técnicas de proyección

UNIVERSIDAD NACIONAL AGRARIA LA MOLINA FACULTAD DE ECONOMA Y PLANIFICACINDEPARTAMENTO ACADMICO DE GESTIN EMPRESARIAL

Unidad 4: Tcnicas de proyeccin en estudios de mercadoPor: Ampelio Ferrando PereaFORMULACIN Y EVALUACIN DE PROYECTOS DE INVERSIN

TCNICAS DE PROYECCIN EN ESTUDIOS DE MERCADO SUMARIOLa tasa intertemporal. La tasa promedio.Correlacin lineal.

LA TASA INTERTEMPORALPara deducir el valor de la tasa de crecimiento intertemporal, se utiliza como base la frmula del inters compuesto

Df = Di (1 + t)n

LA TASA INTERTEMPORALPor ejemplo:Si la demanda de camote morado en TM para los aos del 2004 al 2010 ha sido:

Cul es la tasa de crecimiento?Cul es la demanda para los aos 2011, 2012 y 2013?

20042005200620072008200920105000490053005700550060006200

RESPUESTA a):Df= 6200Di= 5000n= 6t=?CLCULO DE LA TASA INTERTEMPORALt= 0.3650 t= 3.65%

RESPUESTA b):Di= 6200t=0.0365

FRMULA PARA PROYECCIN CON LA TASA INTERTEMPORALDf = Di (1 + t ) nDf(2011) = ?Df(2012) = ? Df(2013) = ?

RESPUESTA b):Di= 6200t=0.0365

PROYECCIN CON LA TASA INTERTEMPORALDf = Di (1 + t ) n

Df(2011) = 6200(1 + 0.0365 )= 6,426 TM

Df(2012) = 6200(1 + 0.0365 )= 6,661 TM

Df(2013) = 6200(1 + 0.0365 )= 6,904 TM

TCNICA DE LA TASA MEDIAConsidera el comportamiento de la variable dependiente respecto a la variable independiente: el tiempo, relacionando incrementos o decrementos porcentuales ao a ao.

CLCULO DE LA TASA MEDIACul es la demanda de aceite de soya para los aos: 2011, 2012 y 2013?

AoDEMANDA DE ACEITE DE SOYA( en miles de litros)Variacin porcentual (%)20014,62520024,03120035,72420045,89820055,61720066,04320076,37620085,98420096,06620106,413totalTasa media

Paso N 01: Clculo de los incrementos o decrementos de la demanda4,625 100%4,031 - XX= 87,16%Esto significa que la demanda en el 2000 representaron el 87.16% de la efectuada en 1999, es decir las ventas decrecieron en 100-87.10= 12.84%. Entonces: Decremento = -12.84De igual manera se calculan incrementos y decrementos para los aos siguientes

CLCULO DE LA TASA MEDIA


AoDemanda de aceite de soya( en miles de litros)Variacin porcentual (%)20014,625---20024,031-12.8420035,72420045,89820055,61720066,04320076,37620085,98420096,06620106,413totalTasa media


AoDemanda de aceite de soya( en miles de litros)Variacin porcentual (%)20014,625---20024,031-12.8420035,72442.0020045,8983.0420055,617-4.7620066,0437.5820076,3765.5.120085,984-6.1520096,0661.3720106,4135.72total41.47Tasa media4.61%

RESPUESTA :

PROYECCIN CON LA TASA INTERTEMPORALDf = Di (1 + t ) n Df(2011) = 6413 (1 + 0.0461 )= 6,709 miles de litrosDf(2012) = 6413 (1 + 0.0461)2 = 7,018 miles de litros Df(2013) = 6413 (1 + 0.0461)3 = 7,341 miles de litrosDATOS:

Di= 6413t=0.0461

REGRESIN LINEAL SIMPLEEs un modelo matemtico para predecir el efecto de una variable sobre otra, ambas cuantitativas. Una variable es la dependiente y otra la independienteSe grafica con el diagrama de dispersin.Dice cmo es la relacin entre las dos variables.El anlisis consiste en encontrar la mejor lnea recta de esos puntos.

SUPUESTOSLa variable X o independiente o predictora (est bajo el control del investigador), la variable Y es la variable dependiente o predicha. Los valores de X son fijos (seleccionados previamente por el investigador).Para cada X, existe un conjunto de valores de Y, que deben seguir una distribucin normal (es decir, los valores de Y deben ser normales), para aplicar con validez los procedimientos de inferencia y/o estimacin.Todas las varianzas de las subpoblaciones de Y son iguales.

DIAGRAMAS DE DISPERSIN ESTADSTICAGrfico de puntos para variables cuantitativas

Disposicin: Eje de abscisas: variable independiente (X) Eje de ordenadas: variable dependiente (Y)

Frecuentemente X es una variable controlada (no aleatoria)

Un punto por cada observacin (par de valores X-Y)

Aproximacin al tipo de relacin existente entre las variables

Para el clculo de la recta de regresin se aplica el mtodo de mnimos cuadrados entre dos variables. Esta lnea es la que hace mnima la suma de los cuadrados de los residuos, es decir, es aquella recta en la que las diferencias elevadas al cuadrado entre los valores calculados por la ecuacin de la recta y los valores reales de la serie, son las menores posibles.GRFICOS DE DISPERSIN / RECTA DE REGRESINy = a + bx

FORMAS TPICAS DE LOS DIAGRAMAS DE DISPERSIN ESTADSTICA

REGRESIN LINEAL

El parmetro b0, conocido como la ordenada en el origen, nos indica cunto vale Y cuando X = 0. El parmetro b1, conocido como la pendiente, nos indica cunto aumenta Y por cada aumento en X. La tcnica consiste en obtener estimaciones de estos coeficientes a partir de una muestra de observaciones sobre las variables Y y X. En el anlisis de regresin, estas estimaciones se obtienen por medio del mtodo de mnimos cuadrados. Logradas estas estimaciones se puede evaluar la bondad de ajuste y significancia estadstica.REGRESIN LINEAL

*Es adimensionalSlo toma valores entre -1y +1 Las variables NO estn correlacionadas r=0Relacin lineal perfecta entre dos variables r = +1 o r=-1Excluimos los casos de puntos alineados horiz. o verticalmente.Cuanto ms cerca est r de +1 o -1 mejor ser el grado de relacin lineal.Siempre que no existan observaciones anmalas.

PROPIEDADES DEL COEFICIENTE DE CORRELACIN r-1+10Relacin inversa perfectaRelacin directa casi perfectaVariablesNO correlacionadas

*Correlacin positivaCorrelacin negativar = + 10 r +1 -1 r 0r = - 1

Information

2Num1

Analysis of Data for Two Numerical Variables7

12

4

Sheets

Rodney Carr, 1997-2003

&LXLStatistics - 2Num&C&A

Data & Description

DatosDescricion119

YX102.44A3:A11

2.4410Two-variableScatterplot102.44B3:B11

6.320Number9206.3L3:L11

3.7330Covariance81.0601388889303.732NUM.XLS

8.1235coef.Corr0.9047977906358.120

94550.8186590419459

105656103

13.470Single-variable7013.4

10.275X7510.2

12.0777Number97712.07

MEDIA46.444444444418

DESV. T24.5617136572

Min10

Max77

Median45

Y

Number9

MEDIA8.3622222222Note: The above options only alter the appearance

DESV. T3.6475155167of the scatterplot. In particular, 'Swap axes' does not

Min2.44exchange the role of the explanatory and dependent

Max13.4variables.

Median9


Swap axes

Vertical axis going down

Data & Description

2.442.44

2.442.44

6.36.3

3.733.73

8.128.12

99

1010

13.413.4

10.210.2

12.0712.07

&LXLStatistics - 2Num&CScatterplot

X

Y

Y = 0.134 X + 2.122

Corr & Linear Regress

Correlation Analysisp

102.44XY = 0.134 X + 2.122

Correlation Coeff=0102.44103.4653209319

Correlation0.9047977906206.3n97712.467855926

303.73418

>0358.1224240

p-value=0.000398909145975.26

5610735.7758

7013.44143.89

7510.2Sxx4826.22

Constant TermSummaryConfidence Ints.7712.07Syy106.43

Set constantLevel0.950.8186590419Sxy648.48

term = 0EstimateSELowerUppers1.6605083909P3:P11

Slope0.13436619390.02390217470.07784657230.1908858156Q3:Q11

Constant2.12165899251.2404591588-0.81155871925.0548767043P3:Q11

Scatterplot with

Regression Line

Decimal places

3

X-Range for

Regression Line

Left10

Right77

Working for hypothesis tests

slopeinterceptcorr

T5.6215049641.71038198035.621504964

Hypothesis TestsANOVAcdf0.99960109090.93453150630.9996010909

SlopeConstantZ3.6694923849

=0=0cdf0.9998784513

Residuals212

Analysis

>00

p-value=0.0003989091p-value=0.1309369874

Prediction and Inverse Prediction

PredictionP.I. for YConfidence and

Level0.95Prediction

XYLowerUpperBands

02.1216589925-2.77946096097.022778946

488.57123630174.431433905112.7110386983

000

000

000

Inverse PredictionC.I. for X

(Calibration)Level0.95

YY-barXLowerUpper

2020.3666666667135.7856998034104.5350344498205.4484062712

20.1

21


Show equation

Alternative

>

Delete), moved or cut cells in a sheet ,- Removed series or legend entries in a chart.

Please close the workbook and re-try the analysis using a fresh copy of the original workbook. If the problem re-occurs please contact Rodney Carr, 14 McGhie Road, Allansford, Vic 3277, Australia Work: Deakin University Warrnambool, Warrnambool, Vic 3280, Australia Phone: 03 5563 3458 email: [email protected] details of how to reproduce the error.

When you press OK the updating routine for this workbook will no longer operate.

E-1

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Rgression Linaire

OK

Dans cette table il y a des stimes de la pente et du terme constant de la droite de rgression, avec une estime de l'cart type (s) de l'erreur commise en utilisant la droite plutt que les vraies valeurs, ainsi que la valeur du carr du coefficient de correlation R^2.

Typiquement on considre qu'il y a une correlation faible pour 0,2 < R < 0,8 et forte pour 0,8 < R, donc faible pour 0,04 < R^2 < 0,64 et forte pour 0,64 < R^2 . Mais attention, on peut avoir dans des cas particuliers un R lev sans relle correlation linaire - toujours vrifier graphiquement l'allure de la distribution!

Des intervalles de confiance usuels sur les paramtres sont aussi donns, avec le niveau de confiance en J12.

Si vous avez choisi de ne pas passer par l'origine ("Constant Term" pas obligatoirement nul), R^2 est la somme des carrs des variations expliqus par la rgression, divis par la sommes des carrs des variations autour de la moyenne; si le terme constant est = 0, R^2 est la somme des carrs des variations expliqus par la rgression, divix par la smme de carrs des valeurs.

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Prdiciton Inverse

OK

Cette table peut tre utilise pour une prdiciton inverse: Dterminer la valeur X unique l'origine des observations (plusieures) Y.

Entrez de 1 10 valeurs de Y (qui corrspondent l'unique X), dans les champs A57-A66. La valeur correspondante de X, avec un intervalle de confiance, est donne en C57-G57. Le niveau de confiance dans la prediction est en G55.

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Rgression linaire

OK

Ici il ya des rgressions linaire sur les variables de la feuille Data & Description.

Pour la plupart des calculs, on suppose que:1. Les observations sont indpendantes.2. La variance de l'erreur est constante (ne dpend pas de la valeur de la variable indpendante)3. L'erreur suit une distribution normale.

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Test d'hypothse pour la pente et le terme constant

OK

Les tests d'hypothse sur la pente et le terme constant peuvent tre conduits ici, avec les conditions usuelles. (cliquez sur "Linar Rgression" pour les voir).

Pour conduire le test, renseigner l'hypothse alternative en C36 ou G36 et avec les boutons d'options. L'hypothse H0 se met jour automatiquement.

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Paste Data

Coller

Annuler

Aide

J'ai copi

Il y a des donnes dans le presse-papiers d'Excel. Cochez les cases appropries puis cliquez Coller pour les coller dans la zone de donnes Data (Colonnes A et B).

Cliquez Aide pour voir d'autes faons d'entrer les donnes.

Mes donnes ont une premire ligne avec le nom de la variable

seulement la variable indpendante (X) (qui ira sur l'axe horizontal)

seulement la variable dpendante (Y) (qui ira sur l'axe vrtical)

les deux variables, la dpendante (Y) dans la premire colonne

les deux variables, la indpendante (X) dans la premire colonne

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Data

OK

Lier Donnes

Effacer donnes

Vos donnes vont dans les colonnes A et B. La variable dpendante (Y), qui va sur l'axe vertical du graphique, en colonne A; l'autre, (le X) en colonne B. Les noms des variables sonten A2 et B2, et les donnes cas par cas dans les lignes en dessous.

Les cas (lignes) vides, ou contenant des donnes non numriques, sont ignores dans l'analyse.

Echanger les variables

Remarque: Si vous avez choisi "Automatically enter data" dans les options de XL Statistics, les donnes slectionnes seront automatiquement lies quand un classeur XL Statistics est choisi depuis le menu XL Statistics.

On peut entrer les donnes normalement, mais on peut aussi:

Organisez vos donnes dans un autre classeur (pas celui-ci), avec les variables en colonnes et une occurrence dans chaque ligne. Vous pouvez avoir un titre en haut de chaque colonne.Copiez (ne Coupez pas) les donnes avec la variable que vous voulez analyser.Double-cliquez sur la cellule "Data", cochez ventuellement des options puis cliquez sur "Coller".

Copier des donnes colles:

*

1.

2.3.

Crer un lien entre Classeurs (les modifications des donnes d'origine seront mises jour dans le "Data" puis l'analyse.)

*

Si plus d'une variable est slectionne (plus d'une colonne), vous pouvez choisir celle que vous voulez analyser grce au menu droulant en haut de la zone Data.

Organisez vos donnes dans un autre classeur (pas celui-ci), avec les variables en colonnes et une occurrence dans chaque ligne. Vous devez avoir un titre en haut de chaque colonne.

1.

2.3.4.

Double-cliquez sur la cellule "Data", cette fentre apparat et cliquez sur "Lier Donnes".Slectionnez les donnes de toutes les variables, y compris le premire ligne de titre.Un petit "Link Data" toolbar apparat, vous pouvez Coller, ou Arrter tout avec le bouton stop.

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Scatterplot: Nuage de points

OK

Ce graphique est bas sur les donnes des colonnes A-B. Les champs vides ou contenant du texte sont ignors . Les lgendes sont les noms en A2 et B2.

Les axes du scatterplot / nuage de poinst peuvent tre changs "Swap axes", et la direction de l'axe vertical peut tre change - Mais cela ne change pas la variable indpendante et la variable dpendante dans les analyses suivantes! Tous les graphiques du classeur, pas seulement celui ci, seront modifis.

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Scatterplot (nuage de points) avec droite de rgression

OK

On peut afficher, en plus du nuage de points, une droite de rgression.Les lgendes des axes sons prises en A2 et B2 sur la feuille Data & Description.

La droite de rgression peut tre trace avec le bouton "Draw line", et son quation affiche avec "Show equation".

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An error has occurred .....

OK

Il y a eu une erreur dans la routine de mise jour (update) de XL Statistics dans 2Num.xls.Veuillez vrifier que vous n'avez PAS: - Sauvegard ce classeur sous un autre nom,- Supprim, dplac ou coup des cellules dans une feuille,- Enlev des sries ou lgendes dans un graphique.

Tentez de tout fermer et r-analysez les donnes avec une version non altre du classeur. Si le problme persiste, contactez (en anglais uniquement): Rodney Carr, 14 McGhie Road, Allansford, Vic 3277, Australia Work: Deakin University Warrnambool, Warrnambool, Vic 3280, Australia Phone: 03 5563 3458 email: [email protected] les dtails sur comment reproduire le problme.

Aprs avoir cliqu OK les routines de mise jour ne vont plus fonctionner.

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Linear regression

OK

In this table are least squares estimates of the slope and intercept, together with estimates of the standard deviation of the error term (s) and the R-square value.

2-sided confidence intervals for the parameters also given (usual assumptions apply). The confidence level is in J12.

If you have chosen to allow a non-zero in your model = 0, the R2-value is the ratio of the sum of squares due to the regression to the corrected sum of squares (about the mean); if the constant term is set = 0 the R2 value is the ratio of the sum of squares due to the regression to the total (uncorrected) sum of squares.

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Inverse Prediction

OK

This table can be used for Inverse Prediction - determining the value of a single X-value given a number of observations of the corresponding Y-value.

Enter up to 10 values of Y that correspond to a single value of X in A57-A66. The corresponding value of X, with a confidence interval, is given in C57-G57. The level of confidence for the prediction is in G55.

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Linear regression

OK

In this box are analyses for a linear relationship between the variables on the Data & Description sheet.

Most of the results assume that1. Observations are independent2. The variance of the error term is constant (doesn't depend on the value of the independent variable)3. The error term is normally distributed.

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Hypothesis tests for Slope and Constant term

OK

Hypothesis tests for the slope and constant term can be carried out in this box. Usual assumptions apply.

To conduct an hypothesis test, fill in the information for the Alternative Hypothesis by setting the value in C36 or G36 and using the option buttons. The information for the Null Hypothesis, H0, is determined automatically.

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Paste Data

Paste

Cancel

Help

I have copied

You have data in Excel's clipboard. Click the appropriate buttons below and press Paste if you wish to copy it into the workbook's Data area (Columns A and B).

Press Help to see other ways of entering data.

My data has a header row with the name of the variable(s)

only the independent (X) variable (to go on the horizontal axis)

only the dependent (Y) variable (to go on the vertical axis)

both variables, dependent (Y) in first column

both variables, independent (X) in first column

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Data

OK

Link data

Clear data

Your data goes in Columns A and B. The dependent variable (on the vertical axis) goes in Column A; the independent one (on the horizontal axis) goes in Column B. The names of the variables go in A2 and B2; case-by-case data row-wise underneath.

Cases (rows) in the data with non-numbers (including blanks) are ignored in the analysis.

Swap variables

Note: If you have clicked "Automatically enter data" in the XLStatistics options, highlighted data will be automatically linked when an XLStatistics workbook is selected from the XLStatistics menu.

Regular operations can be used to enter data but for convenience you can also

Organize your data in a separate workbook (i.e. not this one), with variables in columns and each row a separate case. You can have a header row at the top of each column naming the variables.Copy (don't cut) the data for the variable you wish to analyse.Double-click on the cell labelled "Data", select options and click "Paste".

Paste copied data:

*

1.

2.3.

Link to your data workbook (data is not actually copied and changes to the original data are reflected in the analysis):

*

When linking, if data for more than one variable is highlighted the actual variable to be analysed is chosen using the drop-down list that appears at the top of the Data section.

Organize your data in a separate workbook (i.e. not this one), with variables in columns and each row a separate case. You must have a header row at the top of each column naming the variables.

1.

2.3.4.

Double-click on the cell labelled "Data" and click "Link data".Highlight the data for all variables, including the header row with their names.Click the "Paste" button (picture of a clipboard) on the Link Data toolbar. Click "Stop" to cancel.

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Scatterplot

OK

This scatterplot is based on the data in Columns A-B. Any text or blanks are ignored.

The axis titles are the same as the names you put in A2 and B2.

The axes in the scatterplot can be swapped and the direction of the vertical axis changed - this does NOT change the independent and dependent variables in subsequent analysis. All charts in the workbook (not just this one) are altered, too.

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Scatterplot with regression line

OK

This is a scatterplot of the data to which can be added a regression line, etc.

The axis titles are the same as the names in A2 and B2 on the Data & Description sheet.

The regression line can be drawn by clicking the "Draw line" box.

The equation of the line can be drawn by clicking the "Show equation" box. The number of decimal places can be altered by using the "Decimal places" button.

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OK

There has been an error in the routine used in updating the XLStatistics workbook 2Num.xls.Please check that you have NOT: - Saved this workbook under a different name,- Deleted (using Edit -> Delete), moved or cut cells in a sheet ,- Removed series or legend entries in a chart.



Information

2Num1


12

4

Sheets



Data & Description

DatosDescricion119

YX102.44A3:A11

2.4410Two-variableScatterplot102.44B3:B11

6.320Number9206.3L3:L11

3.7330Covariance81.0601388889303.732NUM.XLS

8.1235coef.Corr0.9047977906358.120

94550.8186590419459

105656103

13.470Single-variable7013.4

10.275X7510.2

12.0777Number97712.07

MEDIA46.444444444418

DESV. T24.5617136572

Min10

Max77

Median45

Y

Number9




Max13.4variables.

Median9


Swap axes


Data & Description

2.442.44

2.442.44

6.36.3

3.733.73

8.128.12

99

1010

13.413.4

10.210.2

12.0712.07


X

Y

Y = 0.134 X + 2.122



102.44XY = 0.134 X + 2.122

Correlation Coeff=0102.44103.4653209319

Correlation0.9047977906206.3n97712.467855926

303.73418

>0358.1224240

p-value=0.000398909145975.26

5610735.7758

7013.44143.89

7510.2Sxx4826.22

Constant TermSummaryConfidence Ints.7712.07Syy106.43

Set constantLevel0.950.8186590419Sxy648.48

term = 0EstimateSELowerUppers1.6605083909P3:P11

Slope0.13436619390.02390217470.07784657230.1908858156Q3:Q11

Constant2.12165899251.2404591588-0.81155871925.0548767043P3:Q11

Scatterplot with

Regression Line

Decimal places

3

X-Range for

Regression Line

Left10

Right77


slopeinterceptcorr

T5.6215049641.71038198035.621504964

Hypothesis TestsANOVAcdf0.99960109090.93453150630.9996010909

SlopeConstantZ3.6694923849

=0=0cdf0.9998784513

Residuals212

Analysis

>00

p-value=0.0003989091p-value=0.1309369874



Level0.95Prediction

XYLowerUpperBands

02.1216589925-2.77946096097.022778946

488.57123630174.431433905112.7110386983

000

000

000



YY-barXLowerUpper

2020.3666666667135.7856998034104.5350344498205.4484062712

20.1

21


Show equation

Alternative

>




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Rgression Linaire

OK





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Prdiciton Inverse

OK



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Rgression linaire

OK



LR-33

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OK



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Paste Data

Coller

Annuler

Aide

J'ai copi








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Data

OK

Lier Donnes

Effacer donnes








*

1.

2.3.


*



1.

2.3.4.


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Linear regression

OK




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Inverse Prediction

OK



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Linear regression

OK



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OK



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Paste Data

Paste

Cancel

Help

I have copied








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Data

OK

Link data

Clear data



Swap variables




Paste copied data:

*

1.

2.3.


*



1.

2.3.4.


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Scatterplot

OK




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Information

2Num1


12

4

Sheets



Data & Description

DatosDescricion119

YX2.442.44A3:A11

2.442.44Two-variableScatterplot2.442.44B3:B11

6.36.3Number96.36.3L3:L11

3.733.73Covariance13.30436944443.733.732NUM.XLS

8.128.12coef.Corr18.128.120

995199

101010103

13.413.4Single-variable13.413.4

10.210.2X10.210.2

12.0712.07Number912.0712.07

MEDIA8.362222222218

DESV. T3.6475155167

Min2.44

Max13.4

Median9

Y

Number9




Max13.4variables.

Median9


Swap axes


Data & Description

2.442.44

2.442.44

6.36.3

3.733.73

8.128.12

99

1010

13.413.4

10.210.2

12.0712.07


X

Y

Y = X



2.442.44XY = X

Correlation Coeff=02.442.442.442.44

Correlation16.36.3n913.413.4

3.733.7375.26

>08.128.12735.7758

p-value=09975.26

1010735.7758

13.413.4735.7758

10.210.2Sxx106.43

Constant TermSummaryConfidence Ints.12.0712.07Syy106.43

Set constantLevel0.951Sxy106.43

term = 0EstimateSELowerUppers0P3:P11

Slope1011Q3:Q11

Constant0000P3:Q11

Scatterplot with

Regression Line

Decimal places

3

X-Range for

Regression Line

Left2.44

Right13.4


slopeinterceptcorr

T000

Hypothesis TestsANOVAcdf000

SlopeConstantZ0

=0=0cdf0

Residuals212

Analysis

>00

p-value=0p-value=0



Level0.95Prediction

XYLowerUpperBands

0000

48484848

000

000

000



YY-barXLowerUpper

2020.366666666720.366666666720.366666666720.3666666667

20.1

21


Show equation

Alternative

>




E-1

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Rgression Linaire

OK





Sum-33

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Prdiciton Inverse

OK



IP-33

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Rgression linaire

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LR-33

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*



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2.3.4.


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SP-33

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OK



RL-33

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E-33

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Linear regression

OK




Sum-34

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Inverse Prediction

OK



IP-34

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Linear regression

OK



LR-34

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OK



HT-34

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Paste Data

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DP-34

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Data

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*

1.

2.3.


*



1.

2.3.4.


D-34

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Scatterplot

OK




SP-34

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RL-34

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Information

2Num1


12

4

Sheets



Data & Description

DatosDescricion119

YX2.442.44A3:A11

2.442.44Two-variableScatterplot2.442.44B3:B11

6.36.3Number96.36.3L3:L11

3.733.73Covariance13.30436944443.733.732NUM.XLS

8.128.12coef.Corr18.128.120

995199

101010103

13.413.4Single-variable13.413.4

10.210.2X10.210.2

12.0712.07Number912.0712.07

MEDIA8.362222222218

DESV. T3.6475155167

Min2.44

Max13.4

Median9

Y

Number9




Max13.4variables.

Median9


Swap axes


Data & Description

2.442.44

2.442.44

6.36.3

3.733.73

8.128.12

99

1010

13.413.4

10.210.2

12.0712.07


X

Y

Y = X



2.442.44XY = X

Correlation Coeff=02.442.442.442.44

Correlation16.36.3n913.413.4

3.733.7375.26

>08.128.12735.7758

p-value=09975.26

1010735.7758

13.413.4735.7758

10.210.2Sxx106.43

Constant TermSummaryConfidence Ints.12.0712.07Syy106.43

Set constantLevel0.951Sxy106.43

term = 0EstimateSELowerUppers0P3:P11

Slope1011Q3:Q11

Constant0000P3:Q11

Scatterplot with

Regression Line

Decimal places

3

X-Range for

Regression Line

Left2.44

Right13.4


slopeinterceptcorr

T000

Hypothesis TestsANOVAcdf000

SlopeConstantZ0

=0=0cdf0

Residuals212

Analysis

>00

p-value=0p-value=0



Level0.95Prediction

XYLowerUpperBands

0000

48484848

000

000

000



YY-barXLowerUpper

2020.366666666720.366666666720.366666666720.3666666667

20.1

21


Show equation

Alternative

>




E-1

&A

Page &P

Rgression Linaire

OK





Sum-33

&A

Page &P

Prdiciton Inverse

OK



IP-33

&A

Page &P

Rgression linaire

OK



LR-33

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Page &P


OK



HT-33

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Page &P

Paste Data

Coller

Annuler

Aide

J'ai copi








DP-33

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Page &P

Data

OK

Lier Donnes

Effacer donnes








*

1.

2.3.


*



1.

2.3.4.


D-33

&A

Page &P


OK



SP-33

&A

Page &P


OK



RL-33

&A

Page &P


OK




E-33

&A

Page &P

Linear regression

OK




Sum-34

&A

Page &P

Inverse Prediction

OK



IP-34

&A

Page &P

Linear regression

OK



LR-34

&A

Page &P


OK



HT-34

&A

Page &P

Paste Data

Paste

Cancel

Help

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DP-34

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Data

OK

Link data

Clear data



Swap variables




Paste copied data:

*

1.

2.3.


*



1.

2.3.4.


D-34

&A

Page &P

Scatterplot

OK




SP-34

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OK





RL-34

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OK




*RELACIN DIRECTA E INVERSAPara valores de X por encima de la media tenemos valores de Y por encima y por debajo en proporciones similares. Para los valores de X mayores que la media le corresponden valores de Y menores. Esto es relacin inversa o decreciente.Para los valores de X mayores que la media le corresponden valores de Y mayores tambin.

Para los valores de X menores que la media le corresponden valores de Y menores tambin. : relacin directa.

Grfico2

64

60

57

77

59

66

61

56

80

65

68

58

77

79

90

52

87

62

67

57

67

84

82

39

78

80

62

76

63

Fuerte relacindirecta.

Hoja1

U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY

0.28209279550.43902892560.5950575838-0.15343165490.240574730317010168605630.9-10515.007333035264

0.64467139160.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8913679189r real68.034482758611.651499115160

0.52906420850.05769547650.9438398223-1.57441758131.587849599815464.757

0.15091860160.83860121620.662221620.98872529190.41853406418063.377

0.38291326010.11387091140.8898571326-1.20619659021.225769024915864.459

0.80245455060.53754795820.49822607190.0942580074-0.004446566317162.566

0.11746811110.4698249680.2895794741-0.0757096811-0.554613554216961.461

0.86564616830.3623377610.1713417684-0.3522171708-0.94887622916660.956

0.72234555310.73047812450.95883435740.61425949151.737316244417664.880

0.36700411250.23698741340.9235514845-0.71602651771.429373400616364.665

0.55871606050.66471351180.41045670910.425361854-0.22637041217462.168

0.36175725350.36272675970.3066671094-0.351179888-0.505319802116661.558

0.02931380190.55083439150.98900851930.12776961942.290661080417164.977

0.10217523180.95588578090.26399508291.7048173074-0.631076828718761.379

0.674278420.96558168580.90703611441.81948976781.322722601118864.590

0.29968969140.18906278910.2130066129-0.8813550865-0.796032136316161.152

0.4637865090.99697854840.14927259042.7454502187-1.039558342319760.787

0.05863233950.53765111760.21743730330.0945177443-0.780877165217161.162

0.03953363160.48295272630.6630831527-0.04274403060.420892443517063.367

0.47112297050.29005181210.3509696513-0.5532332659-0.382704066516461.857

0.11002076870.81017356710.08427214430.8785359286-1.376896737117960.467

0.72529657960.92592929540.84805634671.44612792141.028132991718464.284

0.34903498890.76293712660.97270838780.71578211881.922178021417764.982

0.08395255020.01684722430.1804037537-2.1237079846-0.913827366714960.939

0.7093228480.66791730920.95659177340.43416954991.712435064817464.878

0.47101695160.82722099210.8991330750.94324021231.276627697317964.580

0.06880909080.34869066750.5972566326-0.38885794170.24625268491666362

0.98540780370.70237231980.86871606940.53123577421.120342661417564.376

0.90136719850.20987961530.8718443876-0.80683880891.13515322216264.463

Hoja1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

r=0,9

Hoja2

Hoja3

Grfico8

35

44

63

24

55

29

25

24

42

52

24

29

53

6

26

31

-8

21

34

32

6

27

43

41

44

34

37

37

50

Cierta relacininversa

Hoja1

U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY

0.84371190120.43902892560.5950575838-0.15343165490.240574730317010168605630.7200-110.547735582135

0.30590917570.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.6931993739r real33.103448275915.166534911244

0.54534119620.05769547650.9438398223-1.57441758131.587849599815464.763

0.0072148870.83860121620.662221620.98872529190.41853406418063.324

0.06873210250.11387091140.8898571326-1.20619659021.225769024915864.455

0.22930547090.53754795820.49822607190.0942580074-0.004446566317162.529

0.22035700920.4698249680.2895794741-0.0757096811-0.554613554216961.425

0.33751465980.3623377610.1713417684-0.3522171708-0.94887622916660.924

0.94280061720.73047812450.95883435740.61425949151.737316244417664.842

0.45618808030.23698741340.9235514845-0.71602651771.429373400616364.652

0.43446345790.66471351180.41045670910.425361854-0.22637041217462.124

0.0769471430.36272675970.3066671094-0.351179888-0.505319802116661.529

0.90921836350.55083439150.98900851930.12776961942.290661080417164.953

0.64487470180.95588578090.26399508291.7048173074-0.631076828718761.36

0.52577301590.96558168580.90703611441.81948976781.322722601118864.526

0.82811615720.18906278910.2130066129-0.8813550865-0.796032136316161.131

0.14010696520.99697854840.14927259042.7454502187-1.039558342319760.7-8

0.20183218220.53765111760.21743730330.0945177443-0.780877165217161.121

0.40518825040.48295272630.6630831527-0.04274403060.420892443517063.334

0.5651346180.29005181210.3509696513-0.5532332659-0.382704066516461.832

0.39841003820.81017356710.08427214430.8785359286-1.376896737117960.46

0.99631192490.92592929540.84805634671.44612792141.028132991718464.227

0.9907412970.76293712660.97270838780.71578211881.922178021417764.943

0.28160519090.01684722430.1804037537-2.1237079846-0.913827366714960.941

0.8559068880.66791730920.95659177340.43416954991.712435064817464.844

0.07287398850.82722099210.8991330750.94324021231.276627697317964.534

0.90676773640.34869066750.5972566326-0.38885794170.24625268491666337

0.57726642110.70237231980.86871606940.53123577421.120342661417564.337

0.54484823190.20987961530.8718443876-0.80683880891.13515322216264.450

Hoja1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

0

0

0

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0

0

0

0

0

0

0

0

r=-0,7

Hoja2

Hoja3

REGRESIN LINEAL

REGRESIN LINEALEjemplo: Proyectar la demanda de arroz en miles de toneladas

Cul ser la demanda de arroz para los aos: 2011, 2012 y 2013?

AoDemanda de arroz( en miles de TM)200112200214200315200413200516200719200818200920201022

REGRESIN LINEAL

REGRESIN LINEAL

XYXYX2 Y211221431541351661971882092245149

XYXYX2Y2112122142831545413425168061911471812682016092219845149815

XYXYX2 Y21121211442142841963154592254134216169516802525661911436361718126493248201606440092219881484451498152852559

CLCULO DE b:b= (9x815)-(45)(149)= 630 = 1.166 (9x285)- (45)2 540

CLCULO DE a:a= 149 - 1.1666 (45) = 10.7225 9 9

ECUACIN DE LA RECTAY = 10.7225 + 1.1666x

CLCULO DEL COEFICIENTE DE CORRELACIN r r= 9(815) (45) (149)___________________ (9( 285) (2,025) ) (9(2,559) (22,201)

r= 7,335 6,705_______________________ = 630 = 0.9410 (2,565 2,025) (23,031 22,201) 669.48

r= 0.94

INTERPRETACIN DEL COEFICIENTE DE CORRELACIN rr= 0.94 Existe una muy alta correlacin entre las variables X y Y

PROYECCIN CON ECUACIN DE LA RECTAY = 10.7225 + 1.1666xY (2011) = 10.7225 + 1.1666(10)= 22.389 miles de TMLuego, la proyeccin para los aos 2011, 2012 y 2013 seran:

Y (2013) = 10.7225 + 1.1666(12)= 24.722 miles deTMY (2012) = 10.7225 + 1.1666(11)= 23.555 miles de TM

REGRESIN NO LINEAL

AJUSTE DE VARIABLES A FUNCIONES NO LINEALES Hacer el diagrama de dispersin de las dos variables y evaluar si el patrn resultante sigue la forma lineal o alguna otra funcin.

Identificada dicha funcin, sustituir los valores de una variable con sus valores cuadrados, raz cuadrada, logartmicos o con alguna otra modificacin, y hacer de nuevo la matriz de correlacin.

Identificar la funcin que mejor ajuste por medio de un paquete estadstico y determinar los coeficientes para la construccin de esa ecuacin. EXPONENCIAL:y = a * bxPARABLICA:y = a + b x + c x2nPOTENCIAL: y = a * xbFUNCIONES NO LINEALES

FUNCIONES NO LINEALESExponencialesLogartmicas

técnicas de proyección

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