Achievement Scores III The Academic Performance Index (API), described in Exercise 1...

Achievement Scores III 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.

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 (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.

Reference:

Achievement Tests The Academic Performance Index (API) is a measure of school achievement based on the results of the Stanford 9 Achievement test. Scores range from 200 to 1000, with 800 considered a long-range goal for schools. The following table shows the API for eight elementary schools in Riverside County, California, along with the percent of students at that school who are considered “English Learners” (EL).

a. Which of the two variables is the independent variable and which is the dependent variable? Explain your choice.

b. Use a scatterplot to plot the data. Is the assumption of a linear relationship between x and y reasonable?

c. Assuming that x and y are linearly related, calculate the least-squares regression line.

d. Plot the line on the scatterplot in part b. Does the line fit through the data points?