Multiple Linear Regression Assignment Example | Topics and Well Written Essays - 2000 words

Multiple Linear Regression - Assignment Example del is linear in the sense that every predictor variable is either a constant or the product of a parameter (ÃŽ ²Ã¢â‚¬â„¢s) and a predictor variable (x’s). The researchers further investigated whether the multiple linear regression models provided a better description of the relationship between the wave modes than would a linear regression model with only a linear predictor. In the 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, â€Å"T† is the matrix transpose, â€Å"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.