APPENDIX A - A Description of Mathematical Procedures

Proposing A Model In this investigation, a model of the form: n Y = a0 + E a x. A-1 v=l J J was postulated, where the number of independent variables "n" was originally fifteen. The following experimental hypothesis was to be tested: Null Hypothesis: the coefficients a = 0 J Alternate Hypothesis: One or more of the coefficients a 0 J Correlation and Regression To establish the alternate hypothesis and to test how well the proposed model fits the data, the conventional statistical techniques of correlation analysis and multiple linear regression analysis were used. Additionally, factor analysis was employed to investigate the dependency relationships in the data. Correlation and linear regression are well established statistical procedures in science and engineering. References on these procedures include Spiegel (1961), Anderson (1963), and Draper and Smith (1966). A simple example is stated here. If N observations are made of two variables, x and y, and it is desired to test this data to see if a linear relationship exists, then a model of the form: Y = a0 + a 1 x A-2 is proposed. The values of a0 and al may be calculated from the raw data by the "least square normal equations", which are: