DETECTION AND CORRECTION OF VIOLATIONS OF LINEAR MODEL ASSUMPTIONS BY MEANS OF RESIDUALS

Abstract

The examination of detection and correction of linear model violations by means of residuals is an important step in statistical analyses. Sometimes regression results are non-optimal, biased estimates, increase in Type 1 error rates, poor standard errors, untrustworthy confidence intervals, and insignificance F and T Test. This is as a result of assumption violations arising from non-normality, non-linearity, serial correlation, and multicollinearity All statistical analysis as well as graphical plots was carried out with SPSS 25 statistical package. The chi-squared test of two selected statistical test is greater than chi squared critical or sig value is less than 0.05. This shows evidence of heteroscedasticity(non-constant variance). The variance inflation factor (VIF) of predictors X₁ and X₃ are 50.603 and 49.286 which are appropriately high. This shows evidence of multicollinearity in the model. The ANOVA F test sig value of 0.112 is greater than 0.05. This shows overall non-significance relationship between the variables in the model and provides insight to other violations present. In all, the standardized residuals were used in the analysis instead of ordinary residuals. The Durbin Watson test statistics are 1.470 less than 1.5 specified benchmark showing evidence of serial correlation. Some adjustment such as increase in sample size with a linear and quadratic inheritance were made to correct all model violations and improve on the model through its test statistic, critical values, sig value and residual visual assessment. The best optimal transformation is when VIF is less than 2.500.The VIF<2.500 satisfies the classical regression of normality, constant variance, linearity, independent, with no outlier present and no multicollinearity present in the model.