business research techniques

8/9/2019 Business Research Techniques

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Exchange rate

In finance, an exchange rate(also known as a foreign-exchange rate, forex rate, FXrateor Agio) between two currenciesis the rate at which one currency will be exchanged foranother. It is also regarded as the value of one countrys currency in terms of another currencyFor example, an interbank exchange rate of !"apanese yen("#$, %) to the &nited 'tatesdollar(&') means that %! will be exchanged for each &'! or that &'! will be exchangedfor each %!. xchange rates are determined in theforeign exchange market, which is open to awide range of different types of buyers and sellers where currency trading is continuous* +hours a day except weekends. -n exchange rate thus has two components, the domestic currencyand a foreign currency, and can be uoted either directly or indirectly. In a direct uotation, theprice of a unit of foreign currency is expressed in terms of the domestic currency. In an indirectuotation, the price of a unit of domestic currency is expressed in terms of the foreign currency.-n exchange rate that does not have the domestic currency as one of the two currencycomponents is known as a cross currency, or cross rate also known as a currency uotation, theforeign exchange rate or forex rate.-n exchange rate has a base currency and a counter currency.

In a direct uotation, the foreign currency is the base currency and the domestic currency is thecounter currency. In an indirect uotation, the domestic currency is the base currency and theforeign currency is the counter currency. /ost exchange rates use the &' dollar as the basecurrency and other currencies as the counter currency. 0owever, there are a few exceptions tothis rule, such as the euro and 1ommonwealth currencies like the 2ritish pound, -ustralian dollarand 3ew 4ealand dollar.xchange rates can be floating or fixed. 5hile floating exchange rates 6in which currency rates are determined by market force 6 are the norm for most ma7or nations,some nations prefer to fix or peg their domestic currencies to a widely accepted currency like the&' dollar.xchange rates can also be categori8ed as the spot rate 6 which is the current rate 6 ora forward rate, which is the spot rate ad7usted for interest rate differentials.

9he spot exchange raterefers to the current exchange rate. 9heforward exchange raterefersto an exchange rate that is uoted and traded today but for delivery and payment on a specificfuture date. In the retail currency exchange market, a different buying rateand selling rate willbe uoted by money dealers. /ost trades are to or from the local currency. 9he buying rate is therate at which money dealers will buy foreign currency, and the selling rate is the rate at whichthey will sell the currency. 9he uoted rates will incorporate an allowance for a dealer:s margin(or profit) in trading, or else the margin may be recovered in the form of a ;commission; or insome other way.


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Nominal Effective Exchange Rate - NEER

9he unad7usted weighted average value of a country:s currency relative to all ma7or currenciesbeing traded within an index or pool of currencies. 9he weights are determined by theimportance a home country places on all other currencies traded within the pool, as measured bythe balance of trade.9he 3= represents the relative value of a home country:s currencycompared to the other ma7or currencies being traded (&.'. dollar, "apanese yen, euro, etc.). -higher 3= coefficient (above !) means that the home country:s currency will usually be worthmore than an imported currency, and a lower coefficient (below !) means that the home currencywill usually be worth less than the imported currency. 9he 3= also represents the approximaterelative price a consumer will pay for an imported good.90 nominal exchange rate is simplythe price of one currency in terms of the number of units of some other currency. 9his isdetermined by fiat in a fixed rate regime and by demand and supply for the two currencies in theforeign exchange rate market in a floating rate regime. It is :nominal: because it measures onlythe numerical exchange value, and does not say anything about other aspects such as thepurchasing power of that currency. In a floating rate regime, an increase in the value of thedomestic currency against other currencies is called an appreciation, while a decrease in value iscalled depreciation.In contrast, an increase in the exchange rate in a fixed rate regime is called arevaluation (for an increase) and a decrease in the exchange value of the domestic currency isreferred to as a devaluation.

Maret rate9he maret rate(going rate) for goods or services is the usual price charged for them in a freemarket.If demandgoes up, manufacturers and laborers will tend to respond by increasing theprice they reuire, thus setting a higher market rate. 5hen demand falls, market rates also tend tofall.9he term >market rate? refers to the level of compensation an organi8ation must provide toenable it to effectively compete against other organi8ations in attracting and retaining ualifiedemployees. 5age rates differ among organi8ations and among employees in the sameorgani8ation.It is critical that the organi8ation first identify those organi8ations with which itcompetes in the recruitment and retention of ualified employees and limit market comparisonsto those relevant employers. #ublic and private sector organi8ations within the state of @ansasrepresent the primary organi8ations with whom the 'tate of @ansas competes. 'ome 7obs, e.g.drivers license examiners, are uniue to state government. 9he wage rates of relevant stategovernments are used in conducting market comparisons for such 7obs. 5age rates comparisonsfor other 7obs, e.g. tax examiners, include both instate organi8ations and other state governments.Argani8ations conduct compensation surveys or use relative compensation surveys conducted bythird party sources, such as consulting firms, to identify the wage rates paid by relevant

organi8ations. Argani8ations use the data from these surveys to establish wage rates whichenable the organi8ation to effectively compete in attracting ualified employees and providecompetitive wage rates which effectively reward the employees for their added value as theygrow and contribute throughout their career.
http://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Demandhttp://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Free_markethttp://en.wikipedia.org/wiki/Demand


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!E"ER#$%E&A$"'('")

In statistics, when the standard deviations of a variable, monitored over a specific amount of

time, are nonBconstant. 0eteroskedasticity often arises in two forms, conditional and

unconditional. 1onditional 0eteroskedasticity identifies nonBconstant volatility when future

periods of high and low volatility cannot be identified. &nconditional 0eteroskedasticity is used

when futures periods of high and low volatility can be identified. !etero(different or uneual) is

the opposite of homo (same or eual* $edasticmeans spread or scatter.

5hen variance of error term is not constant but (assumption C of the 1D=/ states that the

disturbances should have a constant (eual) variance independent of t*

Var (ut) =2

9herefore, having an eual variance means that the disturbances are homoskedastic.

0eteroskedasticity arises also when one uses grouped data rather than individual data.

0eteroskedasticity can occur in time series data also.

(onse+uences of !eterosedasticity,

9he conseuences of0eteroskedasticityare*

!) AD' estimators are not 2D&. AD' estimators still unbiased and consistent. 2ecause

none of the explanatory variables is correlated with error term.+) 0eteroskedasticity affects the variance of E (1oBefficient of explanatory variables) and

therefore making the AD' estimators inefficientG) 9 H FBtests are misleading means underestimates the variances of the estimators, leading

to higher values of t and F statistics

&etecting !eterosedasticity,

9wo ways in general*

9he first is the informal way which is done through graphs and therefore we call it the

graphical method.

'catter plot of =esidual 'uare (u2t) and both variables (dependent H independent).

If values seem constant then there will be no 0eteroskedasticity.

#lot the suare of the obtained residuals against fitted $ and the s and see the patterns.


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Numerical methods,

-=10 method

5hite test

AR(! Method,

0oJ 9here is no 0eteroskedasticity

0!J 9here is 0eteroskedasticity

hite (riteria,

0oJ 9here is no 0eteroskedasticity

0!J 9here is 0eteroskedasticity

FB'tats and pB values are the decision criteria of 0eteroskedasticity

Resolving !eterosedasticity,

Ane method is used to remove*

Kuick Lestimate euations optionsL coefficient covariance matrix ('elect white)Lok

(.A$$'(A. .'NEAR RE/RE$$'#N M#&E.,


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/odelstatisticalBtool used in predicting future valuesof a target(dependent)variableon the

basis of thebehaviorof a set of explanatory factors(independent variables). - type ofregression

analysismodel, it assumesthe target variable is predictable, not chaotic or random

Assumptions of classical linear regression model,

01 9he dependent variable is linearly related to the coefficients of the model and the mode is

correctly specified.21 9he independent variable(s) isare uncorrelated with the euation error term.31 9he mean of the error term is 8ero.41 9he error term has a constant variance (homoscedastic error). 3o 0eteroskedasticity.51 9he error terms are uncorrelated with each other. 3o autocorrelation or serial correlation.61 3o perfect multicollinearity. 3o independent variable has a perfect linear relationship

with any of the other independent variables.

71 9he error term is normally distributed (optional assumption for hypothesis testing).

Multicollineraity

/ulticollinearity is a statistical phenomenon in which two or more predictor variables in a

multiple regression model are highly correlated, meaning that one can be linearly predicted from

the others with a nonBtrivial degree of accuracy. In this situation the coefficient estimates of the

multiple regressions may change erratically in response to small changes in the model or the

data. /ulticollinearity does not reduce the predictive power or reliability of the model as a

whole, at least within the sample data themselvesM it only affects calculations regarding

individual predictors. 9his is, a multiple regression model with correlated predictors can indicate

how well the entire bundle of predictors predicts the outcome variable, but it may not give valid

results about any individuals predictor, or about which predictors are redundant with respects to

others. - high degree of multicollinearity can also prevent computer software packages from

performing the matrix inversion reuired for computing the regression coefficients, or it may

make the results of that inversion inaccurate.

'o, when explanatory variables are very highly correlated with each other (correlation

coefficients either very close to ! or to B!), the problem of multicollinearity occurs.

/ulticollinearity refers to situation in which two or more explanatory variables in a multiple

regression model are highly linearly related. 5e have perfect multicollinearity if, for example as

in the euation above, the correlation between two independent variables is eual to ! or B!. In

practice, we rarely face perfect multicollinearity in a data set. /ore commonly, the issue of

multicollinearity arises when there is approximate linear relationship one two or more

independent variables. /ulticollinearityM freuently economic variables share a common time
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trend. For example, prices will be affected by inflation. If there is little variation in the relative

prices, the common trend will result multicollinearity.

"ypes of multicollinearity,

9here are two types of multicollinearity

8erfect multicollinearity

'mperfect multicollinearity

8erfect multicollinearity,

#erfect multicollinearity indicates a perfect linear relationship between the independentvariables, or

N!x! O N+x+ O ... O Nkxk J P,

5here Ni are constants (not all eual 8ero). #erfect multicollinearityM usually by construction of

dummy variables.

5e observe thatX2J2X1

9herefore, although it seems that there are two explanatory variables in fact it is only one. 9his is

becauseX1is an exact linear function ofX2or becauseX1andX2are perfectly collinear.

(onse+uences of perfect multicollinearity,

&nder the perfect multicollinearity, the AD' estimators simply do not exist

If you try to estimate an euation in Qiews and your euation specification suffer from

perfect multicollinearity, Qiews will not give you results but will give you an error

message mentioning multicollinearity.

'mperfect multicollinearity,

5hen there is nonBexact linear relationship among the independent variable or there is imperfect

correlation (rROB!). Imperfect multicollinearity (or near multicollinearity) exists when the

X1 ! + G C S

X2 + S T !P !+


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explanatory variables is an euation are correlated, but this correlation is less than perfect. 9his

can be expressed as*X2=2X1+v

5here v is a random variable that can be viewed as the Uerror in the exact linear relationship. In

this case estimation of AD' is possible but results are not reliable

X1=1, 2,3,4,5

X2= 5,6,7,12,11

Q J G, +, !, G, !

5e may have high =+but very few significant coefficients.

=esults may change with very small changes in data. =esults are very sensitive to small changes.

0igh value of coBefficient and tHfBstat are not reliable. ither we can over estimate or under

estimate the significant of coBefficient.

(onse+uences of imperfect multicolinearity,

5hen imperfect multicollinearity is present*

(a) stimates of the AD' may be imprecise because of large standard errors

(b) -ffected coBefficient may fail to attain statistical significance due to low tBstats

(c) 'ign reversal might exist

(d) -ddition to deletion of few observations may result in substantial changes in the estimated coBefficient

&etecting multicollinearity,

'imple correlation coBefficient* If their is high correlation among the regressionindependent

variables there will be multicollinearity.

0igh =+with insignificant coBefficient*

Qariance Inflating Factor (QIF)* It is also a measure of multicollinarity, higher the =+ will lead to

higher QIF that indicates the higher degree of multicollinearity. QIFJ !!B=+

9olerance (9oD)* 5hen multicollinearity is higher then tolerance will be smaller. 9oDJ!QIF

Resolving multicollinearity,

9he easiest ways to >solve? the problems are*

(a)


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(c) &se a longer run of data(d) 'witch to higher freuency(e) /ulticollinearity is a problem caused by the particular sample available. 1onseuently, the

best solution is to get more andor better data (or incorporate information). Freuently no

good solution.

A9"#(#RRE.A"'#N

9here should be no correlation coBvariance among the disturbance term of two different time

period assumption six of the 1D=/ state that the correlation and covariance between different

disturbances are 8ero

1AQ(Wt Ws)JA

$ER'A. 'N&E8EN&EN(E

9his assumption state that the disturbance Wtand Ws are independently distributed which is called

serial independence.

If this assumption is no longer valid than the disturbances are not independent but pair wise auto

correlated

(A9$E$ #F A9"# (#RRE.A"'#N

-uto correlation most likely to occur in time series data

In crossBsectional we can change the arrangement of the data without altering the result

01 #M'"E& :AR'A;.E$

Ane factor of autocorrelation is omitted variables

'uppose ytis related to +tand Gt but we wrongfully do not include Gtin our

model It means if we exclude the important independent variable of dependent

variable

21 M'$$8E('F'(A"#N

-nother reason is misspecification

'uppose $t is related to +t with a uadratic relationship*

$tJ E!O E+++t O Wt


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2ut we wrongfully assume estimate a straight line*

$tJ E! O E+x++tO Wt

9hen the error term obtained the straight lion will depend on ++t

31 $)$"EMA"'( ERR#R$ #F MEA$9REMEN"

'uppose a company updates its inventory at a given time

If a systematic error occurred then the cumulative inventory stock will be exhibit

accumulated measurement

9hese errors will be show up is auto correlated procedure

#R&ER #F A9"#(#RRE.A"E&

!'9 Arder -utocorrelation

+ndArder -utocorrelation

F'R$" #R&ER A9"# (#RE.A"'#N

If the residual is depending on its on value that is called !

st

order autocorrelation we cancall it -=(!)

9he coefficient of X is called the firstBorder autocorrelation coefficient in ranges from B!

to O!.

It is obvious that the si8e of p will determine the strength of serial correlation.

9here can be three different cases

(a) If p is 8ero , then we have no autocorrelation(b) If p approaches unity, the value of the previous observation of the error become more

important in determing the value of the current error and therefore high degree-utocorrelation exists. In this case we have positive autocorrelation.

(c) If p approaches B! , we have high degree of negative autocorrelation.

!'/!ER #R&ER A9"#(#RRE.A"'#N


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If residual is depending on its p previous term then it is calledpith order of

autocorrelation

'1A3< order occurs when*

WtJ p! WtB! Op+ WtB+ O pG WtBG O et

pBth order occurs when *

WtJ p! WtB! Op+ WtB+ O pG WtBG OYYppWt 6 p O et


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(#N$E


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&9R;'N A"$#N "E$"

9he following assumptions should be satisfied*

!. 9he regression model have a constant

+. -utocorrelation is assumed to be of firstBorder onlyG. 9he euation does not includes a lagged dependent variable like explanatory variable. If its value is in between !.ZC to +.+C there is no autocorrelation. 9he value nearest to +

the less will be the autocorrelation.

&RA;A(%$ #F "!E &9R;'N A"$#N "E$"

!. /ay conclude inconclusive result+. 3ot applicable when a lagged dependent variable is used in the testG. 1ant take into account higher order auto correlation.


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&9MM) :AR'A;.E$*

9hese are categorical variables those show the absence or presence of the characteristics

- dummy variable is one that takes the value P or ! to indicate the presence or absence of

categorical effect that may be expected to change the outcome.

9se of &ummy :ariables

9here are categorical variables which show the absence or presence of the characteristics.Forinstance if we divide the population in 5hite and nonBwhite. 5e assume a dummy variable.

'ntercept &ummy :ariable

9he assumption is that increase in income depends upon experience but is there any differencebetween the initial (Intercept) income of white and nonBwhite employees. 5e will construct the

regression model as*

Yi=1+2X2i+3Di+ui

9$E #F &9MM) :AR'A;.E$

ntering this dummy in the euation we have the following model*

Yi=1+2X2i+3Di+ui

5e have two cases*

Di=0 (Non-white) Yi=1+2X2i+ 3(0)+uiYi=1+2X2i+ui

Di=1 (white) Yi=1+2X2i+3(1)+ui Yi= (1+3)+2X2i+ui

!# "# #8ERA"E

1reate


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AR'MA Models

2ox and "enkins (!ZS) first introduced -=I/- models, the term is derived from*

[ -= J autoregressive[ I J integrated[ /- J moving average

5hen any variable is regressed on its own lagged (previous) value.

Yt = 0+1Yt-1 + ut it is -=(!) process

Yt = 0 +1Yt-1 +2Yt-2+ ------ pYt-p+ ut -=(p) process

Autoregressive models

9he implication behind the -=(!) model is that the time series behaviour of Ytis largely

determined by its own value in the preceding period.

'o, what will happen in t is largely dependent on what happened in t \!, or alternatively what

will happen in t O ! will be determined by the behaviour of the series in the current time t.

"he AR( p) model

[ - generali8ation of the -=(!) model is the -=(p) modelM the number in parenthesisdenotes the order of the autoregressive process and therefore the number of laggeddependent variables that the model will have.

[ For example, the -=(+) model will be an autoregressive model of order two, and willhave the form*

Yt = 0 +1Yt-1 +2Yt-2+ ut

'imilarly, the -=(G) model will be an autoregressive model of order three, and will have the

form*

Yt = 0 +1Yt-1 +2Yt-2+ 3Yt-3+ ut

In general the -=(p) model will be an autoregressive model of orderp, and will havep lagged

terms, as in*

Yt = 0 +1Yt-1 +2Yt-2+ 3Yt-3+ ------ pYt-p+ ut

&sing the summation symbol*

$tJ EPOp]iJ!EiYt\i+ ut


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Moving Average Models

"he MA>0* model, 5hen lags (previous) values of error term are included in regression model,

it is called /- process

9he simplest moving average model is that of order one, or the /-(!) model, which has theform*

Yt = 0+1ut-1 + ut

9hus, the implication behind the /-(!) model is that Ytdepends on the value of the immediate

past error, which is known at time t.

"he MA >+* model

9he general form of the /- model has the form*

Yt = 0 +1ut-1 +2ut-2+ ------ qut-q+ ut

&sing the summation symbol*

Yt J0O i=1 iut\! + ut

$tationarity

- key concept underlying time series processes is that of 'tationarity. - time series is covariance

stationary when it has the following three characteristics* In its simplest terms a time series Ytis

said to be stationary if*

(a)"(Yt) J constant for all tM

(b) #$%(Yt) J constant for all tM and

(c) &ov(Yt) J constant for all t

or if its mean, its variance and its covariance remain constant over time.

9hese uantities would remain the same whether observations for the time series were, for

example, from !ZC to !TC or from !TC to !C.

'tationary is important because if the series is nonBstationary then all typical results of theclassical regression analysis are not valid.

=egressions with nonBstationary series may have no meaning and are therefore called ?spurious@.


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ARMA >Autoregressive Moving Average* Model

5hen variables are depending on its own value or previous value, previous or next value of error

term so we can say that there is -=/- exist in the data.

-=/- (p,) ^-=(p) and /-()_ it will be used when yt is stationary at level or I(P) (order ofintegration is 8ero).

Yt = 0 +1Yt-1 +2Yt-2+ ------ pYt-p O1ut-1 +2ut-2+ ------ qut-q+ ut

Ar

Yt J0O p]iJ!EiYt\I Oi=1 iut\! + ut

If there is no integration so we have exist in -=/-. 5hen data will be stationary so we will be

going for -=/- model for decision making.

AR'MA>Autoregressive 'ntegrated Moving Average* Model

In the stationary data the mean of the variables observations should be same. 9hen the variance

should be same and the coBvariance should be same.

5hen the data is nonBstationary at its original level series then we take the log of the data series

and then we will go for decision making of the data.

For contributing the nonBstationary data into stationary we will go for unit root test.

A&F, >Agmented &icyFuller "est*

For positive -


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E :iews Results

RE/RE$$'#N

(#RE.A"'#N

10-3V

=-9

3=

10-3V

=-9

!.PPPPPP P.TTCPG

3= P.TTCPG !.PPPPPP

:'F

Qariance Inflation Factors


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!E"R#$%E&A$"'('")

/raph

AR(!

0eteroskedasticity 9est* -=10

FBstatistic !P.S+Z+ #rob. F(!,+S) P.PPG!

Abs=Bsuared T.!+CGP #rob. 1hiB'uare(!) P.PP

9est uation*


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REM#:A.


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!'"E

0eteroskedasticity 9est* 5hite

FBstatistic .!TZ+ #rob. F(C,+G) P.PPG+

Abs=Bsuared !C.P!C+ #rob. 1hiB'uare(C) P.P!PG

'caled explained '' !Z.!ZZCP #rob. 1hiB'uare(C) P.PP+

9est uation*


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REM#:A.

'.. of regression !.+CZGT -kaike info criterion G.C!ZG

'um suared resid GZ.++P 'chwar8 criterion G.STZ+!G

Dog likelihood BC.PSGC 0annanBKuinn criter. G.C+CGP

FBstatistic TP.!+PPT


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$lope


23/24

Auto correlation graph

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 13.05087 Prob. F(2,24) 0.0001

Obs*R-squared 15.10827 Prob. !i-"quare(2) 0.0005

#est $quatio%&

'ee%de%t ariabe& R$"+'

et!od& east "quares

'ate& 012315 #i/e& 22&41

"a/e& 1 2

+%cuded obseratio%s& 2

Presa/e /issi% aue aed residuas set to ero.

ariabe oeicie%t "td. $rror t-"tatistic Prob.

$69$:R#$ 0.00153 0.020874 0.073710 0.41

$$R 0.000147 0.0252;2 0.005813 0.54

-0.120;45 1.088124 -0.110874 0.12;

R$"+'(-1) 0.051;0 0.128;5 4.;3228 0.0001

R$"+'(-2) -0.331245 0.13747 -1.70;73 0.1002

R-squared 0.52075 ea% dee%de%t ar -3.13$-15

d


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"u/ squared resid 18.70;07 "c!>ar criterio% 2.77

o i=ei!ood -34.7172 6a%%a%-?ui%% criter. 2.818088

F-statistic ;.525433 'urbi%-@atso% stat 1.47;27

Prob(F-statistic) 0.00105

&9R;'N A"$#N "E$"'ee%de%t ariabe& RA$#:R#$et!od& east "quares

'ate& 012415 #i/e& 14&51

"a/e& 1 2

+%cuded obseratio%s& 2

ariabe oeicie%t "td. $rror t-"tatistic Prob.

$$R -0.033541 0.034832 -0.;222 0.3445

$69$:R#$ -0.221124 0.028804 -7.;7;84 0.0000

33.7722 1.50503; 22.45;0 0.0000

R-squared 0.2825 ea% dee%de%t ar 15.;0;21

dar criterio% 3.483772

o i=ei!ood -45.4;375 6a%%a%-?ui%% criter. 3.38;;2;

F-statistic 1;8.288 Durbin-Watson stat 0.444!Prob(F-statistic) 0.000000

REM#:A. #F A9"#(#RRE.A"'#N

'ee%de%t ariabe& RA$#:R#$

et!od& east "quares

'ate& 012415 #i/e& 14&5

"a/e (adar criterio% 2.30;18

o i=ei!ood -24.5881; 6a%%a%-?ui%% criter. 2.17472;

F-statistic 254.448 'urbi%-@atso% stat 1.51;0;1

Prob(F-statistic) 0.000000

+%erted R Roots .5; -.5;

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