The bottom of page 117 and top of page 118 illustrates how you can get standard errors for a and b and form confidence intervals for a and b.
First, we use the davis file and keep just the women.
use https://stats.idre.ucla.edu/stat/stata/examples/ara/davis if female == 0, clear (From Fox, Applied Regression Analysis. Use 'notes' command for source of data )
We fix the error in subject 12 (see chapter 5 for more about this error).
generate t = measwt if subject==12 replace measwt = measht if subject==12 replace measht = t if subject==12 drop t
Now we run the regression predicting measwt from reptwt. The regression table below shows the Se(A) is 1.744, and the Se(B) is .0305, as shown at the bottom of page 117. The regression table also gives us the confidence interval for A (-1.68378 to 5.238787) and the Confidence interval for B (.9166458 to 1.037803) as shown at the bottom of page 118.
regress measwt reptwt Source | SS df MS Number of obs = 101 ---------+------------------------------ F( 1, 99) = 1024.54 Model | 4334.88935 1 4334.88935 Prob > F = 0.0000 Residual | 418.873025 99 4.23104066 R-squared = 0.9119 ---------+------------------------------ Adj R-squared = 0.9110 Total | 4753.76238 100 47.5376238 Root MSE = 2.0569 ------------------------------------------------------------------------------ measwt | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- reptwt | .9772242 .0305301 32.009 0.000 .9166458 1.037803 _cons | 1.777503 1.744408 1.019 0.311 -1.68378 5.238787 ------------------------------------------------------------------------------
Page 122 shows how to get confidence intervals in a multiple regression, analyzing the duncan prestige data file. We first use the data file.
use https://stats.idre.ucla.edu/stat/stata/examples/ara/duncan, clear (From Fox, Applied Regression Analysis. Use 'notes' command for source of data)
If we run the regression predicting prestige from educ and income, we see that Stata gives us the estimate for the coefficients for educ and income, as well as confidence intervals that correspond to the values shown on page 122.
regress prestige educ income
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 2, 42) = 101.22
Model | 36180.9458 2 18090.4729 Prob > F = 0.0000
Residual | 7506.69865 42 178.73092 R-squared = 0.8282
---------+------------------------------ Adj R-squared = 0.8200
Total | 43687.6444 44 992.90101 Root MSE = 13.369
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prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .5458339 .0982526 5.555 0.000 .3475521 .7441158
income | .5987328 .1196673 5.003 0.000 .3572343 .8402313
_cons | -6.064663 4.271941 -1.420 0.163 -14.68579 2.556463
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Page 123, shows a Test of All Slopes that tests the hypothesis that all of the slopes (coefficients) are 0. Stata provides this test in the top right portion of the regression table above. In fact, you can see that the Analysis of Variance table from the bottom of page 123 corresponds to the top left and top right portion of the Stata output above.
Page 125 shows how you can test whether a subset of the slopes are equal to 0. Fox shows how to test whether the coefficient for educ is significantly different from 0. You can inspect the regression table above and look at the t value and P>|t| value from the table to see that the t value is 5.556 and the p value is 0.000 indicating that the coefficient for educ is significantly different from 0. Had you wanted to test 2 or more coefficients, then you could use the test command as illustrated below. As you see, the test command gives an F test that corresponds to the value shown on page 125.
test educ
( 1) educ = 0.0
F( 1, 42) = 30.86
Prob > F = 0.0000