Which methods are used for analysis of Residuals? (Raja, location unknown)

Another great question Raja! There are several ways that one might analyze residuals and the one that an analyst chooses is depended on their purpose/goal for analyzing the them. For example, if someone is testing whether the variance of their residuals are equal across levels of the predicted value of their model's DV ( an assumption of regression), one would use a scatterplot, placing the predicted value of their DV on the x-axis and the residual scores from the regression model on the y-axis.

NOTE: most statistical software packages will allow you to save both the predicted scores and residual scores of a regression model (in SPSS, simply place a checkmark in the desired boxes in the "save" dialogue of the "regression" analysis).

Conversely, if the residuals are being analyzed in an effort to control for confounds, the residuals of one regression model (a model with the variable/variables that are to be controlled as predictors) might be used as the DV in another model (a model that would feature your target variable of interest as the predictor).

In yet another analysis (of multivariate normality; also an assumption of regression), residual scores may be examined with a histogram to determine if their distribution is "normal."

I hope that is helpful!

What are residuals in regression? How we can find residuals? (Raja, location unknown)

Great question(s), Raja! Residual is a buzz word that is often-used in statistics, which can make things very confusing if you aren't clear what it is. Before I go further in answering this question here (which I will), I'll also refer you to a blog I wrote in October on this very topic, called: "Top Ten Confusing Stats Terms Explained in Plain English (#8 Residual)". While I'm happy to try to address this question here, you might find that the blog posting offers more detail and examples that are useful to understand this complex topic.

That said, here is my attempt to answer this question concisely:

In general, a residual is the difference between the actual value of a dependent variable (DV) and the value of variable that was predicted by a statistical model. In the context of a regression, a residual is how far a predicted value (as determined by the predictors in the model) is from the actual value of the dependent variable. This is also called an "error term" (because it represents how much your regression model was in error, in terms of its ability to predict the value of the DV).

In any statistical model, a residual can be thought of in various contexts. For example, each person will have their own "residual" score (which is simply the difference between the actual and predicted value of the DV), while the model as a whole also has a residual score (which represents how much variability in the DV remained 'unexplained' by the predictors in the model). A residual score serves several purposes, including: 1) determining the accuracy of your model (how much variability is explained by the model) and 2) being used to test the assumptions inherent in the regression analysis (such as the assumption that the residuals are normally distributed OR that their variance is equal across all levels of the predicted value of the DV).

Again, please visit the blog linked above for more in-depth information. Good luck!