MELJUN CORTES IBM SPSS Regression

7/30/2019 MELJUN CORTES IBM SPSS Regression

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Linear Regression Analysis

This contains my personal notes only thus, this is notcomplete. Most of the contents were taken from the trainingmanual of IBM SPSS Modeler. Please refer to the training

manual for a complete discussion.


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Simple Linear Regression Model

Consider the scatterplot:

It shows the relationshipbetween mothers weightand babys birthweight.


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Regression analysis finds a straight line thatsummarizes the relationship of the two

variables such that the distance of the pointsfrom the line is minimum.

Mathematically, the line

can be expressed as anequation:

bweight = B0

+ B1*mweight + E

where:

E ~ N (0, 2)B0 = constantB1 = effect on bweight forevery one pound increase of

mweight


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Using sample data, a table below canbe generated by SPSS.

CoefficientsaModel

Unstandardized CoefficientsStandardized

Coefficients

t

Sig.

B

Std. Error

Beta

1 (Constant) 2426.719 162.194 14.962 .000mweight 3.977 1.214 .167 3.276 .001

a. Dependent Variable: bweight

Mathematically,

Estimated bweight = 2426.719 + 3.977*mweight

Note: This equation can be used in predicting bweight if

information about mweight is available..


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Consider the framework: Age

weight at last menstrual period(mweight)

History of hypertension(ht)

Presence of uterine irritability (ui)

Babys Birth Weight(bweight)

Multiple Linear Regression Model

Mathematically,

bweight = constant + B1*age + B2*mweight + B3*ht + B4*ui + E

B1, B2, B3 and B4, called regression coefficients can be estimated if

sample data are available.

where:

E ~ N (0, 2)


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Mathematically,

bweight = constant + B1*age + B2*mweight + B3*ht + B4*ui + E

B1, B2, B3 and B4, called regression coefficients canbe estimated if sample data are available.

where:

E ~ N (0, 2)


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SPSS generates regression table as follows:

Mathematically,

bweight = 2429.007 + 3.656*age + 4.203*mweight -645.545*ht 530.065*ui + E

Note: This equation can be used to predict bweight if information aboutmothers weight, age, ht and ui are available,


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Uses of Linear Regression Analysis

Regression analysis can be used (in appliedresearch) to test the relationships between anoutcome variable and set of predictor variables.

Regression analysis can be used also to predictthe value of the outcome variable given thevalues of the predictor variables.


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Fraud Detection in Insurance Claim(A Regression Analysis Example)

The following data of patients in a hospital in the U.S are available:

CLAIM- total insurance claim for a single medical treatment performedin a hospital

Age age of patient

LOS length of hospital stay ASG- Severity of illness category. This is based on several healthmeasures and higher scores indicate greater severity of the ilness

n=293

Goals:

1) Build a predictive model for the insurance claim amount;2) Use the model to identify outliers (patient with claim values from

what the model predicts), which might be instances of errors orfraud made in the claims.


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Dataset: InsClaim.dat

CLAIM- total insurance claim for a singlemedical treatment performed in a hospital.

Age age of patient

LOS length of hospital stay\

ASG- Severity of illness category. This isbased on several health measures andhigher scores indicate greater severity ofthe ilness.

n=293


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Diagram in Modeler 15.0

Generated output:

Predicted Claims = $3026.754 + $1105.646*length of stay + $417.194*severity code $33.406*age

In equation format:


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Detecting cases that deviate substantiallyfrom the model (Points Poorly fit by Model).

**Just compute the residual (DIFF = actual claim predicted claim)

Generated outputs:

Examine carefullyif fraud is possible


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Using Linear Models Node to

Perform Regression

It has more features than Regression Node,including:

the bility to create the best subset model,

several criteria for model selection,

the option to limit the number of predictors,

and the use of bagging and boosting.


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Additional Features of Linear Models Node

It automatically prepare the data for modeling, bytransforming the target and predictors in order tomaximize the predictive power of the model.

This includes: outlier handling, adjusting the measurement level of

predictors, and merging similar categories.

It automatically creates dummy variables from

categorical fields (that have nominal or ordinalmeasurement level).

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MELJUN CORTES IBM SPSS Regression