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id gender height weight 1 F 56 117 2 F 60 125 3 F 64 133 4 F 68 141 5 F 72 149 6 F 54 109 7 F 62 128 8 F 65 131 9 F 65 131 10 F 70 145 11 M 64 211 12 M 68 223 13 M 72 235 14 M 76 247 15 M 80 259 16 M 62 201 17 M 69 228 18 M 74 245 19 M 75 241 20 M 82 269 |
The parameter estimates (coefficients) for females and males are shown below, and the results do seem to suggest that height is a stronger predictor of weight for males (3.19) than for females (2.1).use http://www.ats.ucla.edu/stat/stata/faq/compreg2, clear sort gender by gender: regress weight height
We can compare the regression coefficients of males with females to test the null hypothesis Ho: Bf = Bm, where Bf is the regression coefficient for females, and Bm is the regression coefficient for males. To do this analysis, we first make a dummy variable called female that is coded 1 for female, and 0 for male and femht that is the product of female and height. We then use female height and femht as predictors in the regression equation.-> gender=F Source | SS df MS Number of obs = 10 ---------+------------------------------ F( 1, 8) = 359.81 Model | 1319.56112 1 1319.56112 Prob > F = 0.0000 Residual | 29.3388815 8 3.66736019 R-squared = 0.9782 ---------+------------------------------ Adj R-squared = 0.9755 Total | 1348.90 9 149.877778 Root MSE = 1.915 ------------------------------------------------------------------------------ weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- height | 2.095872 .110491 18.969 0.000 1.84108 2.350665 _cons | -2.39747 7.053272 -0.340 0.743 -18.66234 13.8674 ------------------------------------------------------------------------------ -> gender=M Source | SS df MS Number of obs = 10 ---------+------------------------------ F( 1, 8) = 669.93 Model | 3882.53627 1 3882.53627 Prob > F = 0.0000 Residual | 46.3637317 8 5.79546646 R-squared = 0.9882 ---------+------------------------------ Adj R-squared = 0.9867 Total | 3928.90 9 436.544444 Root MSE = 2.4074 ------------------------------------------------------------------------------ weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- height | 3.189727 .1232367 25.883 0.000 2.905543 3.473912 _cons | 5.601677 8.930197 0.627 0.548 -14.99139 26.19475 ------------------------------------------------------------------------------
The output is shown belowgenerate female=. replace female = 1 if gender == "F" replace female = 0 if gender == "M" generate femht = female*height regress weight female height femht
The term femht tests the null hypothesis Ho: Bf = Bm. The T value is -6.52 and is significant, indicating that the regression coefficient Bf is significantly different from Bm.Source | SS df MS Number of obs = 20 ---------+------------------------------ F( 3, 16) = 4250.11 Model | 60327.0974 3 20109.0325 Prob > F = 0.0000 Residual | 75.7026131 16 4.73141332 R-squared = 0.9987 ---------+------------------------------ Adj R-squared = 0.9985 Total | 60402.80 19 3179.09474 Root MSE = 2.1752 ------------------------------------------------------------------------------ weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- female | -7.999147 11.37055 -0.703 0.492 -32.10363 16.10533 height | 3.189727 .1113503 28.646 0.000 2.953675 3.425779 femht | -1.093855 .1677774 -6.520 0.000 -1.449528 -.7381831 _cons | 5.601677 8.068862 0.694 0.497 -11.50355 22.7069 ------------------------------------------------------------------------------
Parameter
Variable Estimate
INTERCEP 5.601677 : This is the intercept for the males (omitted group)
This corresponds to the intercept for males in
the separate groups analysis.
FEMALE -7.999147 : Intercept Females - Intercept males
This corresponds to differences of the
intercepts from the separate groups analysis.
and is indeed -2.397470040 - 5.601677149
HEIGHT 3.189727 : Slope for males (omitted group), i.e. Bm.
FEMHT -1.093855 : Slope for females - Slope for males
(i.e. Bf - Bm).
From the separate groups, this is indeed
2.095872170 - 3.189727463 .
Note that we constructed all of the variables manually to make it very clear
what each variable represented. However, in day to day use, you would
probably be more likely to use the xi prefix to generate the dummy
variables and interactions for you. For example,
xi: regress weight i.female*height
i.female _Ifemale_0-1 (naturally coded; _Ifemale_0 omitted)
i.female*height _IfemXheigh_# (coded as above)
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 3, 16) = 4250.11
Model | 60327.0974 3 20109.0325 Prob > F = 0.0000
Residual | 75.7026131 16 4.73141332 R-squared = 0.9987
-------------+------------------------------ Adj R-squared = 0.9985
Total | 60402.8 19 3179.09474 Root MSE = 2.1752
------------------------------------------------------------------------------
weight | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ifemale_1 | -7.999147 11.37055 -0.70 0.492 -32.10363 16.10533
height | 3.189727 .1113503 28.65 0.000 2.953675 3.425779
_IfemXheig~1 | -1.093855 .1677774 -6.52 0.000 -1.449528 -.7381831
_cons | 5.601677 8.068862 0.69 0.497 -11.50355 22.7069
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