Concept of Regression in Research Methodology.pdf

Regression
Types of Regression
Regression Analysis
Example

1. REGRESSION
Dr. Balamurugan M
Associate Professor
Acharya Institute of Graduate Studies
Bangalore

2. Regression
•Regressionanalysismeasuresthenatureandextentofthe
relationshipbetweentwoormorevariables,thusenables
ustomakepredictions.
•Regressionisthemeasureoftheaveragerelationship
betweentwoormorevariables.

3. Correlation vs. Regression
•Degree&NatureofRelationship
CorrelationisameasureofdegreeofrelationshipbetweenX
&Y.
Regressionstudiesthenatureofrelationshipbetweenthe
variablessothatonemaybeabletopredictthevalueofone
variableonthebasisofanother.
•Cause&EffectRelationship
Correlationdoesnotassumecauseandeffectrelationship
betweentwovariables.
Regressionclearlyexpressesthecauseandeffectrelationship
betweentwovariables.Theindependentvariableisthecause
anddependentvariableiseffect.

4. Correlation vs. Regression
•Prediction
Correlationdoesnothelpinmakingpredictions.
Regressionenableustomakepredictionsusing
regressionline.
•Symmetric
Correlationcoefficientsaresymmetrical.
Regressioncoefficientsarenotsymmetrical.

5. Copyright © 2016 Pearson Education, Ltd. Chapter 12, Slide 5
12.1 Regression Models
Y
X
Y
X
Y
Y
X
X
Linear relationships Curvilinear relationships

6. Copyright © 2016 Pearson Education, Ltd. Chapter 12, Slide 6
Types of Relationships
Y
X
Y
X
Y
Y
X
X
Strong relationships Weak relationships

7. Copyright © 2016 Pearson Education, Ltd. Chapter 12, Slide 7
Types of Relationships
Y
X
Y
X
No relationship

8. Regression Analysis
Regressionanalysisisusedto:
Predictthevalueofadependentvariablebasedonthevalueofat
leastoneindependentvariable.
Explaintheimpactofchangesinanindependentvariableonthe
dependentvariable.
Dependentvariable:Thevariablewewishtopredictor
explain.
Independentvariable:Thevariableusedtopredictorexplain
thedependentvariable.

9. Simple Linear Regression
Model
•Onlyoneindependentvariable,X
•RelationshipbetweenXandYisdescribedbyalinear
function
•ChangesinYareassumedtoberelatedtochangesinX

10. Copyright © 2016 Pearson Education, Ltd. Chapter 12, Slide 10 ii10i
εXββY 
Linear component
Simple Linear Regression Model
Population
Y intercept
Population
Slope
Coefficient
Random
Error
term
Dependent
Variable
Independent
Variable
Random Error
component

11. Copyright © 2016 Pearson Education, Ltd. Chapter 12, Slide 11
Simple Linear Regression Equation
(Prediction Line)i10i XbbY
ˆ

The simple linear regression equation provides an
estimateof the population regression line
Estimate of
the regression
intercept
Estimate of the
regression slope
Estimated
(or predicted)
Y value for
observation i
Value of X for
observation i

12. Interpretation of the Slope
and Intercept
•b
0istheestimatedmeanvalueofYwhenthevalueofX
iszero.
•b
1istheestimatedchangeinthemeanvalueofYasa
resultofaone-unitincreaseinX.

13. Example
•Arealestateagentwishestoexaminethe
relationshipbetweenthesellingpriceofahome
anditssize(measuredinsquarefeet)
•Arandomsampleof10housesisselected
•Dependentvariable(Y)=housepricein$1000s
•Independentvariable(X)=squarefeet

14. Data

15. 0
50
100
150
200
250
300
350
400
450
0 500 1000 1500 2000 2500 3000
House Price ($1000s)
Square Feet Scatter Plot
House price model: Scatter Plot

16. 0
50
100
150
200
250
300
350
400
450
0 50010001500200025003000
Square Feet
House Price ($1000s) Graphical Representation
House price model: Scatter Plot and Prediction Linefeet) (square 0.10977 98.24833 price house 
Slope
= 0.10977
Intercept
= 98.248

17. Simple Linear Regression
Example: Interpretation
b
0istheestimatedmeanvalueofYwhenthevalueofXiszero
(ifX=0isintherangeofobservedXvalues)
Becauseahousecannothaveasquarefootageof0,b
0hasno
practicalapplication.
b
1estimatesthechangeinthemeanvalueofYasaresultofa
one-unitincreaseinX.
Here,b
1=0.10977tellsusthatthemeanvalueofahouse
increasesby.10977($1000)=$109.77,onaverage,foreach
additionalonesquarefootofsize.feet) (square 0.10977 98.24833 price house 

18. 317.85
0)0.1098(200 98.25
(sq.ft.) 0.1098 98.25 price house


 Predict the price for a house
with 2000 square feet:
The predicted price for a house with 2000
square feet is 317.85($1,000s) = $317,850
Simple Linear Regression Example:
Making Predictions

19. THANK YOU