The Academic Performance Index (API), described in Exercise 12.11, is a measure of school achievement based on the results of the Stanford 9 Achievement Test. The API scores for eight elementary schools in Riverside County, California, are shown below, along with several other independent variables.

The variables are defined as

x₁ = 1 if the school was given a financial award for meeting growth goals, 0 if not.

x₂ = % of students who qualify for free or reduced price meals

x₃ = % of students who are English Language Learners

x₄ = % of teachers on emergency credentials

x₅ = API score in 2000

The MINITAB printout for a first-order regression model is given below.

a. What is the model that has been fit to this data? What is the least-squares prediction equation?

b. How well does the model fit? Use any relevant statistics from the printout to answer this question.

c. Which, if any, of the independent variables are useful in predicting the API, given the other independent variables already in the model? Explain.

d. Use the values of R² and R²(adj) in the following printout to choose the best model for prediction. Would you be confident in using the chosen model for predicting the API score for next year based on a model containing similar variables? Explain.

Transcribed Image Text:

% Meals x2 API Score y Awards x1 School 588 Yes 58 2 659 710 No 62 3 Yes No 66 4 657 36 5 669 No 40 6 641 No 51 557 No 73 743 Yes 22 School % ELL xX3 % Emergency Xạ Previous Year's API x5 34 16 533 22 5 655 14 19 695 30 14 680 5 11 13 670 26 2 636 39 14 532 6 4 705