Understanding the Regression Results Table

  Source |       SS       df       MS                  Number of obs =    1028
---------+------------------------------               F(  1,  1026) =  203.57
   Model |  32312938.7     1  32312938.7               Prob > F      =  0.0000
Residual |   162857898  1026  158730.895               R-squared     =  0.1656
---------+------------------------------               Adj R-squared =  0.1647
   Total |   195170837  1027  190039.764               Root MSE      =  398.41

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 mxtrent |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
 totminc |   .0384581   .0026954     14.268   0.000       .0331689    .0437474
   _cons |   167.3393   13.43667     12.454   0.000       140.9728    193.7058
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The results in the upper right corner can be informative with respect to this regression. "Number of obs" means number of observations (also called n). In this case we have 1028 households that met our requirement for this analysis (cases with missing data are automatically excluded). "F" stands for F distribution and it used test the overall statistical significance of the regression. (1, 1026) stands for the degrees of freedom in the numerator and the denominator. "Prob > F" shows the probability that your regression is statistically insignificant. The fact that our regression here has Prob > F = 0.000 means that it is almost certain that our "best-fit" line explains something about the relationship between total monthly household income and total monthly household expenditure. As mentioned before, "R-squared" is a measure of how much of the variance around Y does X account for. Because the lowest possible R-squared is 0.0 and the highest is 1.0, our R-squared of 0.1656 means that we are explaining just over 16% of the variance in total monthly household expenditures by using total monthly household income. "Adj R-squared" is just the R-squared adjusted by the degrees of freedom. "Root MSE" is the square root of the mean squared error. It is an unbiased, independent estimate of the standard deviation.

"Std. Err." is the sample's standard deviation (also known as Standard Error). "t" is the value on the t distribution associated with our coefficients. This value tells us, with a certain level of confidence, that our results are not due to chance alone. For samples larger than 30, a t value larger than 1.96 implies that our coefficient is significantly different from zero. "P > |T|" is the probability that our statistic is greater than the critical value of 1.96. For both cases (totminc and _cons), the probability that these coefficients are not different from the null hypothesis of zero, is basically none. [95% Conf. Interval] stands for a 95% confidence interval. Or that with 95% confidence, the true slope or our regression line lies between .0331689 and .0437474.

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