Scatterplot with regression curve and confidence band for the regression curve.

For multiple regression overlaying data and fit is difficult because the "curve" is a multi-dimensional response-surface that is not easy to visualize in a two-dimensional plot. I would show the regression curves the different predictors for some fixed values of the other predictors (again with confidence bands).

The coefficients of the model could be shown in a dot plot, like here:

https://dsparks.files.wordpress.com/2011/02/cp.png

but I find this not a very good idea because the coefficients will all have entirely different meanings so I don't see any value in showing them side-by-side in a plot (what implies that they might/should be compared - what usually makes not much sense!)

Hi

In terms of visual representation, link here is good support:

https://uk.sagepub.com/sites/default/files/upm-binaries/58381_Chapter_13.pdf

Hi Mohammed,

It depends on your objective. I suggest you explore R software (https://www.r-project.org) using the ggplot2 package (http://ggplot2.org), which can generate visually appealing graphics for presenting your results. The R Graphics Cookbook by Winston Chang (http://www.cookbook-r.com/Graphs/) also provides good practical recipes for visualising data using R. I hope this helps.

Best, Don

Asif -

The usual residual plots are useful.  For multiple regression, you can plot the estimated residuals versus a preliminary prediction of y, or any other size measure you could use in place of x in simple regression, to consider your error structure.

The following link goes to a conference paper where I took that a bit further, and used the results of residual plots to then plot the behavior of the data to estimate the level of heteroscedasticity, the coefficient of heteroscedasticity.  Those graphs can also help indicate if you have nonlinearity.  But this may be too involved if you do not have time to look into it:  

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

For multiple regression, as I think Jochen indicated, there are interrelationships among regressors which modify relationships, but I still think that it might be somewhat informative to plot one regressor at a time, and even one regressor against another, to learn more about your data. 

Here is an excel tool for plotting confidence bands on simple regression through the origin with what I have found to be a robust regression weight scheme, often used in econometrics, that I also found useful in working with establishment surveys.  It might be modified to fit other models.

 https://www.researchgate.net/publication/263265199_CRE_Conf_Bound_and_Graphs_Example_for_Section_4_of_Properties_of_WLS_article

Note that estimated heteroscedastic residuals are factored into random and nonrandom factors.  The random factors of the estimated residuals, when plotted against x, or whatever 'size' measure you are using, should show no pattern, though I think it more robust against data measurement errors to under-compensate.  The regression weights for OLS are all equal, so that a factoring of the estimated residuals is not necessary, though OLS is really a special case of WLS, and I think OLS is overused.

Graphics in general are very useful, and if you do plot residuals it can be very informative just to do that.  Note that it is the residuals, or random factors of them, that we would like to be normally distributed, though that is generally not crucial, and the x and y data can have any distributions.

As noted by others, there are graphics packages that can be useful.  Even spreadsheet graphics can be very helpful.

Best wishes - Jim 

PS - Please note from the abstract to my confidence band tool that it is more efficient to use something like STDI from SAS PROC REG, for example, to construct such plots.  Certainly it would be easier to modify for other models.  But it depends upon what is available to you, and if you understand how the spreadsheet is constructed, you will likely understand the process better and be less likely to use your software incorrectly. -  You could first use your software to duplicate what I did in that spreadsheet to see if 'answers' agree.  

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

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

You can use the scatter diagram for simple regression cases.

CaviR ( www.cavir-statistics.com ) is a statistical web application in which you get your one-, two- and three-way interaction results in just a second.

How does it work?

1. Upload your SPSS file

2. Go to the required analysis

3. Select the relevant variables (covariates, dependent, independent, moderator, etc.)

4. Get your regression analyses, simple slope analyses, plots (with and without confidence intervals) in just a second!

5. Save the plots by right-clicking to your personal computer.

If you have more questions, just send me a message!

The following may be of interest here:

https://www.researchgate.net/publication/313925533_Comparing_Model_Performances_Graphically

Joachim Waterschoot notes some software that I suppose is worth checking into if you are in need of that help. However, one should always be careful to know what any software you use is doing, and what you really need to do. "Black boxes" can be very misleading. There is no substitute for understanding the methodology and understanding what is applicable.

James R Knaub I totally agree with your point. I encourage to do analyses step by step by yourself so you know what happened with your data and how you get the results. The main reason I developed CaviR is to avoid practical difficulties (e.g.,getting regression analyses plots, nice-looking correlation matrices, etc.) and, thereby, to save time. You get the same results (which I checked in different datasets) in a few seconds - which normally takes 20 minutes or more.

If CaviR users would meet any difficulties or ambiguities, they are free to report these

Thank's joachim

CaviR works fine, very useful for me, specially for regressions with error bands and JN plot. Plots are beautiful.

I think I really need to learn R as the plots are much better than SPSS or excel.

Great job!