Assumption of a linear relationship between the independent and dependent variable(s) standard multiple regression can only accurately estimate the relationship between dependent and independent variables if the relationships are linear in nature.
The four assumptions are: linearity of residuals independence of residuals normal distribution of residuals equal variance of residuals linearity – we draw a scatter plot of residuals and y values y values are taken on the vertical y axis, and standardized residuals (spss calls them zresid) are then plotted on the horizontal x axis. Standard linear regression models with standard estimation techniques make a number of assumptions about the predictor variables, the response variables and their relationship numerous extensions have been developed that allow each of these assumptions to be relaxed (ie reduced to a weaker form), and in some cases eliminated entirely.
This article explains regression assumptions, interpretation of plots and solution to improve regression model while working on non-linear data going deeper into regression analysis with assumptions, plots & solutions going deeper into regression analysis with assumptions, plots & solutions analytics vidhya content team, july 14, 2016.
There are four principal assumptions which justify the use of linear regression models for purposes of inference or prediction: (i) linearity and additivity of the relationship between dependent and independent variables: (a) the expected value of dependent variable is a straight-line function of each independent variable, holding the others fixed.
Regarding the first assumption of regression”linearity”-the linearity in this assumption mainly points the model to be linear in terms of parameters instead of being linear in variables and considering the former, if the independent variables are in the form x^2,log(x) or x^3this in no way violates the linearity assumption of the model. The assumption of independence/no autocorrelation (ols assumption 5) – as discussed previously, this assumption is most likely to be violated in time series regression models and, hence, intuition says that there is no need to investigate it.
Assumptions of linear regression building a linear regression model is only half of the work in order to actually be usable in practice, the model should conform to the assumptions of linear regression.