mo&ro 1.regresi (dr.etty elika)

7/31/2019 Mo&Ro 1.Regresi (Dr.etty Elika)

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Regression Analysis


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Scatter plots

Regression analysis requires intervaland ratio-level data.

To see if your data fits the models of

regression, it is wise to conduct ascatter plot analysis.

The reason?

Regression analysis assumes a linearrelationship. If you have a curvilinearrelationship or no relationship,regression analysis is of little use.


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Types of Lines


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Scatter plot

15.0 20.0 25.0 30.0 35.0

Percent of Population 25 years and Over with Bachelor's Degree or More,March 2000 estimates

20000

25000

30000

35000

40000

Pe

rsonalIncomePerCap

ita,currentdollars,

1999

Percent of Population with Bachelor's Degree by Personal Income Per Capita

This is a linearrelationship

It is a positiverelationship.

As population withBAs increases sodoes the personal

income per capita.


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Regression Line

15.0 20.0 25.0 30.0 35.0


20000

25000

30000

35000

40000

PersonalIncomePerCapita,currentdollars,

1999


R Sq Linear = 0.542

Regression line isthe best straight linedescription of the

plotted points anduse can use it todescribe theassociation between

the variables.


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Things to remember

Regressions are still focuses on

association, not causation.

Association is a necessaryprerequisite for inferring causation,

but also:1. The independent variable must preceded

the dependent variable in time.

2. The two variables must be plausibly linedby a theory,

3. Competing independent variables mustbe eliminated.


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Regression Table

The regressioncoefficient is not agood indicator for thestrength of the

relationship.Two scatter plots withvery different

dispersions couldproduce the sameregression line.

15.0 20.0 25.0 30.0 35.0


20000

25000

30000

35000

40000

Per

sonalIncomePerCapita,

currentdollars,

1999


R Sq Linear = 0.542

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Population Per Square Mile

20000

25000

30000

35000

40000

PersonalIncomePerCapita,

currentdollars,

1999


R Sq Linear = 0.463


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Regression coefficient

The regression coefficient is the slope ofthe regression line and tells you whatthe nature of the relationship betweenthe variables is.

How much change in the independentvariables is associated with how muchchange in the dependent variable.

The larger the regression coefficient themore change.


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Pearsons r

To determine strength you look at howclosely the dots are clustered around theline. The more tightly the cases are

clustered, the stronger the relationship,while the more distant, the weaker.

Pearsons r is given a range of-1 to + 1

with 0 being no linear relationship at all.


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Reading the tables

When you run regression analysis on SPSS you get a3 tables. Each tells you something about therelationship.

The first is the model summary.

The R is the Pearson Product Moment CorrelationCoefficient.

In this case R is .736

R is the square root of R-Squared and is thecorrelation between the observed and predictedvalues of dependent variable.

Model Summary

.736a .542 .532 2760.003Model1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

Predictors: (Constant), Percent of Population 25 years

and Over with Bachelor's Degree or More, March 2000

estimates

a.


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R-Square

R-Square is the proportion of variance in thedependent variable (income per capita) which can bepredicted from the independent variable (level ofeducation).

This value indicates that 54.2% of the variance inincome can be predicted from the variable education.

R-Square is also called the coefficient ofdetermination.

Model Summary

.736a .542 .532 2760.003Model1

R R Square

Adjusted

R Square

Std. Error of

the Estimate



estimates

a.


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Adjusted R-square

The adjusted R-square attempts to yield a more honestvalue to estimate the R-squared for the population. Thevalue of R-square was .542, while the value of AdjustedR-square was .532. There isnt much difference because

we are dealing with only one variable.When the number of observations is small, there will bea much greater difference between R-square andadjusted R-square.By contrast, when the number of observations is very

large, the value of R-square and adjusted R-square willbe much closer.

Model Summary

.736a .542 .532 2760.003

Model

1

R R SquareAdjustedR Square

Std. Error ofthe Estimate



estimates

a.

ANOVA


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ANOVA

The p-value associated with this F value is very small (0.0000).These values are used to answer the question "Do theindependent variables reliably predict the dependent variable?".

The p-value is compared to your alpha level (typically 0.05) and,if smaller, you can conclude "Yes, the independent variablesreliably predict the dependent variable".

If the p-value were greater than 0.05, you would say that thegroup of independent variables does not show a statisticallysignificant relationship with the dependent variable, or that thegroup of independent variables does not reliably predict thedependent variable.

ANOVAb

4.32E+08 1 432493775.8 56.775 .000a

3.66E+08 48 7617618.586

7.98E+08 49

Regression

ResidualTotal

Model

1

Sum of

Squares df Mean Square F Sig.

Predi ctors: (Constant), Percent of Population 25 years and Over with Bachelor's

Degree or More, March 2000 estimates

a.

Dependent Variable: Personal Income Per Capi ta, current doll ars, 1999b.


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Coefficients

B - These are the values for the regression equationfor predicting the dependent variable from the

independent variable.These are called unstandardized coefficientsbecause they are measured in their naturalunits. As such, the coefficients cannot be comparedwith one another to determine which one is moreinfluential in the model, because they can bemeasured on different scales.

Coefficientsa

10078.565 2312.771 4.358 .000

688.939 91.433 .736 7.535 .000

(Constant)

Percent of Population

25 years and Over

with Bachelor's

Degree or More,

March 2000 estimates

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Personal Income Per Capita, current dollars, 1999a.


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Coefficients

This chart looks at two variables and shows howthe different bases affect the B value. That is whyyou need to look at the standardized Beta to seethe differences.

Coefficientsa

13032.847 1902.700 6.850 .000

517.628 78.613 .553 6.584 .000

7.953 1.450 .461 5.486 .000

(Constant)


25 years and Over

with Bachelor's

Degree or More,


Population Per

Square Mile

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.



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Coefficients

Beta - The are the standardized coefficients.

These are the coefficients that you would obtain if youstandardized all of the variables in the regression, includingthe dependent and all of the independent variables, and ranthe regression.

By standardizing the variables before running the regression,you have put all of the variables on the same scale, and youcan compare the magnitude of the coefficients to see whichone has more of an effect.

You will also notice that the larger betas are associated with

the larger t-values.

Coefficientsa

10078.565 2312.771 4.358 .000

688.939 91.433 .736 7.535 .000

(Constant)


25 years and Over

with Bachelor's

Degree or More,


Model1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.



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The Basic Regression Model

Simple Linear RegressionY = a + bX

Multiple Linear Regression

Y = a + b1X1 + b2X2 +b3X3 +


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Model Summary

.849a .721 .709 2177.791

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

Predictors: (Constant), Population Per Square Mi le,

Percent of Population 25 years and Over with

Bachelor's Degree or More, March 2000 estimates

a.

ANOVAb

5.75E+08 2 287614518.2 60.643 .000a

2.23E+08 47 4742775.141

7.98E+08 49

Regression

Residual

Total

Model

1

Sum of

Squares df Mean Square F Sig.

Predictors: (Constant), Population Per Square Mil e, Percent of Population 25 years

and Over with Bachelor's Degree or More, March 2000 estimates

a.

Dependent Variable: Personal Income Per Capi ta, current dollars, 1999b.

Multiple

Regression


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Coefficientsa

13032.847 1902.700 6.850 .000

517.628 78.613 .553 6.584 .000

7.953 1.450 .461 5.486 .000

(Constant)


25 years and Over

with Bachelor's

Degree or More,


Population Per

Square Mile

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.


Multiple

Regression


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1.00.80.60.40.20.0

Observed Cum Prob

1.0

0.8

0.6

0.4

0.2

0.0

Ex

pectedCumP

rob

Normal P-P Plot of Regression Standardized Residual

Dependent Variable: Jumlah Penjualan

T


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Tugas

Pilih salah satu kasus pada bidang

apa saja yang dapat analisis denganRegresi Berganda

Olah Data anda menggunakan salahsatu perangkat lunak yang sesuai.

Maknai hasil pengolahan data

tersebut.

mo&ro 1.regresi (dr.etty elika)

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