# Diagram for correlation and regression

I would like to include a diagram for a set of correlations of IVs with a DV. I have also run a multiple regression model. Would something like the below diagram look ok? And possibly writing: H1, H2... on the arrows representing the hypothesized relationships? (which were tested using Pearson Correlation). Or does the below represent the whole regression? I am not using SEM, do let me know if such diagram is only applicable to SEM.

(source: popularsocialscience.com)

If you want to report bivariate correlations of salary with your other variables, I'd do so in a table-formatted correlation matrix. Readers will generally appreciate knowing other bivariate correlations as well, as between age and competence, and they really don't take any extra space to include, e.g.:

Table 1. Fake correlation matrix.

Variable    Salary     Gender    Age    Education
Competence  -.50**     -.70***   .15    .40*
Education    .30       -.10      .20
Age          .30        .00
Gender       .20


Note. *$p<.05$. **Dilbert Principle. ***Tactical surrender.

In Table 1, $|r|<.40$ do not achieve $p<.05$; only larger, significant correlations get asterisks. This is the easy, conventional way to embed information about null hypothesis tests of no relationship.

As @Penguin_Knight says, your figure does imply a structural equation model where salary is regressed onto the other four variables simultaneously (i.e., multiple regression, not Pearson's $r$). Since you're not estimating latent variables, it would please the structural equation modelers among us if you use rectangular boxes instead of circles around your variables – this indicates that you measured your variables directly (simple sums or averages of several items on a scale would also count as measured directly enough). Figures with all rectangular boxes represent path analyses, which are just structural equation models with only measured variables...and multiple regression models are just very simple path analyses! In that sense, you actually have fit very simple SEMs.

Standard path diagrams put regression coefficients next to unidirectional (regressive or asymmetric) paths. I would recommend following this convention as well. If you want to represent information about null hypothesis tests visually, path diagrams sometimes do this by drawing paths as dotted lines instead of solid lines to indicate that the path coefficient did not differ significantly from zero. If you have more unusual hypotheses in mind, I don't think you should try to depict these visually, unless you've got very many unusual hypotheses of the same kind to represent.

• Hi, so if I understood well, I should do a diagram like this one: support.sas.com/documentation/cdl/en/statug/63347/HTML/default/… for my regression. Is there no need to include the constant term? Commented Mar 1, 2014 at 9:08
• For your multiple regression, yes, but with all four independent variables. If any of those do not improve the model of salary significantly, you may wish to draw the insignificant paths as dotted lines. I recommend not using such a figure for bivariate correlations like Pearson's $r$. Commented Mar 1, 2014 at 9:12
• yes I understand thanks. So let's say all my IVs are significant predictors p<.05, should I include a separate box with the constant term? Commented Mar 1, 2014 at 9:15
• I'm not sure what you're asking; do you mean the intercept of the multiple regression model? If so, this constant can be represented as a triangle (the symbol for constants – as distinct from variables) with a 1 inside, and the intercept's value appears as a coefficient next to a path leading from it to the DV. See the multiple regression path diagram example here. As you'll see, even more details could be included, such as IV means, variances, and covariances...but much of this is optional. Commented Mar 1, 2014 at 9:23
• yes I meant the intercept. Ok thanks will do that (though will not be including any paths between my IVs or the intercept with the IVs) Commented Mar 1, 2014 at 9:33

From just the graph, I will associate this with a conceptual framework or a multiple linear regression model. If you put H1, H2 on each arrow, I will more incline to think those are hypotheses for each association after the other three independent variables are adjusted for. For this reason, I'd consider using it to show pair-wise correlation test hypotheses a bad idea.

You may use the arrow to show regression coefficients from the multiple regression, however. Acceptance for such practice may differ field by field, I'd survey around before making the decision.

This kind of graph is associated with SEM, but I do not think SEM exclusively owns it. Other methods such as path analysis (heavily related to SEM), directed acyclic graph, and even general conceptual framework use this kind of graphical expression. Even if it's considered as an SEM, it's still correct; the current form is how one would specify in SEM in order to run a very simple multiple linear model.

And a side comment, given the number of predictors being just four and the structure not being overly complicated, I don't think this graph is a space-conscious choice. You could have described the method in two sentences, and report the result of the regression in a 5x4 table (5 rows for title and 4 predictors, 4 columns for variable names, regression coefficient, SE or CI, and p-value.)

• I will definitely report the values and tables but I would have liked to insert a diagram before the regression results aswell as a visual aid to explain what I am proposing. Commented Feb 28, 2014 at 16:26

A matrix of pairwise correlations is a fairly standard plot for multiple regression, something you'd often do before you started to assess multicolinearity etc. There are plenty of examples at this rblogger's article. For your data, you might get a plot something like this.

(produced using splom from lattice package)

• think you forgot to link the rbloggers article Commented Mar 1, 2014 at 8:43