What factors affect the quality of education in our schools? The article “How Much Is En...

What factors affect the quality of education in our schools? The article “How Much Is Enough? Applying Regression to a School Finance Case” (Statistics and the Law, [New York: Wiley, 1986]: 257– 287) used data from n = 88 school districts to carry out a regression analysis based on the following variables:

y = average language score for fourth-grade students

Background variables:

x ₁ = occupational index (% managerial and professional workers in the community)

x ₂ = median income

Peer group variables:

x ₃ = % Title I enrollment

x ₄ = Hispanic enrollment (_ 1 if > 5% and 0 otherwise)

x ₅ = logarithm of fourth-grade enrollment

x ₆ = prior test score (from 4 years previous to year under study)

School variables:

x ₇ = administrator-teacher ratio

x ₈ = pupil-teacher ratio

x ₉ = certified staff-pupil ratio

x ₁₀, x₁₁ _ indicator variables for average teaching experience (x₁₀ = 1 if less than 3 years and 0 otherwise, x₁₁ = 1 if more than 6 years and 0 otherwise)

a. Is there a useful linear relationship between y and at least one of the predictors? Test the relevant hypotheses using a .01 significance level.

b. What is the value of adjusted R²?

c. Calculate and interpret a 95% confidence interval for β₁.

d. Does it appear that one or more predictors could be eliminated from the model without discarding useful information? If so, which one would you eliminate first? Explain your reasoning.

e. Suppose you wanted to decide whether any of the peer group variables provided useful information about y (provided that all other predictors remained in the model). What hypotheses would you test (a single H₀ and H_a)? Could one of the test procedures presented in this chapter be used? Explain.