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This is a beginner question, hopefully this is allowed here. I understand that scatterplots can be useful in showing the relationship between two variables, so I generated several plots of the independent variables i'm interested in in their respective relationship with the dependent variable. However, my final regression that I will include the variables of interest in will have to include fixed effects and robust standard errors. My scatterplots do not take those factors into account.

Where is thus the meaning of these plots when the coefficients will likely drastically change in the final model which includes FE and robust std. errors?

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    $\begingroup$ Asking for robust standard errors (robust meaning Huber-White-sandwich etc.) won't change the coefficient estimates. As for fixed effects, it might help if you gave more information on the structure of the model. When there are several predictors added variable plots after model fitting are often a good idea as an attempt to think about each predictor. $\endgroup$
    – Nick Cox
    Apr 30, 2017 at 17:37
  • $\begingroup$ Scatterplot is a primordial way of showing data, the basics of all. Note that many special types of plots - some very different in look from the scatterplot - are actually a modified or developed scatterplot. $\endgroup$
    – ttnphns
    May 1, 2017 at 6:19

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Marginal plots ($y$ vs $x_j$, for $j=1,2,...,p$) may be largely uninformative.

The actual conditional relationship between $y$ and $x_j$ given the other predictors may be completely different, it might even go in the other direction, as in this illustration from the Wikipedia article on Simpson's paradox (it has a variety of names in different situations), which basically tells the story:

Illustration of the quantitative version of Simpson's paradox: a positive trend appears for two separate groups (blue and red), whereas a negative trend (black, dashed) appears when the groups are combined.
$^\text{(This work has been released into the public domain by its author, Schutz)}$

As we see, while the relationship between y and x within each group is positive and linear, if you ignore the group variable the overall correlation is negative.

If you had many such groups (and noisier within-group relationships) or a continuous second variable, then the issue would not necessarily be at all obvious from the plot - you might see a decreasing relationship which gave no indication of the actual increasing relationship in the regression model containing both variables.

You could have non-linear relationships look linear or linear ones look nonlinear through similar effects (particularly if you have interactions in the model). Marginal plots may sometimes be worse than useless (since, for example, they may lead people to ignore relationships that are actually present, or believe in illusory effects that are the product of other things).

You might consider looking at partial residual plots or added variable plots to get a clearer picture of the conditional relationships.

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