When do we use dummy variables

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Last name. Work email. Phone number. Last question, we promise! For now, the key outputs of interest are the least-squares estimates for regression coefficients. They allow us to fully specify our regression equation:. This is the only linear equation that satisfies a least-squares criterion. That means this equation fits the data from which it was created better than any other linear equation. The fact that our equation fits the data better than any other linear equation does not guarantee that it fits the data well.

We still need to ask: How well does our equation fit the data? To answer this question, researchers look at the coefficient of multiple determination R 2. When the regression equation fits the data well, R 2 will be large i. Luckily, the coefficient of multiple determination is a standard output of Excel and most other analysis packages.

Here is what Excel says about R 2 for our equation:. The coefficient of muliple determination is 0. Translation: Our equation fits the data pretty well. At this point, we'd like to assess the relative importance our independent variables. We do this by testing the statistical significance of regression coefficients. Before we conduct those tests, however, we need to assess multicollinearity between independent variables. If multicollinearity is high, significance tests on regression coefficient can be misleading.

But if multicollinearity is low, the same tests can be informative. To measure multicollinearity for this problem, we can try to predict IQ based on Gender. That is, we regress IQ against Gender. The resulting coefficient of multiple determination R 2 k is an indicator of multicollinearity.

When R 2 k is greater than 0. For this problem, R 2 k was very small - only 0. Given this result, we can proceed with statistical analysis of our independent variables. With multiple regression, there is more than one independent variable; so it is natural to ask whether a particular independent variable contributes significantly to the regression after effects of other variables are taken into account.

The answer to this question can be found in the regression coefficients table:. The regression coefficients table shows the following information for each coefficient: its value, its standard error, a t-statistic, and the significance of the t-statistic.

In this example, the t-statistics for IQ and gender are both statistically significant at the 0. This means that IQ predicts test score beyond chance levels, even after the effect of gender is taken into account. And gender predicts test score beyond chance levels, even after the effect of IQ is taken into account. The regression coefficient for gender provides a measure of the difference between the group identified by the dummy variable males and the group that serves as a reference females.

Here, the regression coefficient for gender is 7. This suggests that, after effects of IQ are taken into account, males will score 7 points higher on the test than the reference group females.

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A dummy variable is a numerical variable used in regression analysis to represent subgroups of the sample in your study. In research design, a dummy variable is often used to distinguish different treatment groups. In the simplest case, we would use a 0,1 dummy variable where a person is given a value of 0 if they are in the control group or a 1 if they are in the treated group.

Dummy variables are useful because they enable us to use a single regression equation to represent multiple groups. Another advantage of a 0,1 dummy-coded variable is that even though it is a nominal-level variable you can treat it statistically like an interval-level variable if this made no sense to you, you probably should refresh your memory on levels of measurement.

For instance, if you take an average of a 0,1 variable, the result is the proportion of 1 s in the distribution. To illustrate dummy variables, consider the simple regression model for a posttest-only two-group randomized experiment.