# Statistics: what variables would be used in a multiple regression model for ACT scores

Home-Schooled Pupils are Making Colleges Sit Up and Take Notice

The Wall Street Journal, February 11, 2000.

Education in the home rather than in public schools is becoming more popular in this country. More children are withdrawing from public schools in favor of learning their lessons at home. One of the possible reasons for this movement is the increasing violence in public schools. After the disaster in Littleton, Colorado, the number of registered home-schooled children rose 10%.

Not only are more children staying at home, they seem to be doing very well academically. College-admissions tests indicate that for reading, English and science, home-schooled scores are better than public-school scores. For the ACT, home-schoolers scored 23.4, 24.4 and 21.9 compared to national averages of 20.5, 21.4 and 21.0. Only in math did home-schooled children do worse than the national average (20.4 compared to 20.7). The SAT had similar results with children studying at home scoring 1083 compared to the national average of 1016.

Interestingly, children schooled at home do not come from the highest income levels. The average income for the homes of these children is $40,000 to $50,000 as opposed to the national median income of $50,000 to $60,000. Their parents, however, do have more education than the national average. Home-schooled children also do not fit the racial stereotype, as 8% are nonwhite.

1. Based on this article and your knowledge of college-admissions tests, what variables would you include in a multiple regression model to predict ACT scores? Be certain to include dummy variables (categorical variables).

2. After deciding on the variables to include in the model, explain how stepwise regression, R2 adjusted and Cp could be used to improve upon the model.

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#### Solution Preview

To begin, the variables you should use in multiple regression analysis are:

1. Students per teacher. You will find that the fewer students per teacher, the higher the achievement scores on ACT. This can also be expressed as a ratio, such as 15:1, which means 15 students to 1 teacher.

2. Time allotted per subject. Again, you will find that as the amount of time increases for home-schooled students the better their performance on ACT. A reason for this is that a student will have more personalized instruction and the teacher can spend more time with ...

#### Solution Summary

In a 380 word solution, the response suggests a number of variables together with commentary about their predictive use. Further discussed is the decision that maybe made to change the variables as you work with the problem.