Analysing the Effect of the Deviation of Covariates Using Multiple Regression
Analysing the Effect of the Deviation of Covariates Using Multiple Regression

Summary/Abstract: Comparing data sets to highlight statistical differences is achieved by applying the t test (two samples) or ANOVA technique (2 or more samples). However, the cause-effect link is not demonstrated using these, even if a statistical significance is obtained. Multiple regression identifies and controls the effect of covariates which can contribute to explaining the observed variation of dependent variable, while reducing the variance error (unexplained variation). For an analysis with known covariates of interest that can affect the dependent variable, an effect adjustment by ANCOVA method is needed. Analysis of Covariance (ANCOVA) is an extension of ANOVA that provides a way to statistically control the (linear) effect of covariates for which no descriptive examination is wanted. ANCOVA's advantage consists in calculating the adjusted averages and applying their comparison test based on analysis of control variables (covariates). A tough condition in ANCOVA is the homogeneity of regression slopes. In the case of biological data, this condition is difficult to achieve, with the effects of covariates presenting major differences. Therefore, we have proposed and analysed a multiple linear regression model inspired by the ANCOVA technique in which the condition of homogeneity of the slopes can be not fulfilled. The proposed model includes the averages of the groups defined by the independent variable and the deviations of the covariates as slopes with different values. The model was applied to medical data. Comparison of the multiple linear regression model that includes all covariates was compiled for comparison, highlighting the differences between the two methods.

• Details
• Contents