Abstract
Linear regression is one of the frequently used statistical methods that have applications in all field of daily life. In a statistical perspective, the regression analysis is used for studying the relationship between a dependent variable and a set of independent variables. The ridge regression is the most widely model in solving the multicolinearity problem, and it''''s an alternative to OLS.Multicollinearity is the most common problem in multiple regression models in which there exists a perfect relationship between two explanatory variables or more in the model. In this study, ridge regression model was used to estimate linear regression model. This result was compared with result obtained using ordinary least squares model in order to find the best regression model. We have used meteorological data in this study. The results showed that the ridge regression method can be used to resolve the multicollinearity problem, without deleting the independent correlated variables of the model and able to estimate parameters with lower standard error values.
Highlights
Linear regression is one of the frequently used statistical methods that have applications in all field of daily life
The parameter estimations ( calculated with k in the range of [0, 1] in order to see the effects of multicollinearity, trying to resolve with ridge regression technique, on the coefficientsare given in table (2)
We noted that ridge regression model is better than ordinary least square model when the multicollinearity problem is exist because it has smaller mean square errors of estimators, smaller standard deviation for all estimators and has large coefficient of determination
Summary
Linear regression is one of the frequently used statistical methods that have applications in all field of daily life. The regression analysis is used for studying the dependence relationship between a dependent (response) variable and a set of independent (predictor) variables (Rawlings et al, 1998). There are several techniques used for the reduction of multicolinearity problem Some of these techniques can be listed as: obtaining more data, the removal of one or more independent variables from the model, clustering the independent variables, and biased estimation techniques (Tunah and Siklar, 2015). The ridge regression is the most widely model in solving the multicolinearity problem, and it's an alternative to OLS. The aims of this study are to study the ridge regression method, which resolves multicolinearity without removing independent variables from the model but provides biased estimator to study the effect of some meteorological factors on the rainfall
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