# Multiple Linear Regression Linear Programming Decision Theory

In the Multiple linear regression model, y (the response) is the ISOw (westward-moving intraseasonal modes) and x (the predictor variable) is the ISOe (eastward-moving intraseasonal modes). ISOe is further broken down to into more variables by applying power functions of the predictor variable to create a polynomial. Higher power terms are included in the model in order to seek evidence of any improvements in how they increase the accuracy of how wave modes are displayed. This selection is arbitrary and purely based on the assumption that it may lead to the development of a better model for depicting the relationship between the independent and dependent variables. Each of the introduced independent variables is then evaluated for significance (at the 5% level of significance) in order to establish its relevance to the entire model. Each item with a coefficient whose p-value falls below the 0.05 (5%) threshold is considered as being statistically significant. Such variables are retained in the model. The test of significance was repeated several times using the bootstrapping technique.A^sub s, T^ = (X^sup T^^sub t^X^sub t^)^sup -1^X^sup T^^sub t^Y^sub s,t+T^ by solving for a specified lag for the regression coefficients. In this equation, T is the matrix transpose, a the coefficients, and s the grid points (more easily interpreted as the lags). The regression equation involving the nonlinear terms is then tested for suitability against the ordinary linear regression. The model that appears to explain more variance in the response is deemed better.The analyses confirmed that the multiple linear regression model applied was able to reveal processes that help ascertain the relationships between interacting wave modes. The researchers noted that the inclusion of the non-linear terms in the models helped in improving the resolution of wave interaction than when purely linear versions of the models were applied. In investigating the characteristics of the regression coefficients, the authors observed that these coefficients were statistically significant, signifying the importance of each of the predictors in the prediction model.