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<br />-2- <br />u <br />is viewed as a viable alternative to other methods of setting re vegetation <br />success criteria by the Division. <br />In order to evaluate Trapper's 1987 regression proposal I have reviewed their <br />1981 proposal for use of linear regression, the correspondence generated <br />subsequent to that proposal, evaluations of the proposal by statisticians, and <br />several texts. I present the following evaluation based on nU' review and <br />evaluation. <br />ression and Correlation Significance <br />On page 4-107 of the package Trapper states, "A high r2 is indicative of <br />good correlation. In the analysis of biological relationships an r2 of .5 <br />or greater is considered acceptable". By definition, the coefficient of <br />determination (r2) for regression is the amount (proportion or percentage) <br />of the total variation in the dependent variable that is explained or <br />accounted for by the independent variable in the fitted equation. If we <br />accept this definition, then Trapper is proposing that an acceptable level of <br />explanation in the regression is 50%. This is no better than flipping a coin <br />which gives the exact same proportion of explanation, 50%. In order to accept <br />any regression equation for use as a standard, a level of r2 much greater <br />than .5 will need to be established. I would suggest no lower than 95%. <br />On page 4-107 Trapper proposes the F ratio as a means of explaining variation <br />from the proposed regression line. A definition of the F ratio is the <br />division of the regression mean square by the residual mean square. This <br />allows the testing of the hypothesis that there is no functional relationship <br />between the dependent and independent variable(s). The test requires <br />comparing the calculated F ratio to a table value. As in other statistical <br />testing, should the calculated value be greater that the table value, the <br />hypothesis that there is no relationship is rejected. The F ratio will serve <br />as a useful measure of the importance of a variable within the regression <br />equation. <br />Regression Assumptions <br />Trapper has proposed to utilize stepwise multiple regression techniques to <br />predict the value of herbaceous cover or herbaceous production from a <br />combination of other variables (herbaceous reference area cover, herbaceous <br />reference area production, growing season length, annual precipitation, <br />average annual temperature, and others). As stated in Steel and Torrie's, <br />Principles and Procedures of Statistics: <br />"When interest is primarily in estimation or prediction of values of one <br />characteristic from knowledge of several other characteristics, we need a <br />single equation that relates the dependent variables and the independent one. <br />Multiple regression techniques provide the necessary equation." <br />By definition, multiple regression can be employed when "one has simultaneous <br />measurements for more than two variables, and one of the variables is assumed <br />to be dependent upon the others (Zar, 1974). Multiple correlation occurs, "if <br />none o~riables is assumed to be functionally dependent on any other" <br />ar, 1974). <br />