It is important to consider multiple perspectives of a conce

It is important to consider multiple perspectives of a concept. Therefore...when should we not use the regression equation? (250 words)

Solution

The regression equation can not be used in many situations because of its certain assumptions. Before using linear regression on any data, we must first verify the assumptions which are-

So, based on the assumptions, we can list the following situations where we can\'t use the regression equation-

1) In case of multiple linear regression, if the dependent variable must have linear relationship with the independent variables individually. If any one of the variables among the independent variables is not having linear relationship with the dependent variable, then we can\'t include it in the model. Even in case of simple linear regression if the independent variable is not linearly related to the dependent variable, that means if the scatter plot of both the variables doesn\'t show linear relation then we can\'t use the simple linear regression in this case.

2) If there is multicollinearity in the variables that means if any two or more of the independent variables are correlated with each other in a multiple linear regression case, then we can not use the multiple linear regression in that case. This gives a wrong interpretation of the coefficient of determination of the model i.e. R² value. This is because it can increase the variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model. The result is that the coefficient estimates are unstable and difficult to interpret. Multicollinearity saps the statistical power of the analysis, can cause the coefficients to switch signs, and makes it more difficult to specify the correct model.

3) If the data of the independent variables are not collected independently and randomly, then also we can not use the concept of linear regression. The values of independent variable are supposed to have been collected randomly rather than bound with some constraints.

4) The distribution of the dependent variable and the error term must be normal else we can\'t use the concept of linear regression.