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I am doing multiple regression on a subset of the NLYS79 dataset, namely a subset containing 540 respondents. And am interested in the significance of race upon earnings. My variables here are: years in school, ASVABC(a measure of intelligence), ethnicity is black, ethnicity is white, female, tenure, hours per week worked and married*male.

$$\log(\text{earnings}) = \alpha +\beta_1\text{ASVABC}+\beta_2\text{ethblack}+ \beta_3\text{ethwhite}+\beta_4\text{female} \\+\beta_5\text{Schooling}+\beta_6 \text{tenure}+\beta_7\text{hours}+\beta_8\text{married*male}$$

For all these variables we have a source containing information about how this affects the wage.

Now my question is: all my variables except ethblack/ethwhite are significant (|t-statistic| > 2) am i safe to conclude anything from my data? How do I know that there is something wrong with my regression equation?

In essence my result is something I want: which I have now, but the whole "ommission of variable" thing is puzzling me at the moment.

I know there are things wrong with my dataset, for example I do not have a 'fair' distribution of the races black, white and hispanic are 63, 599, 34 respectively.

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    $\begingroup$ I suspect that this is not what you mean when you say "something wrong with your regression equation", but you should be aware that the NLSY is a complex survey and fitting a regression in standard software ignoring the design will result in invalid coefficient estimates and hypothesis tests. See the NLSY documentation for details. I've found that Stata is the most user-friendly tool that supports regression on data from complex surveys. $\endgroup$ – Jeremy Coyle Jan 29 '14 at 16:17
  • $\begingroup$ Ill adjust my question a bit to give some more information $\endgroup$ – WiseStrawberry Jan 29 '14 at 16:18
  • $\begingroup$ I am using eviews. $\endgroup$ – WiseStrawberry Jan 29 '14 at 16:28
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Regarding significance: That is partly dependent on sample size. I googled and the NLYS data set is pretty big (N ~ 10,000) so even small effects will be statistically significant. Look at effect sizes.

Regarding ethblack and ethwhite: How did the data set code race? You are here comparing each of these groups to anyone who was in neither group.

And, as to whether there is anything wrong with your equation - well, there's nothing wrong with the equation itself! But you need to check the assumptions. If you are doing ordinary least squares regression, then you need to check independence, homoscedasticity and so on. If you are using R there is a nice set of default plots (see plot(yourmodelname). If you are using SAS try adding PLOTS = ALL.

Finally - other variables. Model building is an art. What other variables are in the data set?

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    $\begingroup$ I am however using a subset of the NLYS79 dataset. But these are things I will of course mention in my analysis. what other variables? my god man. Religion, age, whether or not the person has a library card.. et cetera.. Thing is I wanted to add a lot of variables, including BMI, length, and other things. But my professor said that would take a lot of work commenting on the outcomes. $\endgroup$ – WiseStrawberry Jan 29 '14 at 16:22
  • $\begingroup$ I have multiple dummy variables, I am using ETHBLACK, ETHWHITE, there is another (ETHHISP) which I did not add in the equation because of autocorrelation (atleast I think that's the reason ;)) $\endgroup$ – WiseStrawberry Jan 29 '14 at 16:25
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    $\begingroup$ Hmmm. If this data set follows current census guidelines then "Hispanic" is an ethnicity and "Black" and "White" are races; one can be White and Hispanic or Black and Hispanic. But if not: It is true that you have to leave one category out of categorical variables, for comparison. But which one do you want to be the reference group? I suggest using Whites as the comparison group. Here you are comparing Whites and Blacks to Hispanics (who may have income in-between the other two). $\endgroup$ – Peter Flom Jan 29 '14 at 16:30
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    $\begingroup$ You did not add ETHHISP because--presuming you have exactly three ethnic categories--it is already covered by ETHBLACK, ETHWHITE, and the intercept term. This is important to understand because it affects how you interpret the coefficients and determine significance. For more on this issue, search our site for dummy coding. $\endgroup$ – whuber Jan 29 '14 at 16:32
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    $\begingroup$ Yes, that is what I suggest. $\endgroup$ – Peter Flom Jan 29 '14 at 16:54
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In general you want to adjust for confounders - things that you believe affect both your outcome (earnings) and your exposure (race). Adjusting for variables downstream from race means that you are eliminating the ability to detect an effect of race on earnings operating through those variables. For instance, maybe there is an effect of race on earnings mediated through educational attainment. By adjusting for educational attainment, you would be blocking your ability to detect such an effect. It's possible that this is what you want.

To answer your question about knowing if there is something wrong with your regression equation, you should be performing a suite of regression diagnostics, especially if you plan to use the p-value or t-statistic estimates from standard software. Here is a page to get you started.

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