# Stata interpret xtreg

This allows the user, as well as other Stata commands, to easily make use of this information. Stata calls these returned results. Returned results can be very useful when you want to use information produced by a Stata command to do something else in Stata. For example, if you want to mean center a variable, you can use summarize to calculate the mean, then use the value of the mean calculated by summarize to center the variable.

Using returned results will eliminate the need to retype or cut and paste the value of the mean. Another example of how returned results can be useful is if you want to generate predicted values of the outcome variable when the predictor variables are at a specific set of values, again here, you could retype the coefficients or use cut and paste, but returned results make the task much easier.

The best way to get a sense of how returned results work is to jump right in and start looking at and using them. The code below opens an example dataset and uses summarize abbreviated sum to generate descriptive statistics for the variable read. This produces the expected output, but more importantly for our purposes, Stata now has results from the summarize command stored in memory.

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But how do you know what information has been stored? Above is a list of the returned results, as you can see each result is of the form r … where the ellipses "…" is a short label. As you might imagine, different commands, and even the same command with different options, store different results. Below we summarize the variable read again, but add the detail option. Then we use return list to get the list of returned results.

Difference in Differences Estimation in Stata

Just as the detail option adds additional information to the output, it also results in additional information stored in the returned results. The new list includes all of the information returned by the sum command above, plus skewness; kurtosis; and a number of percentiles, including the 1st r p25 and 3rd r p75 quartiles and the median r p Now that we have some sense of what results are returned by the summarize command, we can make use of the returned results.

Following through with one of the examples mentioned above, we will mean center the variable read. Notice that instead of using the actual value of the mean of read in this command, we used the name of the returned result i. As the code above suggests, we can use returned results pretty much the same way we would use an actual number. This is because Stata uses the r … as a placeholder for a real value. For another example of this, say that we want to calculate the variance of read from its standard deviation ignoring the fact that summarize returns the variance in r Var.

We can do this on the fly using the display command as a calculator. The second line of code below does this. We can even check the result by cutting and pasting the value of the standard deviation from the output, which is done in the third command below. The results are basically the same, the very slight difference is rounding error because the stored estimate r sd contains more digits of accuracy than the value of the standard deviation displayed in the output.

Now that you know a little about returned results and how they work you are ready for a little more information about them. Commands that perform estimation, for example regressions of all types, factor analysis, and anova are e-class commands.

Other commands, for example summarize, correlate and post-estimation commands, are r-class commands. The distinction between r-class and e-class commands is important because Stata stores results from e-class and r-class commands in different "places. First, you need to know whether results are stored in r or e as well as the name of the result in order to make use of them.

A potentially more important ramification of the difference in how results from r-class and e-class commands are returned is that returned results are held in memory only until another command of the same class is run. That is, returned results from previous commands are replaced by subsequent commands of the same class.This page shows an example regression analysis with footnotes explaining the output.

These data were collected on high schools students and are scores on various tests, including science, math, reading and social studies socst.

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The variable female is a dichotomous variable coded 1 if the student was female and 0 if male. Source — This is the source of variance, Model, Residual, and Total. The Total variance is partitioned into the variance which can be explained by the independent variables Model and the variance which is not explained by the independent variables Residual, sometimes called Error. These can be computed in many ways.

S Y — Ypredicted 2. Hence, this would be the squared differences between the predicted value of Y and the mean of Y, S Ypredicted — Ybar 2. The total variance has N-1 degrees of freedom.

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The model degrees of freedom corresponds to the number of predictors minus 1 K You may think this would be since there were 4 independent variables in the model, mathfemalesocst and read.

But, the intercept is automatically included in the model unless you explicitly omit the intercept. For the Model. These are computed so you can compute the F ratio, dividing the Mean Square Model by the Mean Square Residual to test the significance of the predictors in the model.

Number of obs — This is the number of observations used in the regression analysis. The p-value associated with this F value is very small 0.

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The p-value is compared to your alpha level typically 0. You could say that the group of variables math and female can be used to reliably predict science the dependent variable. If the p-value were greater than 0. Note that this is an overall significance test assessing whether the group of independent variables when used together reliably predict the dependent variable, and does not address the ability of any of the particular independent variables to predict the dependent variable.

The ability of each individual independent variable to predict the dependent variable is addressed in the table below where each of the individual variables are listed. R-squared — R-Squared is the proportion of variance in the dependent variable science which can be predicted from the independent variables math, femalesocst and read. This value indicates that Note that this is an overall measure of the strength of association, and does not reflect the extent to which any particular independent variable is associated with the dependent variable.

Adj R-squared — Adjusted R-square. As predictors are added to the model, each predictor will explain some of the variance in the dependent variable simply due to chance. One could continue to add predictors to the model which would continue to improve the ability of the predictors to explain the dependent variable, although some of this increase in R-square would be simply due to chance variation in that particular sample.

The adjusted R-square attempts to yield a more honest value to estimate the R-squared for the population.

### Stata: Data Analysis and Statistical Software

The value of R-square was. In other words, this is the predicted value of science when all other variables are 0.Why Stata? Supported platforms. Stata Press books Books on Stata Books on statistics. Policy Contact. Bookstore Stata Journal Stata News. Contact us Hours of operation. Advanced search. The results that xtreg, fe reports have simply been reformulated so that the reported intercept is the average value of the fixed effects.

With no further constraints, the parameters a and v i do not have a unique solution. You can see that by rearranging the terms in 1 :. Thus, before 1 can be estimated, we must place another constraint on the system. Any constraint will do, and the choice we make will have no effect on the estimated b. Changing the value of a would merely change the corresponding values of v i. Nor do we have to constrain a; we could place a constraint on v i.

The constraint that xtregfe places on the system is computationally more difficult:. If the panels are unbalanced the v i are effectively weighted by the number of observations in the panel.

Because the constraint we choose is arbitrary, we chose a constraint that makes interpreting the results more convenient. This constraint has no implication since we had to choose some constraint anyway. The primary advantage of this constraint is that if you fit some model and then obtain the predictions. That would be the only difference; the predictions would differ by a constant namely, by their respective values of a. Using the constraint c1 has another advantage.

Let us draw a distinction between models and estimators. That is. Equation 3 is the way many people think about the fixed-effects estimator. From 1it also follows that. Thus the left-side variable is y it minus the within-group means but with the grand mean added back in, and the right-side variables are x it minus the within-group means but with the grand mean added back in. Obviously, adding in grand means to the left and right sides has no affect on the estimated b.

Fixed-effects regression is supposed to produce the same coefficient estimates and standard errors as ordinary regression when indicator dummy variables are included for each of the groups.Why Stata?

Supported platforms. Stata Press books Books on Stata Books on statistics. Policy Contact. Bookstore Stata Journal Stata News. Contact us Hours of operation. Advanced search. Stata fits fixed-effects withinbetween-effects, and random-effects mixed models on balanced and unbalanced data. We use the notation. We have used factor variables in the above example. The terms c. The syntax of all estimation commands is the same: the name of the dependent variable is followed by the names of the independent variables.

Note that grade and black were omitted from the model because they do not vary within person. An observation in our data is a person in a given year. The dataset contains variable idcodewhich identifies the persons — the i index in x[i,t]. Before fitting the model, we typed xtset to show that we had previously told Stata the panel variable. Told once, Stata remembers.

To fit the corresponding random-effects model, we use the same command but change the fe option to re. We can also perform the Hausman specification test, which compares the consistent fixed-effects model with the efficient random-effects model. To do that, we must first store the results from our random-effects model, refit the fixed-effects model to make those results current, and then perform the test. In addition, Stata can perform the Breusch and Pagan Lagrange multiplier LM test for random effects and can calculate various predictions, including the random effect, based on the estimates.

Equally as important as its ability to fit statistical models with cross-sectional time-series data is Stata's ability to provide meaningful summary statistics. The negative minimum for hours within is not a mistake; the within shows the variation of hours within person around the global mean In this FAQ we will try to explain the differences between xtreg, re and xtreg, fe with an example that is taken from analysis of variance.

The example below has 32 observations taken on eight subjects, that is, each subject is observed four times. The eight subjects are evenly divided into two groups of four.

The design is a mixed model with both within-subject and between-subject factors. The within-subject factor b has four levels and the between-subject factor a has two levels. We will begin by looking at the within-subject factor using xtreg-fe. The fe option stands for fixed-effects which is really the same thing as within-subjects.

Notice that there are coefficients only for the within-subjects fixed-effects variables. Following the xtreg we will use the test command to obtain the three degree of freedom test of the levels of b.

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Next, we will use the be option to look at the between-subject effect. This time notice that only the coefficient for a is given as it represents the between-subjects effect. Stata's xtreg random effects model is just a matrix weighted average of the fixed-effects within and the between-effects. In our example, because the within- and between-effects are orthogonal, thus the re produces the same results as the individual fe and be.

The coefficients and test for the re model are the same as the coefficients and test from the separate fe and be models this will likely only happen if the data are balanced as they are here. Click here to report an error on this page or leave a comment.Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals.

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### Regression Analysis | Stata Annotated Output

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