These are the important assumptions we need to verify before conducting the actual regression analysis? How do we carry out the Data inspections for #3, #4, #6?

Assumptions: 1. a continuous dependent and an independent variable. 2. Linear relationship between the two var 3. independence observations 4. homoscedascity must exist 5. no significant outliers 6. residuals (errors) of the regression line are approximately normally distributed. 7. there is independence of observations.

  • $\begingroup$ does your question ( I believe it does but I have been advised to ask ) deal with time series or spatial data ? $\endgroup$ – IrishStat Sep 2 '17 at 17:07

There are plenty of procedures for checking the validity of those assumptions.

For independence of observations (3 in you numbering), you usually plan for it during the experiment's design phase, or handle it through different techniques.

Numbers 4 and 6 can be done by:

  • analyzing the residuals plots against the dependent variable and histogram. If it looks uniformly random and the histogram looks like a Gaussian variable, you are usually good to go. But some people prefer a more "rigorous" approach through tests, so I recommend checking this page and this page. There are many different approaches each with its strengths and weakness. Also, there are different types of residuals (transformations of the residuals, or generated with different procedures) please refer to this blog post for an overview of a few of them.

For outliers, it is usually important to take care of them since they can bias your estimates. Again there are many different ways to detect and account for this problem. Cook's distance is one of them. Usually robust regression methods are used to account for outliers without detecting and removing them.

  • $\begingroup$ when analyzing time series data there a ton of more things to do .Your summary is correct for cross-sectional data only. $\endgroup$ – IrishStat Sep 2 '17 at 17:25
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    $\begingroup$ True, but in my mind time series analysis is a different subject then regression analysis. When he asked for the assumption to cunduct regression analysis I defaulted to classic regression analysis. Also, the assumption of independence among observations not possible in time series analysis, hence the need for different techniques. $\endgroup$ – Guilherme Marthe Sep 2 '17 at 17:30
  • $\begingroup$ My question is for Linear or Multiple Linear Regression. Thanks $\endgroup$ – Vyas Sep 2 '17 at 17:52
  • $\begingroup$ when he asked "How do we carry out the Data inspections for #3" , this inadvertently keyed me to think that he might be referring to time series data. $\endgroup$ – IrishStat Sep 2 '17 at 18:08
  • $\begingroup$ I checked if the value of Durbin-Watson test was close to 2 to ensure that the residuals were independent of each other, hence fulfilling criterion #3. $\endgroup$ – Vyas Sep 4 '17 at 0:53

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