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Multiple regression analysis allows us to assess the significance of the influence of a set of independent factors on a quantitative variable under study and construct a model to calculate the value of this variable. Regression analysis, for example, offers the greatest potential for users of contextual advertising, because by conducting such an analysis, we can, with a limited budget, determine the optimal average click rate and select the advertising pages that will maximize audience reach and site traffic.
The equation for multiple linear regression is:
y ^=b_0+b_1*x_1+b_2*x_2+⋯+b_m*x_m
Before using this method, a correlation analysis is required to exclude independent variables whose correlation exceeds 0.8. Correlation analysis is performed only between quantitative variables.
Cost of regression analysisA limitation of this method is that it can only be applied to quantitative variables. However, it is possible to use binary variables alongside quantitative ones, and even to use exclusively binary quantitative variables as independent variables when constructing a model.
Regression Analysis TrainingMethod application algorithm: Conduct a stepwise regression analysis. Evaluate the R^2 parameter, which reflects the model's goodness of fit to the input data. If R^2 is close to one, a good model has been obtained. Interpretation of the results. The coefficients of the regressors included in the model and their impact on the dependent variable are estimated.
The criterion for the adequacy of the constructed model is also the measure of agreement – the determination coefficient R^2. If the dependent variable takes on values that have a sequential arrangement on the time scale, the value of the DW indicator is also taken into account, which must fall within the range from 1.7 to 2.3 so that the au-correlation of the residuals is equal to zero and does not affect the result
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