The Academic Performance Index (API), described in Exercise 12.13, is a measure of school achievement based on the results of the Stanford 9 Achievement Test. The API scores for 12 elementary schools in Riverside County, California, are shown below, along with several other independent variables.5

The variables are defined as
y = API score in 2010
x1 = % of students who are "English learners"
x2 = % of students who receive a free or reduced cost lunch
x3 = Average parent education level (with 1 = Not a high school graduate, 2 = High school graduate, 3 = Some college, 4 = College graduate, 5 = Graduate school)
x4 = % of students in Gifted and Talented Education Program
x5 = API score in 2009
The MINITAB printout for a first-order regression model is given below.
Regression Analysis: y versus x1, x2, x3, x4, x5
The regression equation is
y = 15 - 0.306 x1 + 0.076 x2 - 48.1 x3
+ 1.93 x4 + 1.13 x5

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.

API Score, y El(%) Xt Free Avg Parent Gifted and Previous Reduced Education Talented(%) Year's API, x School Lunch%), x2 Level, X3 1.70 2.91 2.21 2.19 2.84 1.70 2.79 1.72 2.14 3.22 2.14 1.46 745 71 808 18 798 791 2 79 76 10 801 751 778 39 57 34 87 10 841 706 665 690 78 28 12 685 77 Predictor Constant Coef 14.9 -0.3060 0.0763 -48.06 1.927 1.1269 SE Coef 179.7 0.6483 0.2885 34.33 1.450 0.2503 0.08 0.936 -0.47 0.654 0.26 0.800 -1.40 0.211 1.33 0.232 4.50 0.004 x4 s 17 .0180 R-Sq 95.4% R-Sq ( adj ) 91 . 6% - Analysis of Variance Source Regression Residual Error Total DF MS 2 5 36121.2 7224.2 24.94 0.001 2 2 1737.7 289.6 11 37858.9 Source DF Seq ss 1 28748.4 701.0 591.6 212.3 5868.0 x4