non-linear regressionin cases where dependent variable is related polynomially to independent variablei the regression function has independent variablespower of more than it is also termed as polynomial regression regression techniques may also be classified as non-parametric assumptions regression analysis has few general assumptions while specific analysis techniques have added (or reducedassumptions as well the following are important general assumptions for regression analysisthe training dataset needs to be representative of the population being modeled the independent variables are linearly independenti one independent variable cannot be explained as linear combination of others in other wordsthere should be no multicollinearity homoscedasticity of errori the variance of erroris consistent across the sample evaluation criteria evaluation of model performance is an important aspect of data science use cases we should be able to not just understand the outcomes but also evaluate how models compare to each other or whether the performance is acceptable or not in generalevaluation metrics and performance guidelines are pretty use case and domain specificregression analysis often uses few standard metrics esidual analysis regression is an estimation of target variable using the regression function on explanatory variables since the output is an approximationthere will be some difference between the predicted value of target and the observed value residual is the difference between the observed and the predicted (output of the regression functionmathematicallythe residual or difference between the observed and the predicted value of the ith data point is given asei regression model that has nicely fit the data will have its residuals display randomness ( lack of any patternthis comes from the homoscedasticity assumption of regression modeling typically scatter plots between residuals and predictors are used to confirm the assumption any patternresults in violation of this property and points toward poor fitting model normality test ( - plotthis is visual/graphical test to check for normality of the data this test helps us identify outliersskewnessand so on the test is performed by plotting the data verses theoretical quartiles the same data is also plotted on histogram to confirm normality the following are sample plots showcasing data confirming the normality test (see figure -