In re: High-Tech Employee Antitrust Litigation

Filing 716

Omnibus Declaration of Christina J. Brown in Support of #715 Reply re Joint Motion to Exclude the Expert Testimony of Edward E. Leamer, Ph.D. , #714 Reply to Joint Motion to Strike the Improper Rebuttal Testimony in Dr. Leamer's Reply Expert Report or, in the Alternative, MOTION for Leave to Submit a Reply Report of Dr. Stiroh filed by Apple Inc.. (Attachments: #1 Exhibit A, #2 Exhibit B, #3 Exhibit C, #4 Exhibit D, #5 Exhibit E, #6 Exhibit F, #7 Exhibit G, #8 Exhibit H, #9 Exhibit I, #10 Exhibit J, #11 Exhibit K, #12 Exhibit L, #13 Exhibit M, #14 Exhibit N, #15 Exhibit O, #16 Exhibit P, #17 Exhibit Q)(Related document(s) #715 , #714 ) (Brown, Christina) (Filed on 2/27/2014) Modified text on 2/28/2014 (dhmS, COURT STAFF).

EXHIBIT I

OMNIBUS BROWN DECLARATION

Stata 13 help for regress

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Stata 13 help for regress
Title
[R] regress -- Linear regression
Syntax
regress depvar [indepvars] [if] [in] [weight] [, options]
options
Description
------------------------------------------------------------------------Model
noconstant
suppress constant term
has user-supplied constant
hascons
tsscons
compute total sum of squares with constant; seldom
used
SE/Robust
vce(vcetype)
Reporting
level(#)
beta
eform(string)
depname(varname)
display_options

vcetype may be ols, robust, cluster clustvar,
bootstrap, jackknife, hc2, or hc3
set confidence level; default is level(95)
report standardized beta coefficients
report exponentiated coefficients and label as
string
substitute dependent variable name; programmer's
option
control column formats, row spacing, line width,
display of omitted variables and base and empty
cells, and factor-variable labeling

noheader
suppress output header
suppress coefficient table
notable
plus
make table extendable
mse1
force mean squared error to 1
coeflegend
display legend instead of statistics
------------------------------------------------------------------------indepvars may contain factor variables; see fvvarlist.
depvar and indepvars may contain time-series operators; see tsvarlist.
bootstrap, by, fp, jackknife, mfp, mi estimate, nestreg, rolling,
statsby, stepwise, and svy are allowed; see prefix.
vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate
prefix.
Weights are not allowed with the bootstrap prefix.
aweights are not allowed with the jackknife prefix.
hascons, tsscons, vce(), beta, noheader, notable, plus, depname(), mse1,
and weights are not allowed with the svy prefix.
aweights, fweights, iweights, and pweights are allowed; see weight.
noheader, notable, plus, mse1, and coeflegend do not appear in the dialog

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box.
See [R] regress postestimation for features available after estimation.
Menu
Statistics > Linear models and related > Linear regression
Description
regress fits a model of depvar on indepvars using linear regression.
Here is a short list of other regression commands that may be of
interest. See estimation commands for a complete list.
Command
Description
------------------------------------------------------------------------areg
an easier way to fit regressions with many dummy
variables
arch
regression models with ARCH errors
arima
ARIMA models
boxcox
Box-Cox regression models
cnsreg
constrained linear regression
eivreg
errors-in-variables regression
etregress
linear regression with endogenous treatment effects
frontier
stochastic frontier models
gmm
generalized method of moments estimation
heckman
Heckman selection model
intreg
interval regression
ivregress
single-equation instrumental-variables regression
ivtobit
tobit regression with endogenous variables
newey
regression with Newey-West standard errors
nl
nonlinear least-squares estimation
nlsur
estimation of nonlinear systems of equations
qreg
quantile (including median) regression
reg3
three-stage least-squares (3SLS) regression
rreg
a type of robust regression
gsem
generalized structural equation models
sem
linear structural equation models
sureg
seemingly unrelated regression
tobit
tobit regression
truncreg
truncated regression
xtabond
Arellano-Bond linear dynamic panel-data estimation
xtdpd
linear dynamic panel-data estimation
xtfrontier
panel-data stochastic frontier model
xtgls
panel-data GLS models
xthtaylor
Hausman-Taylor estimator for error-components models
xtintreg
panel-data interval regression models
xtivreg
panel-data instrumental-variables (2SLS) regression
xtpcse
linear regression with panel-corrected standard errors
xtreg
fixed- and random-effects linear models
xtregar
fixed- and random-effects linear models with an AR(1)
disturbance
xttobit
panel-data tobit models
------------------------------------------------------------------------Options

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+-------+
----+ Model +-----------------------------------------------------------noconstant; see [R] estimation options.
hascons indicates that a user-defined constant or its equivalent is
specified among the independent variables in indepvars. Some caution
is recommended when specifying this option, as resulting estimates
may not be as accurate as they otherwise would be. Use of this
option requires "sweeping" the constant last, so the moment matrix
must be accumulated in absolute rather than deviation form. This
option may be safely specified when the means of the dependent and
independent variables are all reasonable and there is not much
collinearity between the independent variables. The best procedure
is to view hascons as a reporting option -- estimate with and without
hascons and verify that the coefficients and standard errors of the
variables not affected by the identity of the constant are unchanged.
tsscons forces the total sum of squares to be computed as though the
model has a constant, that is, as deviations from the mean of the
dependent variable. This is a rarely used option that has an effect
only when specified with noconstant. It affects only the total sum
of squares and all results derived from the total sum of squares.
+-----------+
----+ SE/Robust +-------------------------------------------------------vce(vcetype) specifies the type of standard error reported, which
includes types that are derived from asymptotic theory (ols), that
are robust to some kinds of misspecification (robust), that allow for
intragroup correlation (cluster clustvar), and that use bootstrap or
jackknife methods (bootstrap, jackknife); see [R] vce_option.
vce(ols), the default, uses the standard variance estimator for
ordinary least-squares regression.
regress also allows the following:
vce(hc2) and vce(hc3) specify an alternative bias correction for the
robust variance calculation. vce(hc2) and vce(hc3) may not be
specified with the svy prefix. In the unclustered case,
vce(robust) uses (sigma-hat_j)^2={n/(n-k)}(u_j)^2 as an estimate
of the variance of the jth observation, where u_j is the
calculated residual and n/(n-k) is included to improve the
overall estimate's small-sample properties.
vce(hc2) instead uses u_j^2/(1-h_jj) as the observation's
variance estimate, where h_jj is the diagonal element of the hat
(projection) matrix. This estimate is unbiased if the model
really is homoskedastic. vce(hc2) tends to produce slightly more
conservative confidence intervals.
vce(hc3) uses u_j^2/(1-h_jj)^2 as suggested by Davidson and
MacKinnon (1993), who report that this method tends to produce
better results when the model really is heteroskedastic.
vce(hc3) produces confidence intervals that tend to be even more
conservative.

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See Davidson and MacKinnon (1993, 554-556) and Angrist and
Pischke (2009, 294-308) for more discussion on these two bias
corrections.
+-----------+
----+ Reporting +-------------------------------------------------------level(#); see [R] estimation options.
beta asks that standardized beta coefficients be reported instead of
confidence intervals. The beta coefficients are the regression
coefficients obtained by first standardizing all variables to have a
mean of 0 and a standard deviation of 1. beta may not be specified
with vce(cluster clustvar) or the svy prefix.
eform(string) is used only in programs and ado-files that use regress to
fit models other than linear regression. eform() specifies that the
coefficient table be displayed in exponentiated form as defined in
[R] maximize and that string be used to label the exponentiated
coefficients in the table.
depname(varname) is used only in programs and ado-files that use regress
to fit models other than linear regression. depname() may be
specified only at estimation time. varname is recorded as the
identity of the dependent variable, even though the estimates are
calculated using depvar. This method affects the labeling of the
output -- not the results calculated -- but could affect subsequent
calculations made by predict, where the residual would be calculated
as deviations from varname rather than depvar. depname() is most
typically used when depvar is a temporary variable (see [P] macro)
used as a proxy for varname.
depname() is not allowed with the svy prefix.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt),
pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation
options.
The following options are available with regress but are not shown in the
dialog box:
noheader suppresses the display of the ANOVA table and summary statistics
at the top of the output; only the coefficient table is displayed.
This option is often used in programs and ado-files.
notable suppresses display of the coefficient table.
plus specifies that the output table be made extendable.
often used in programs and ado-files.

This option is

mse1 is used only in programs and ado-files that use regress to fit
models other than linear regression and is not allowed with the svy
prefix. mse1 sets the mean squared error to 1, thus forcing the
variance-covariance matrix of the estimators to be (X'DX)^-1 (see
Methods and formulas in [R] regress) and affecting calculated
standard errors. Degrees of freedom for t statistics is calculated
as n rather than n-k.

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Stata 13 help for regress

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coeflegend; see [R] estimation options.
Examples:

linear regression

Setup
. sysuse auto
Fit a linear regression
. regress mpg weight foreign
Fit a better linear regression, from a physics standpoint
. gen gp100m = 100/mpg
. regress gp100m weight foreign
Obtain beta coefficients without refitting model
. regress, beta
Suppress intercept term
. regress weight length, noconstant
Model already has constant
. regress weight length bn.foreign, hascons
Examples:

regression with robust standard errors

----------------------------------------------------------------------. sysuse auto, clear
. generate gpmw = ((1/mpg)/weight)*100*1000
. regress gpmw foreign
. regress gpmw foreign, vce(robust)
. regress gpmw foreign, vce(hc2)
. regress gpmw foreign, vce(hc3)
----------------------------------------------------------------------. webuse regsmpl, clear
. regress ln_wage age c.age#c.age tenure, vce(cluster id)
----------------------------------------------------------------------Example:

weighted regression

. sysuse census
. regress death medage i.region [aw=pop]
Examples:

linear regression with survey data

Setup
. webuse highschool
Perform linear regression using survey data
. svy: regress weight height
Setup
. generate male = sex == 1 if !missing(sex)
Perform linear regression using survey data for a subpopulation
. svy, subpop(male): regress weight height

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Video example
Simple linear regression in Stata
Stored results
regress stores the following in e():
Scalars
e(N)
e(mss)
e(df_m)
e(rss)
e(df_r)
e(r2)
e(r2_a)
e(F)
e(rmse)
e(ll)
e(ll_0)
e(N_clust)
e(rank)

number of observations
model sum of squares
model degrees of freedom
residual sum of squares
residual degrees of freedom
R-squared
adjusted R-squared
F statistic
root mean squared error
log likelihood under additional assumption of
i.i.d. normal errors
log likelihood, constant-only model
number of clusters
rank of e(V)

Macros
e(cmd)
e(cmdline)
e(depvar)
e(model)
e(wtype)
e(wexp)
e(title)
e(clustvar)
e(vce)
e(vcetype)
e(properties)
e(estat_cmd)
e(predict)
e(marginsok)
e(asbalanced)
e(asobserved)

regress
command as typed
name of dependent variable
ols or iv
weight type
weight expression
title in estimation output when vce() is not ols
name of cluster variable
vcetype specified in vce()
title used to label Std. Err.
b V
program used to implement estat
program used to implement predict
predictions allowed by margins
factor variables fvset as asbalanced
factor variables fvset as asobserved

Matrices
e(b)
e(V)
e(V_modelbased)

coefficient vector
variance-covariance matrix of the estimators
model-based variance

Functions
e(sample)

marks estimation sample

References
Angrist, J. D., and J.-S. Pischke. 2009. Mostly Harmless Econometrics:
An Empiricist's Companion. Princeton, NJ: Princeton University
Press.

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Davidson, R., and J. G. MacKinnon. 1993. Estimation and Inference in
Econometrics. New York: Oxford University Press.

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2/27/2014