CPS on Web: Explanation of Regression Table

Explanation of Table of Regression Statistics
Source \| SS df MS Number of obs = 1296 ---------+------------------------------ F( 2, 1293) = 67.24 Model \| 231.885897 2 115.942948 Prob > F = 0.0000 Residual \| 2229.46518 1293 1.72425768 R-squared = 0.0942 ---------+------------------------------ Adj R-squared = 0.0928 Total \| 2461.35108 1295 1.9006572 Root MSE = 1.3131 ------------------------------------------------------------------------------ child18 \| Coef. Std. Err. t P>\|t\| [95% Conf. Interval] ---------+-------------------------------------------------------------------- grdatn \| .0494785 .2159076 0.229 0.819 -.3740891 .4730461 grdatnsq \| -.0022512 .0028281 -0.796 0.426 -.0077992 .0032969 _cons \| 2.981764 4.09651 0.728 0.467 -5.05477 11.0183 ------------------------------------------------------------------------------ Referring to the example above, at the upper left is an analysis-of-variance (ANOVA) table. The column headings SS, df, and MS stand for "Sum of Squares", "degrees of freedom", and "Mean Square", respectively. The total sum of squares is 2431.4: 231.9 accounted for by the model and 2229.5 left unexplained. Since the regression included a constant, the total sum reflects the sum after removal of means, as does the sum of squares due to the model. The table also reveals that there are 1295 total degrees of freedom (counted as 1296 observations less one for the mean removal), of which 2 are consumed by the model, leaving 1293 for the residual. The mean square error (MS) is defined as the residual sum of squares divided by the corresponding degrees of freedom. To the right of the ANOVA table are presented other summary statistics. The F statistic associated with the ANOVA table is 67.24. The statistic has 2 numerator and 1293 denominator degrees of freedom. The F statistic tests the hypothesis that all coefficients excluding the constant are zero. The chance of observing an F statistic that large or larger is reported as 0.0000, meaning a number smaller than 0.00005. The R-squared (R²) for the regression is 0.0942, and the R-squared adjusted for degrees of freedom (R²_a) for the regression is 0.0928. The root mean square error, labelled "Root MSE" is 1.3131. Note that the root mean square error is the square root of the mean square error reported for the residual in the ANOVA table. The lower part of the output is a table of the estimated coefficients. The first line of the table indicates that the dependent variable is child18. Thereafter follow the three estimated coefficients. The estimated model is
2.98 + (.049 * grdatn) - (.0022 * grdatnsq)
Reported to the right of the coefficients in the output are the standard errors. For instance the standard error for the coefficient on grdatn is .2159. The corresponding t statistic is 0.229, which has a significance level of 0.819 in a two-tailed test. The 95 percent confidence interval for the coefficient is [-.374, .473]. For reference, the graph corresponding to this example is shown below. Note that the varying circle sizes represent the weight of each observation as specified using the Apply Weights option.

Text adapted from the Stata Reference Manual, copyright © 1985-2000 by Stata Corporation