (n-1) )

we substitute

Sy = √(14087.5 / (100-1) )

Sy = √(14087.5 / 99)

Sy = √142.297979

Sy = 11.92887

Therefore, the sample standard deviation of test scores across the 100 classrooms is 11.92887

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: