Check this link, hope that helps a bit

Good luck

https://www.youtube.com/watch?v=iMdtTCX2Q70

Any book on statistics will provide a sufficient answer about linear regression. I have a massive book (1396 pages) on the topic called "Applied Linear Statistical Models" Fifth Edition by Kutner, Nachtsheim, Neter and Li. However, you don't need to go to such lengths if all you are interested in knowing is what is a residual.

You can also go to the help file in your statistics program for a very nice description. For example, in Stata you can look up "regress postestimation diagnostic plots" and you'll get the following:

rvfplot residual-versus-fitted plot

avplot added-variable plot

avplots all added-variables plots in one image

cprplot component-plus-residual plot

acprplot augmented component-plus-residual plot

rvpplot residual-versus-predictor plot

lvr2plot leverage-versus-squared-residual plot

I hope this helps

Ariel

You may find this book

Chatterjee, S., Hadi, A. S. and Price, B. (2000). Regression Analysis by Example. 3rd

ed., John Wiley & Sons, New York.

It is a nice simple  book

Thank you for your answers,

I have already attached a residual plot, and here it is a bar graph for the data. Why  is the seventh case considered as outlier??

Hi Nisreen,

This is not a residual graph, it is a simple bar graph. Without knowing what the X and Y axes represent, and without some sense of the scale, it is impossible to intuit what I am looking at. That said, it appears that the 6th case (blue) is an "outlier" simply because it extends further down than any other bar. Again, without context, this is a a meaningless graph.

I hope this helps

Ariel

@Mr. Linden,

X,Y: orientation( measured in degrees) for Region Of Interest in two separated images. 

I have already attached the residual plot in the question.

Here it is again.

Where is the case #7 in the scatterplot (upper graph)?

As per my first post, I suggest you run your regression and then run the appropriate post-estimation graph. I gave you a list of several to choose from.

@ Mr. Linden,

Thank you very much. I have revised the MatLab Code, there was a "little" mistake which lead to these results. I fixed it. Now everything is OK.

Nisreen

Great!

A "must" in the analysis of residuals of linear regression is the work by Besley, Kuh and Welsh:

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

 1980 John Wiley & Sons,

Please, find the last electronic edition (2005) at the following URL :

http://onlinelibrary.wiley.com/book/10.1002/0471725153

You will find many ideas for graphics to detect influential points, analyze multicollinearity and, more generally, to resolve many of the problems encountered in the use of linear regression as a modeling tool.

By targeting your tutorial search  with this "oldy but goldy" reference, you will find many examples already programmed, as in the following tutorial to detect  muticolinearity with the SAS software.

Best regards

As previously mentioned, the book "Regression Analysis by Example" is a good starting point of this topic.

kinds,

Nisreen -

The study of estimated residuals can help you to estimate the coefficient of heteroscedasticity and look for nonlinearity.  The attached might be of interest to you.  It takes the results of residual plots and applies those results further in a different graphical analysis for purposes of estimating the coefficient of heteroscedasticity, for linear regression, but you can see what happens when there is nonlinearity. Note that graphics shown (in addition to x,y scatterplots) are not residual plots, but a further step, as described in the paper.

 https://www.researchgate.net/publication/263809034_Alternative_to_the_Iterated_Reweighted_Least_Squares_Method_-_Apparent_Heteroscedasticity_and_Linear_Regression_Model_Sampling

Note that linear regression through the origin (yielding ratio estimators), can be very useful in survey statistics, perhaps most especially for establishment surveys. They may also be quite useful for econometric and other applications. 

Cheers - Jim 

Conference Paper Alternative to the Iterated Reweighted Least Squares Method ...

Nisreen - 

Actually, since you put your question under the topic "basic" statistical analysis, I think you may want to start from the beginning, and in many ways, I think you will find the handbook at the following URL useful:

 http://www.itl.nist.gov/div898/handbook/

For regression, you might start with

"4.1.4.1. Linear Least Squares Regression" in that handbook.  Please see this:

 http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd141.htm

But there might always be misleading or not-so-great parts to virtually any handbook, so see my caution about what they have on weighted least squares (WLS) linear regression in section 3, especially page 5, in the paper on WLS at the link attached. 

 https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys

Note that the equal weights found in OLS may be a common default, but often one that makes little or no sense. 

Best wishes - Jim 

Article Properties of Weighted Least Squares Regression for Cutoff S...

This can be useful https://www.reneshbedre.com/blog/linear-regression.html

I generally suggest using a "graphical residual analysis," to check fit, and some kind of "cross-validation" might be used to avoid overfitting to your particular sample.

From the graphical residual analysis you can learn a great deal. You might notice heteroscedasticity, though it is not always obvious. You might consider the following:

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression

But as far as books go, the one Ariel suggested (Kutner, Nachtsheim, Neter and Li) is probably good. I liked another book by the first three authors. It might have been an earlier version. For a short introduction, I like Applied Linear Regression by Weisberg, published by Wiley. I have the old edition. More advanced is Applied Regression Analysis and Generalized Linear Models, 2nd ed, 2008, John Fox, Sage.

Renesh's writeup appears to be a good starting place for beginners, but I'll point out something here about a classic assumption that you will often see, that is not only not necessary, but not natural. He includes this: "Errors (residuals) should have equal variance (Homoscedasticity)." That is for OLS, but as pointed out in Ken Brewer's book, for "sample survey populations" Ken shows that OLS should not be expected. This is covered in https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity. Thus weighted least squares regression is important. The project I referenced earlier covers this:

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression

If you assume OLS for an hypothesis test, that is not your only problem. Hypothesis tests need more than a p-value to be meaningful. Now you have another problem area.