### Stata Textbook Examples Applied Regression Analysis Chapter 9: Statistical Theory for Linear Models

Linear Contrasts on page 209 using the data file friendly. Stata does not have a built-in contrast command; however, ATS has developed a program that will do ANOVA contrasts. You can download contrast from within Stata by typing findit contrast (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
use http://www.ats.ucla.edu/stat/stata/examples/ara/friendly, clear
(From Fox, Applied Regression Analysis.  Use 'notes' command for source of data)

encode(cond), gen(mycond)
codebook mycond

mycond ------------------------------------------------- Experimental Condition
type:  numeric (long)
label:  mycond

range:  [1,3]                        units:  1
unique values:  3                    coded missing:  0 / 30

tabulation:  Freq.   Numeric  Label
10         1  Before
10         2  Meshed
10         3  SFR

sort mycond
by mycond: summarize correct

-> mycond=  Before
Variable |     Obs        Mean   Std. Dev.       Min        Max
---------+-----------------------------------------------------
correct |      10        36.6   5.337498         24         40

-> mycond=  Meshed
Variable |     Obs        Mean   Std. Dev.       Min        Max
---------+-----------------------------------------------------
correct |      10        36.6   3.025815         30         40

-> mycond=     SFR
Variable |     Obs        Mean   Std. Dev.       Min        Max
---------+-----------------------------------------------------
correct |      10        30.3   7.334091         21         39

anova correct mycond, class(mycond)

Number of obs =      30     R-squared     =  0.2433
Root MSE      = 5.52067     Adj R-squared =  0.1873

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |      264.60     2      132.30       4.34     0.0232
|
mycond |      264.60     2      132.30       4.34     0.0232
|
Residual |      822.90    27  30.4777778
-----------+----------------------------------------------------
Total |     1087.50    29       37.50

contrast mycond, values( -0.5 -0.5 1)

Contrast variable mycond (-.5 -.5 1)
source           SS          df      MS        Dep Var  =  correct
---------+---------------------------------    N of obs =       30
contrast |      264.6         1    264.6000    F        =     8.68
error    |      822.9        27     30.4778    Prob > F =   0.0065
---------+---------------------------------

contrast mycond, values( 1 -1 0)

Contrast variable mycond (1 -1 0)
source           SS          df      MS        Dep Var  =  correct
---------+---------------------------------    N of obs =       30
contrast |          0         1      0.0000    F        =     0.00
error    |      822.9        27     30.4778    Prob > F =   1.0000
---------+---------------------------------
Calculation on page 214 and on page 222 using data file duncan.
use http://www.ats.ucla.edu/stat/stata/examples/ara/duncan.dta, clear
(From Fox, Applied Regression Analysis.  Use 'notes' command for source of data)

set matsize 50
gen c=1
mkmat c income educ, matrix(X)
mkmat prestige, matrix(y)
matrix b=inv(X'*X)*X'*y
matrix list b

b[3,1]
prestige
c  -6.0646629
income   .59873282
educ   .54583391
Calculation on page 222.
matrix r=y-X*b
matrix v=(r'*r)/42
matrix V2=v*inv(X'*X)
matrix d=diag(vecdiag(V2))
matrix a=cholesky(d)
matrix list a

symmetric a[3,3]
c     income       educ
c  4.2719412
income          0  .11966735
educ          0          0  .09825264

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