statistik dan ekonometrik

5/24/2018 Statistik Dan Ekonometrik

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Oleh:

Prof. Tri Widodo, Ph.D


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Statistics is the science

of collecting, organizing,

presen ng, ana yz ng,

and interpreting

in making more

effective decisions.

First PhD Class: Lets cross the street and do your

economics!

What is Meant by Statistics?


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Statistical techniques are

used extensively by

marketing, accounting,quality control,

,

sports people, hospital

educators, politicians,

physicians, and many

others.

Who Uses Statistics?


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Descri tive StatisticsDescri tive Statistics: Methods of or anizinsummarizing, and presenting data in an informative way.

EXAMPLE : Election Result

Types of Statistics


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Inferential StatisticsInferential Statistics:: A decision, estimate,prediction, or generalization about a population,based on a sample.

A PopulationPopulation A SampleSample is as a

of all possibleindividuals

portion, or part,

of the population

objects, ormeasurements of

nterest.

Types of Statistics


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Contoh: Hasil penelitian heboh mengenai virginitas: 93%

Sampling

Sampel

Parameter Statistics

Statistik Inferensi

Ho:; H1:


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DATA

Qualitative or attribute Quantitative or numerical

discrete

(number of children)

continuous

(time taken for an exam)

Summary of Types of Variables


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Describing Data: Frequency Distributions and GraphicDescribing Data: Frequency Distributions and GraphicPresentationPresentation

.

,

polygon, and cumulative frequency polygon.

Present data using such graphic techniques as line

, , .


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The three commonly used graphic forms are

Histograms, Frequency PolygonsHistograms, Frequency Polygons and a

Cumulative FrequencyCumulative Frequencydistribution.

H stogram s a graph n wh ch the class

midpoints or limits are marked on the horizontal.

The class frequencies are represented by the

adjacent to each other.

Graphic Presentation of aFrequency Distribution


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, ,

variance, and the standard deviation of ungrouped data.

Explain the characteristics, uses, advantages, and

disadvantages of each measure of dispersion.


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It is calculated byTheArithmetic MeanArithmetic Mean is3- 11

summ ng e va uesand dividing by thenumber o values.

the most widely used

measure of location and

the data.

The major characteristics of the mean are:Average

Joe

It requires the interval scale.

ll values are used.

It is unique.

The sum of the deviations from the mean is 0.

Characteristics of the Mean


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e s e

midpoint of the values after

There are as manyvalues above thefrom the smallest to the

lar est.

the data array.

For an even set of values, the median will be thearithmetic avera e o the two middle numbers and is

found at the (n+1)/2 ranked observation.

The Median


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TheModeMode is another measure of location and

represents the value of the observation that appearsmost frequently.

Data can have more than one mode. If it has twomodes, it is referred to as bimodal, three modes,

trimodal, and the like.


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is ersionis ersion

30

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refers to the

spread or 1520

variability inthe data.0

5

10

0 2 4 6 8 10 12

easures o spers on nc u e e o ow ng: ,,

mean deviation, variance, and standardmean deviation, variance, and standard

deviationdeviation.

value Measures of Dispersion


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s2 = (X - X)-

2ss =

Sample variance and standard deviation


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Chapter Four

DataData

Develop and interpret a stem-and-leaf display.

Develop and interpret a dot plot.

Compute and interpret quartiles, deciles, and percentiles.

Compute and understand the coefficient of variation and the

coefficient of skewness.

Draw and interpret a scatter diagram.


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Dot Plot

Dot plots: Report the details of each observation

Dot Plot


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Stem-and-leaf Displays

Note: an advanta eStem-and-lea

of the stem-and-leafdisplay over adisplay: A statisticaltechnique forrequency

distribution is we do

not lose the identit

sp ay ng a se odata. Each

numerical value isof each observation.divided into two

parts: the leading

stem and thetrailing digits the

Stem-and-leaf Displays

leaf.


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ox p ot is a graphicaldisplay, based on quartiles,

data.

are needed to

construct a box plot:the inimum Value,the First Quartile,

,Third Quartile, andtheMaximum

Box Plots

a ue.


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Q1 Q3MaxMin Median

12 14 16 18 20 22 24 26 28 30 32


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Skewness is the

lack of symmetry ofthe distribution.

Thecoefficient ofA value o 0 indicates a s mmetric

s ewnesscan rangefrom -3.00 up to 3.00

distribution.

formula:

Some software packages use a different formula

which results in a wider range for the coefficient.

MedianXsk = 3Movie


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diagram: A

techni ue

ar a es mus e a eas n erva sca e .

used to showthe

Relationship can be positive (direct) or

relationship

between .

Example

The twelve days of stock prices and the overall marketindex on each day are given as follows:

Scatter diagram


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Estimation an on i ence Interva sEstimation an on i ence Interva s

.

.


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con idence interval

A point estimate is

is a range of values

w i t h i n w h i c h t h e(statistic) used to

e s t i m a t epopulation parameter

is expected to occur.population value( p a r a m e t e r ) .

The two confidencen erva s a are use

extensively are then Interval Estimate

s t a t e s t h e r a n g e.

population parameter

Point and Interval Estimates


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standard deviation is

unknown, the

s

underlying population

is approximately

normal and the sam le

n

size is less than 30 we

use the t distribution.

The value of t for a given confidence level depends

upon its degrees of freedom.

Point and Interval Estimates


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Confidence interval for the mean

szX

95% CI for the population mean

s

X 96.1 n

s

Intervals for n.


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Ekonometrik

Ekonomi Matematika


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Linear Regression an orre ationLinear Regression an orre ation

Draw a scatter diagram.

Understand and interpret the terms dependent variable and independent

variable.

Calculate and interpret the coefficient of correlation, the coefficient of

determination, and the standard error of estimate.

Conduct a test of hypothesis to determine if the population coefficient of

correlation is different from zero.

Calculate the least squares regression line and interpret the slope and interceptvalues.

Construct and interpret a confidence interval and prediction interval for the

dependent variable.

Set up and interpret an ANOVA table.


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Correlation Anal sisCorrelation Anal sis is a rou o statistical techni ues tomeasure the association between two variables.

Advertising Minutes and $ Sales

is a chart that portrays10

15

20

25

30

les($thousan

ds)

between two variables.0

70 90 110 130 150 170 190

Advertising Minutes

S

TheIndependentIndependent

VariableVariableprovides theTheDependentDependent

basis for estimation. Itis the predictor variable.

being predicted or estimated.

Correlation Analysis


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The Coe icient o CorrelationCoe icient o Correlation (r) is a measure of thestrength of the relationship between two variables.

Also called Pearsons r and It re uires interval or

Pearson s

earson s pro uct moment

correlation coefficient. ratio-scaled data.

-1.00 to 1.00.

-

-1 1

. .

indicate perfect and

trong correlation.

Negative values indicate aninverse relationship and

Values close to 0.0 indicateweak correlation.

The Coefficient of Correlation, r

direct relationship.

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10

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Y

0

0 1 2 3 4 5 6 7 8 9 10

X

Perfect Negative Correlation

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10

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1

Y

0

0 1 2 3 4 5 6 7 8 9 10

X

Perfect Positive Correlation

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10

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1

Y

0

0 1 2 3 4 5 6 7 8 9 10

X

Zero Correlation

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10

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1

Y

X

Strong Positive Correlation

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proportion of the total variation in the dependent

variable Y that is ex lained or accounted or b the

variation in the independent variable (X).

It is the square of the coefficient of correlation.

It ranges from 0 to 1.It does not give any information on the direction

of the relationship between the variables.

Coefficient of Determination

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variable (X) to estimate the dependent variable (Y).

The relationship Both variables

variables is linear.

interval scale.

The least squares criterion

is used to determine the

equation. That is the term(Y Y)2 is minimized.Regression Analysis

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The regression equation is Y= a + bXThe regression equation is Y= a + bX

wherewhere

Y is the average predicted value of Y for any X.Y is the average predicted value of Y for any X.

a is the Ya is the Y--intercept.intercept.

s e es ma e va ue w en =s e es ma e va ue w en =

,,in Y for each change of one unit in Xin Y for each change of one unit in X

The least squares principle is used to obtain aThe least squares principle is used to obtain aand b.and b.

Regression Analysis

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