Regression analysis can be used to summarize data as well as to study relations between the variables. If the number of independent variables is more than one, multiple linear regression analysis is used and general regression equation with four independent variables can be expressed as
where A is constant of regression and B is coefficient of regression. The values of the constant and coefficients are determined using the least-squares method which minimizes the error, seen as E in the above regression equation (Akkaya, 1998). A commonly used measure of goodness of fit of a linear model is R2, sometimes called the coefficient of determination. It is defined as the proportion of the variation in the dependent variable and expressed as
where Y is the value of Y predicted by the regression line, Yi is the value of Y observed, and Y is the mean value of the Y^s . If all the observations fall on the
regression line, R is 1. If there is no linear relationship between the dependent
and independent variables, R is 0. The significance level of the constant and coefficients is statistically tested using the T distribution (Koutsoyiannis, 1989; Cuhadaroglu and Demirci, 1997).
A variety of regression models can be constructed from the same set of variables. In the present study, a stepwise regression model was used. Stepwise regression of the independent variables is basically a combination of backward and forward procedures in essence and is probably the most commonly used method. In this method, the first variable is selected in the same manner as in the forward selection. If the variable fails to meet the entry requirements, the procedure terminates with no independent variables entering into the equation. If it passes the criterion, the second variable based on the highest partial correlation is selected. If it passes the entry criterion, it also enters the equation.
After the first variable is entered, stepwise selection differs from forward selection: the first variable is examined to see whether it should be removed according to the removal criterion as in backward elimination. In the next step, variables not in the equation are examined for removal. Variables are removed until none of the remaining variables meet the removal criterion. Variable selection terminates when no more variables meet entry and removal criteria. In the statistical analysis, the correlations between the air pollutant concentrations and meteorological factors have been analyzed. In spite of establishing the correlations between the air pollutant concentrations and meteorological factors by Eq. (31.1), the equations expressed as
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