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)
 A: 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.)
A: 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.
A: 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)
