# How to analyse three independent variables and two dependent variables?

I have measured the following variables on 200 individuals.

• Independent variables:

• Measures of personality
• Extraversion
• Conscientiousness
• Leader Member Exchange (LMX) quality
• Dependent variable

• Measures of sales performance
• Sales achieved
• Repeat sales

Should I use Multiple regression? I seem to have 3 IVs and 2 DVs, which is causing confusion.

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What is your sample (individuals; members with in teams)? What is your sample size? –  Jeromy Anglim Aug 21 '11 at 8:15
@Jeromy Anglim: Individuals... Sample size is 200. –  Andrei Aug 21 '11 at 9:39
Okay. Thanks. I've updated your question with this info. –  Jeromy Anglim Aug 21 '11 at 10:34
@Andrei But what is your research question? It is difficult to answer without knowing what kind of relationships you're after. –  chl Aug 21 '11 at 11:00
@chl: The primary aim of the study is to determine if personality, specifically Extraversion and Conscientiousness, and Leader-Member Exchange (LMX) quality predict sales performance (sales achievement and repeat sales). –  Andrei Aug 22 '11 at 5:28

Of course, it all depends on your research question, but here are a few ideas.

### Basic set of analyses:

• Produce a correlation matrix using all five variables.
• Run two regressions with your three predictors in both, and one of your performance measures as dependent variables in each of the regressions.
• If it made sense (and it might not) you could create a performance index that was a composite of your two dependent variables and use that as a dependent variable in your regression.

### Selection of more sophisticated options:

• You could run a canonical correlation analysis (see here for my tips on getting started) with your predictors on side and your outcome measures on the other side.
• You could do a few things with structural equation modelling. If your measures are based on scales, you could estimate the relationships between latent variables. You could also constrain weights to explore various more focused hypotheses.
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Andrei's other question says that the variables are ordinal, not continuous. Would your suggestions still apply in that case? –  mark999 Aug 21 '11 at 21:11
@mark999 Personality traits and management constructs like LMX are typically measured using multi-item scales (e.g., a 10 item scale with Likert responses with 5 options for each item). Researchers typically perform analyses that treat these variables as numeric variables (e.g., multiple regression and correlation). For most purposes, I think this is preferable. I'd be a little bit more worried about the DVs in this example. Amount of sales and repeat sales could be quite positively skewed. –  Jeromy Anglim Aug 22 '11 at 1:10

I'm going to take a different approach to Jeromy's answer. The first, and most important, thing to do here is plot the data.

Look at scatterplots of all your independent variables against your dependent variables. If you use R, the pairs.panels() function in the psych package will give you a lot of useful information.

Once you've looked at scatterplots, you'll have a better idea of how your variables relate. I've lost track of the amount of times that model results which seemed confusing made a lot more sense when I plotted my results.

I highly recommend ggplot2 (again if you are using R), you can use the qplot() function, which allows you to add 3 or more variables to a scatterplot by altering colour, shape and size of points based on the levels of another variable.

Then, and only then, should you model your data (using something like regression). Then plot new variables based on the results of your model. This interplay between plotting and modelling is key to how I (and I suspect others) create good models.

In terms of your two dependent variables, I would first plot them against one another to examine if they are highly correlated. If they are, then you can probably create one model with whichever you prefer (but you should replicate this model with the other to be sure). If they are not, then create two seperate models for each of your dependents, and graph them to look for outliers or violations of the model assumptions. While you could use canonical correlations or MANOVA's I would probably build separate models first and then perhaps combine them into one multivariate model, all going well.

If you're not using R, I highly recommend that you start, if only for the wonderful ghraphics possible. Jeromy's blog has some really good resources to get you started if you're from a social sciences background (indeed that's how I got started).

Best of luck, and welcome to the site.

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+1 for the importance of plotting and thinking before diving into modelling. –  Jeromy Anglim Aug 21 '11 at 11:34