number of predictors increases, but we are not concerned with these calculations here. In-
stead, we will begin with an example and assume that the solution was obtained by any
available computer program, such as SPSS, Minitab, or SAS. (A free Java program is avail-
able on the Web at http://www.statcrunch.com. You need to register, but it is free and painless.
I would strongly recommend starting it up in a Web browser and using it as you read this
chapter. The main data file used here can be imported from this book’s Web site and is
named Tab15-1.dat.)
This example that we will use originated in a paper by Guber (1999), but I have added
variables to carry the analysis further in the exercises at the end of this chapter. There has
been an ongoing debate in this country about what we can do to improve the quality of pri-
mary and secondary education. It is generally assumed that spending more money on educa-
tion will lead to better prepared students, but that is just an assumption. Guber (1999)
addressed that question by collecting data for each of the 50 (U.S.) states. She recorded the
amount spent on education, the pupil/teacher ratio (PTratio), average teacher’s salary, the per-
centage of students in that state taking the SAT exams (PctSAT), and the combined SAT
score. I have dropped the separate Verbal and Math scores and added the percentage of stu-
dents in each state taking the ACT and the mean ACT score for that state. The data are shown
in Table 15.1. An abstract, and a complete copy, of this paper is available at http://www
.amstat.org/publications/jse/v7n2_abstracts.html.15.1 Multiple Linear Regression 517Table 15.1 Data on performance versus expenditures on education
State Expend PTratio Salary PctSAT SAT PctACT ACT
Alabama 4.405 17.2 31.144 8 1029 61 20.2
Alaska 8.963 17.6 47.951 47 934 32 21.0
Arizona 4.778 19.3 32.175 27 944 27 21.1
Arkansas 4.459 7.1 28.934 6 1005 66 20.3
California 4.992 24.0 41.078 45 902 11 21.0
Colorado 5.443 18.4 34.571 29 980 62 21.5
Connecticut 8.817 14.4 50.045 81 908 3 21.4
Delaware 7.030 16.6 39.076 68 897 3 21.0
Florida 5.718 19.1 32.588 48 889 36 20.4
Georgia 5.193 16.3 32.291 65 854 16 20.2
Hawaii 6.078 17.9 38.518 57 889 17 21.6
Idaho 4.210 19.1 29.783 15 979 62 21.4
Illinois 6.136 17.3 39.431 13 1048 69 21.2
Indiana 5.826 17.5 36.785 58 882 19 21.2
Iowa 5.483 15.8 31.511 5 1099 64 22.1
Kansas 5.817 15.1 34.652 9 1060 74 21.7
Kentucky 5.217 17.0 32.257 11 999 65 20.1
Louisiana 4.761 16.8 26.461 9 1021 80 19.4
Maine 6.428 13.8 31.972 68 896 2 21.5
Maryland 7.245 17.0 40.661 64 909 11 20.7
Massachusetts 7.287 14.8 40.795 80 907 6 21.6
Michigan 6.994 20.1 41.895 11 1033 68 21.3
Minnesota 6.000 17.5 35.948 9 1085 60 22.1
Mississippi 4.080 17.5 26.818 4 1036 79 18.7
Missouri 5.383 15.5 31.189 9 1045 64 21.5
Montana 5.692 16.3 28.785 21 1009 55 21.9
(continues)