Regression Analysis-Economic Statistics.ppt

Regression Analysis -Meaning, Uses, Properties Difference between Regression and Correlation and Methods of Studying Regression are included in the ppt (only Theory part)

1. ECONOMIC STATISTICS
Dr. A. SATHEESHBABU
Assistant Professor, Department of Economics
VIVEKANANDA COLLEGE
(Residential & Autonomous –A Gurukula Institute of Life Training)
TIRUVEDAKAM WEST, MADURAI DIST –625 234, TAMIL NADU

3. REGRESSION ANALYSIS
•Introduction
•Theword“Regression”wasintroducedbySir
FrancisGaltonin1877.
•Theword“Regression”means“Return”or
“GoingBack”.
•Regression Line
•ThetermRegressionLinewasintroducedby
SirFrancisGalton
•Thelinedescribingtheaveragerelationship
between twovariablesisknown asthe
RegressionLine.

4. REGRESSION ANALYSIS
•Meaning
•Thestatisticalmethodwhichhelpsus
toestimatetheunknownvalueofone
variablefromtheknownvalueofthe
related variable iscalled as
Regression.
•Definition
•AccordingtoBlair,“Regressionisthe
measure oftheaveragerelationship
betweentwoormorevariableinterms
oftheoriginalunitsofthedata.

5. USES OF REGRESSION ANALYSIS
•ItisusedinStatisticsinallthosefieldswhere
twoormorerelativevariablesarehaving
tendencytogobacktotheaverage.
•Itiswidelyusedinsocialscienceslike
economics,naturalandphysicalsciencesetc.,
•Ithelpstopredictthevalueofdependent
variablesfromthevaluesofindependent
variables.
•Itisveryhelpfultostudybusinesspredictions.
•Ithelpstocalculatecoefficientofcorrelation
(r)andcoefficientofdetermination(r
2
).
•Itisusedmorethanthecorrelationanalysisin
manyscientificstudies.
•Manypredictionsandtheoriesineconomics
havebeendiscovered withthehelpof
Regression.

6. Differences Between Correlation
and Regression
S.No.
Correlation Regression
1 Correlation isthe relationship
between two or more variable
which vary in sympathy with
the other in the same or the
opposite direction.
Regression means goingback
and it is mathematical measure
showing the average relationship
between two variables
2 Both thevariables X and Y are
random variables.
Here, X is a randomvariable and
Y is a fixed variable. Sometimes
both the variables may be
random variables.
3 Itfinds out the degree of
relationship between two
variables and not the cause
and effect of the variables.
It indicatesthe cause and effect
relationship between the
variables and estimates the
functional relationship.

7. S.No.
Correlation Regression
4 It isused for testing and
verifying the relationship
between two variables and
gives limited information.
Besidesverification, it is used for
the prediction of one value, in
relationship to the other given
value.
5 The Coefficient of correlation is
a relative measure. The range
of relationship lies between ±1
The Regression coefficient is an
absolute figure.
6 There may be nonsense
correlation between two
variables.
There is nononsense regression
between two variables.
7 It has limited application,
because it is confined only to
linear relationship between
variables.
It has widerapplication, as it
studies linear and non-linear
relationship between variables.

8. S.No.
Correlation Regression
8 It is not very useful forfurther
mathematical treatment.
It is widely used for further
mathematical treatment.
9 Ifthe coefficient of correlation
is positive, then the two
variables are positively
correlated and vice-versa.
Itexplains that the decrease in
one variable is associated with
the increase in the other
variable.
10It is immaterialwhether X
depends upon Y or Y depends
upon X.
There is a functional relationship
between the two variables so
that we may identify between
the independent and dependent
variables.

9. Properties of Regression
•Thegeometricmeanbetweenregression
coefficientisthecoefficientofcorrelation,
symbolically
r=√bxyXbyx
•Bothregressioncoefficientsbxyandbyx
willhavesamealgebraicsign.
•Valueofboththeregressioncoefficients
liesbetween±1.
•Ifbxyandbyxarepositive,rwillbe
positiveandviceversa.
•Arithmeticmeanofbxyandbyxisequalto
orgreaterthanr.
•Regressioncoefficientareindependentof
changeoriginbutnotofscale.

10. Methods of Studying Regression
MethodsofStudyingRegression
Graphic Method Algebraic Method
Regression Equation
Y on XX on Y

11. Methods of Studying Regression
Thepointsareplottedonagraphpaper
representingthepairsofvaluesofthe
concernedvariables.Inthisdiagramthe
independent variable istaken on
horizontalaxis(Xaxis)anddependent
variableontheverticalaxis(Yaxis).
Aregressionlinemaybedrawninbetween
thesespointsbyfreehandorbyascale
rule.
Graphic Method

12. Methods of Studying Regression
1.RegressionEquationofYonX
Y
c=a+b
x
Tofindouta&bvalues,
ΣY=Na+ΣXb
ΣXY=ΣXa+ΣX
2
b
Algebraic Method
Regression Equations
Method: 1) Direct Method

13. Methods of Studying Regression
2.RegressionEquationofXonY
X
c=a+b
y
Tofindouta&bvalues,
ΣX=Na+ΣYb
ΣXY=ΣYa+ΣY
2
b
Algebraic Method
Regression Equations
Method: 1) Direct Method

14. Methods of Studying Regression
1.RegressionEquationofYonX
Y
c=a+b
x
Tofindouta&bvalues,
Y–Y=r_____X–X
Algebraic Method
Regression Equations
Method: 2) Deviation Taken from Arithmetic Mean
σy
σx

15. Methods of Studying Regression
2.RegressionEquationofXonY
X
c=a+b
y
Tofindouta&bvalues,
X–X=r_____Y–Y
Algebraic Method
Regression Equations
Method: 2) Deviation Taken from Arithmetic Mean
σx
σy

16. Methods of Studying Regression
1.RegressionEquationofYonX
Y
c=a+b
x
Tofindouta&bvalues,
Y–Y=r_____X–X
Algebraic Method
Regression Equations
Method: 3) Deviation Taken from Assumed Mean
σy
σx

17. Methods of Studying Regression
2.RegressionEquationofXonY
X
c=a+b
y
Tofindouta&bvalues,
X–X=r_____Y–Y
Algebraic Method
Regression Equations
Method: 3) Deviation Taken from Assumed Mean
σx
σy

18. Methods of Studying Regression
1.RegressionEquationofYonX
Y
c=a+b
x
Tofindouta&bvalues,
Y–Y=r_____X–X
r=√byxXbxy
Algebraic Method
Regression Equations
Method: 4) By using Correlation Coefficient
σy
σx

19. Methods of Studying Regression
2.RegressionEquationofXonY
X
c=a+b
y
Tofindouta&bvalues,
X–X=r_____Y–Y
r=√bxyXbyx
Algebraic Method
Regression Equations
Method: 4) By Using Correlation Coefficient
σx
σy