PURPOSE: On November 2, 1982, Missouri voters approved Proposition C, an initiative measure to increase the sales tax for the schools and to reduce property taxes. The measure also made changes in the distribution formula for state school aid, including the addition of a new cost of education index. The law provides that the cost index for a school district shall be the proportional relationship between a statistically predicted average teacher salary for that district and the average predicted teacher salary for all school districts in the state. The law requires the Department of Elementary and Secondary Education to establish the statistical procedure for determining each district’s cost index. This rule establishes the procedure as required.

1. (1) Similar to the Consumer Price Index that varies from city to city, the cost of education index indicates the relative price a school district must pay, on the average, to hire a teacher. Average teacher salaries vary among districts not only because of economic factors but also because of local policy and practice. The cost of education index has been developed so as to hold constant those factors within the control of a school district. Variations in the index are based entirely on statistically significant factors beyond the district’s control.
2. (2) Twenty-six (26) independent variable factors for each school district are used in the statistical analysis on which the cost index is based. These factors have been suggested in research elsewhere as being correlated with teacher salaries. The factors are listed in Appendix A. The value of each factor as used to determine the cost of education index for a given school year will be based on data for the second preceding school year.
3. (3) In order to predict the average teacher salary for each district, a statistical procedure called stepwise multiple linear regression analysis is used. This procedure is used to determine the combination of variable factors that predicts average teacher salary most efficiently. Appendix A documents the regression model used and indicates the statistical characteristics of the variables selected. To ensure continuity in the calculation and application of the cost of education index, the most efficient model will be determined every three (3) years using the twenty-six
4. (26) variables and the stepwise multiple linear regression analysis described in this rule.
5. (4) Each district’s predicted average salary is determined by an equation in which state average values are used for the controllable factors and actual values for each district are used for the uncontrollable factors. The prediction equation is included in Appendix A. It will be used annually to determine the cost index for each district, with updated values for each variable in the model. The average predicted teacher salary for all school districts in the state is calculated by adding each districts’s predicted salary and dividing by the number of school districts. The average salary predicted for each district is then divided by the state predicted average salary. The resulting ratio is the cost of education index for that district.

AUTHORITY: section 163.011, RSMo Supp. 1992.* This rule was previously filed as 5 CSR 40-660.030. Original rule filed March 2, 1983, effective Aug. 12, 1983. *Original authority: 163.011, RSMo 1963, amended 1967, 1973, 1977, 1982, 1985, 1986, 1988, 1992. APPENDIX A DETERMINATION OF THE COST OF EDUCATION INDEX This appendix provides additional detail on the statistical procedures used in calculating the cost of education index. It includes a list- 5 CSR 30-660 ing of the twenty-six (26) variables studied in preparing the index, the statistical characteristics of the eight (8)-variable model that most efficiently accounts for the variation in teachers salaries among districts and the predicted equation used to calculate each school district’s predicted average teacher salary. Variables Studied. The following variable factors are used in the analysis to determine the cost of education index: 1. Female teachers as a percentage of total teaching staff; 2. Percent of teaching staff with mas- ter’s degree or above; 3. Percent of nonacademic teaching time (special education and vocational divided by total teaching minutes); 4. Percent of teaching staff tenured; 5. Average years teachers employed; 6. Average years teachers in teaching; 7. Number of students per full-time teachers; 8. Number of students per nonclassroom professional personnel; 9. District classification; 10. District type (elementary and high school); 11. Equalized assessed valuation per eli- gible pupil; 12. Average income per state income tax return; 13. Aid to families with dependent chil- dren (AFDC) pupils as a percentage of enrollment; 14. Minority students as a percentage of enrollment; 15. Handicapped pupils as a percentage of enrollment; 16. Average daily attendance as a per- centage of average daily membership; 17. Free lunch students as a percentage of fall enrollment; 18. Fall enrollment; 19. True market value per square mile (equalized assessed value divided by square miles in district); 20. County population divided by square miles in county; 21. Second preceding year’s enrollment as a percent of fifth preceding year’s enrollment; 22. Student mobility (transfers in plus transfers out divided by fall enrollment); 23. Student dropout rate (number of dropouts divided by fall enrollment plus transfers in minus transfers out); 24. County crime rate (number of offenses reported to Department of Public Safety divided by county population); 25. School district located within thirty (30) miles of a state university; and 26. Average county teacher salary. Determining the Best Model—Statistical Characteristics. To determine the variables to include in the regression model, a technique is used known as Maximum R improvement (MAXR) from the Statistical Analysis System (SAS), a computer program proprietary to SAS Institute, Inc. of Raleigh, North Carolina. The MAXR method first finds the one (1) variable that produces the highest correlation (r) and then adds to the model the next variable that would yield the greatest increase in the multiple correlation coefficient (R). The program then compares each of the two (2)- selected variables to each variable not in the model, compares possible switches and selects the three (3) variables that yield the greatest increase in R and so forth. The program continues until the increase in R is less than a predetermined value. The present best model contains eight (8) variables and has a square multiple correlation coefficient (R2) of 0.8520. This means that the eight (8)-variable model for the prediction of a district’s average salary accounts for eighty-five and two-tenths percent (85.2%) of the variation in average salaries among Missouri school districts. The best model will be determined every three (3) years from all of the variable factors identified for the cost index study. The F-ratios in the second table indicate the relative power of each variable in this regression model to predict average teacher salaries. The two (2) variables which are the best predictors are the district’s enrollment and the average number of years teachers have been employed in the district. The county population density is the weakest predictor in the eight (8)-variable model. Regression Error Total Multiple-R2= 0.8520 Variable Controllable Controllable Controllable Controllable Noncontrollable Noncontrollable Noncontrollable Noncontrollable MATT BLUNT TABLE I—Analysis of Variance for the Eight-Variable Regression Model Degrees of Freedom Name of Variable X1—Percent of Female Teachers X2—Percent of Teachers With Master’s Degree or Above X3—Average Years Teachers Employed in District X4—Type of District X5—Average Personal Income Within District X6—Log of County Population Density X7—Log of District Enrollment X8—Average Teacher Salary in County Equation Constant Sum of Squares 3,526,421,724 612,738,697 4,139,160,421 TABLE II—Statistical Characteristics of Variables Prediction Equation Coefficient Mean Square 440,802,717 1,136,806 -2.41 +2.95 +263.73 -1,312.32 +0.09 -224.03 +831.03 +0.48 -4,811.54 F Ratio 387.76 F Level of Ratio Significance 25.03 46.93 152.03 57.19 24.73 5.73 173.33 73.90 5 CSR 30-660 Level of Significance 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0170 0.0001 0.0001 The effect of the four (4) controllable variables on the predicted salary of each district is made uniform by using the state average value instead of district values for each of these variables when calculating the predicted salary for individual school districts. Holding these variables constant has the effect of changing the value of the constant portion of the equation and reducing the actual number of variables used to predict the average salary of teachers in a district. This is done to reduce the effect of local policy decisions which account for part of the actual differences in teacher salaries among districts. Logarithmic values for county population density and district enrollment are used in this study because previous studies have indicated a curvilinear relationship between these variables and district average teacher salaries across the state. The Prediction Equation. The coefficients for the prediction equation that resulted from the eight (8)-variable regression model are shown here. Using these coefficients, the prediction equation may be written as follows: Yp = 4811.54 — 2.41X1 + 2.95X2 + 263.73X3 — 1,312.32X4 + 0.09X5 — 224.03X6 + 831.03X7 + 0.48X8 The predicted average salary (Yp) for a given district may be obtained by substituting the state average value for each controllable variable and the district’s unique value for each noncontrollable variable into the prediction equation in place of each variable’s symbol. The algebraic sum of all resulting products is the predicted average salary.