Download Stata Commands for Multiple Regression in Sociology: UNC Chapel Hill, Soci708-001 and more Study notes Statistics in PDF only on Docsity!
University of North Carolina Chapel Hill
Soci708-001 Statistics for Sociologists
Fall 2009
Professor François Nielsen
Stata Commands for Module 11 – Multiple Regression
For further information on any command in this handout, simply type help
followed by the name of the command in Stata.
See also the Stata and SAS Guide pdf (click on Documents in side bar; guide
is linked under Software Documentation).
1 Statistical Functions in Stata
The following statistical functions in Stata are useful for regression work. The
regression printout itself usually comprises all necessary statistics.
1.1 Normal Distribution Functions
The function normal(z) returns P ( Z ≤ z ), the area under the standard normal
curve to the left of z. (Compare with Table A.)
. display normal(1.207) .
The function invnormal(p) returns z such that P ( Z ≤ z ) = p , i.e. z such that
the area under the standard normal curve to the left of z is p. (Compare with
Table A and Table D, bottom row.)
. display invnormal(0.975)
1.2 Student t Distribution Functions
The function ttail(df, t) returns P ( T > t ), the area under the Student’s t
distribution with df degrees of freedom to the right of t. (Compare with Table
D.)
. display ttail(7, 1.960) .
The function invttail(df, p) returns t such that P ( T > t ) = p , i.e. t such
that the area under Student’s t distribution with df degrees of freedom to the
right of t is p. (Compare with Table D.)
. display invttail(7, 0.025)
1.3 F Distribution Functions
The function Ftail(n1, n2, f) returns P ( F > f ), the area under the F
distribution with n1 and n2 degrees of freedom to the right of f. (Compare
with Table E.)
. display Ftail(1, 14, 21.55) .
The function invFtail(n1, n2, p) returns f such that P ( F > f ) = p , i.e. f
such that the area under the F distribution with n1 and n2 degrees of freedom
to the right of f is p. (Compare with Table E.)
. display invFtail(1, 14, .00038068)
2 Descriptive Statistics, Correlations, and Scatterplot Matrix
I am using as an example the CSDATA from IPS6e (see Appendix D-2 for de-
scription). The units are 224 Computer Science majors at a large university. To
enter the data in Stata I retrieved the csdata.xls file in the CD-ROM, selected
the data and copied them to the clipboard (Ctrl-C). Then in Stata I opened the
Data Editor (Data -> Data Editor) and pasted the data (Ctrl-V). Then I closed
the Data Editor by clicking on ×. (You can save the data as a *.dta file if
desired with File -> Save ...) Then I listed the first 5 cases.
. list in 1/
+--------------------------------------------------+
| obs gpa hsm hss hse satm satv sex |
|---|
- | 1 3.32 10 10 10 670 600 1 |
- | 2 2.26 6 8 5 700 640 1 |
- | 3 2.35 8 6 8 640 530 1 |
- | 4 2.08 9 10 7 670 600 1 |
- | 5 3.38 8 9 8 540 580 1 | +--------------------------------------------------+
The response variable of interest is grade point average after three semesters
(gpa). The explanatory variables are high school grades in mathematics (hsm),
science (hss) and English or language arts (hse); SAT score in math (satm)
and verbal (satv); and sex (1=male, 2=female).
First I produced descriptive statistics for all the variables I intend to put in
the regression with the command su (for summarize).
. su hsm hss hse satm satv gpa
Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- hsm | 224 8.321429 1.638737 2 10 hss | 224 8.089286 1.699663 3 10 hse | 224 8.09375 1.507874 3 10 satm | 224 595.2857 86.40144 300 800 satv | 224 504.5491 92.61046 285 760 -------------+-------------------------------------------------------- gpa | 224 2.635223 .7793949 .12 4
Figure 1: Scatterplot matrix of variables for the gpa regression (CSDATA).
Produced with Stata command graph matrix hsm hss hse satm satv
gpa, half xsize(4) ysize(4)
. reg gpa hsm hss hse satm satv, level(99)
To obtain standardized coefficients (in place of the confidence intervals
shown by default) use the option beta.
. reg gpa hsm hss hse satm satv, beta
Source | SS df MS Number of obs = 224 -------------+------------------------------ F( 5, 218) = 11. Model | 28.6436439 5 5.72872878 Prob > F = 0. Residual | 106.819145 218 .489996078 R-squared = 0. -------------+------------------------------ Adj R-squared = 0. Total | 135.462789 223 .607456452 Root MSE =.
gpa | Coef. Std. Err. t P>|t| Beta -------------+---------------------------------------------------------------- hsm | .1459611 .039261 3.72 0.000. hss | .0359053 .0377984 0.95 0.343. hse | .0552926 .0395687 1.40 0.164. satm | .0009436 .0006857 1.38 0.170. satv | -.0004078 .0005919 -0.69 0.492 -. _cons | .3267187 .3999964 0.82 0..
Using the command vif after running a regression will calculate the vari-
ance inflation factors (VIF). These are measures of collinearity, the degree to
which each explanatory variable is associated with all the other explanatory
variables. A VIF above 10 is considered bothersome, but there is no VIF above
10 in this particular example. (We are not going to use vif in this class.)
. vif
Variable | VIF 1/VIF -------------+---------------------- hsm | 1.88 0. hss | 1.88 0. hse | 1.62 0. satm | 1.60 0. satv | 1.37 0. -------------+---------------------- Mean VIF | 1.
4 Analysis of Residuals
To calculate the predicted values of gpa and the gpa residuals I can use the
command predict, with the option xb and residuals, respectively, assign-
ing variable names of my choice. Then to check the distribution of residuals
I draw a histogram of the residuals (shown in Figure 2) and a normal quan-
tile plot of the residuals (shown in Figure 3). The only fancy options I use is
xsize(3.5) ysize(3.5) with the normal quantile plot, to make the plot
square. Together with the straight line that Stata draws automatically the
square format shows deviations of the plot from linearity better than a rect-
angular plot (compare with IPS6e Figure 11.5 p.620). We can see the left-skew
in the distribution.
Figure 3: Normal quantile plot of residuals for the gpa regression (CSDATA).
Produced by Stata command qnorm gparesid, xsize(3.5) ysize(3.5)
Figure 4: Residual plot for the gpa regression (CSDATA). Produced by Stata
command twoway (scatter gparesid gpapredict), yline(0)
for Stata; see IPS6e p.594 for formulas). I check the values for the first 5
observations. Note that the SE of forecast is always larger than the SE for
the mean response, as the SE of forecast contains individual variation in the
response variable in addition to uncertainty about the mean response.
. predict gpasepred, stdp . predict gpaseforecast, stdf . list gpapredict gpasepred gpaseforecast in 1/
+--------------------------------+
| gpapre~t gpasep~d gpasef~t |
|---|
- | 3.085806 .0871256 .7053984 |
- | 2.165682 .1740038 .7212998 |
- | 2.539919 .0932556 .7061818 |
- | 2.773967 .1156441 .7094855 |
- | 2.532883 .0898973 .7057461 | +--------------------------------+
