PPT - Regression analysis | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

 Page 1


PRESENTATION
 ON 
REGRESSION ANALYSIS
Page 2


PRESENTATION
 ON 
REGRESSION ANALYSIS
Definition
 The Regression Analysis  is a technique of studying the dependence of one variable (called 
dependant variable), on one or more variables (called explanatory variable), with a view to 
estimate or predict the average value of the dependent variables in terms of the known or 
fixed values of the independent variables.
THE REGRESSION TECHNIQUE IS PRIMARILY USED TO :
• Estimate the relationship that exists, on the average, between the dependent variable and the 
explanatory variable
• Determine the effect of each of the explanatory variables on the dependent variable, 
controlling the effects of all other explanatory variables
• Predict the value of dependent variable for a given value of the explanatory variable
Page 3


PRESENTATION
 ON 
REGRESSION ANALYSIS
Definition
 The Regression Analysis  is a technique of studying the dependence of one variable (called 
dependant variable), on one or more variables (called explanatory variable), with a view to 
estimate or predict the average value of the dependent variables in terms of the known or 
fixed values of the independent variables.
THE REGRESSION TECHNIQUE IS PRIMARILY USED TO :
• Estimate the relationship that exists, on the average, between the dependent variable and the 
explanatory variable
• Determine the effect of each of the explanatory variables on the dependent variable, 
controlling the effects of all other explanatory variables
• Predict the value of dependent variable for a given value of the explanatory variable
Assumptions of the Linear Regression 
Model
1. Linear Functional form
2. Fixed independent variables
3. Independent observations
4. Representative sample and proper specification of the model 
(no omitted variables)
5. Normality of the residuals or errors
6. Equality of variance of the errors (homogeneity of residual 
variance)
7. No multicollinearity
8. No autocorrelation of the errors
9. No outlier distortion
Page 4


PRESENTATION
 ON 
REGRESSION ANALYSIS
Definition
 The Regression Analysis  is a technique of studying the dependence of one variable (called 
dependant variable), on one or more variables (called explanatory variable), with a view to 
estimate or predict the average value of the dependent variables in terms of the known or 
fixed values of the independent variables.
THE REGRESSION TECHNIQUE IS PRIMARILY USED TO :
• Estimate the relationship that exists, on the average, between the dependent variable and the 
explanatory variable
• Determine the effect of each of the explanatory variables on the dependent variable, 
controlling the effects of all other explanatory variables
• Predict the value of dependent variable for a given value of the explanatory variable
Assumptions of the Linear Regression 
Model
1. Linear Functional form
2. Fixed independent variables
3. Independent observations
4. Representative sample and proper specification of the model 
(no omitted variables)
5. Normality of the residuals or errors
6. Equality of variance of the errors (homogeneity of residual 
variance)
7. No multicollinearity
8. No autocorrelation of the errors
9. No outlier distortion
•
Regression analysis is the most often applied technique of statistical 
analysis and modeling.  
• If two variables are involved, the variable that is the basis of the 
estimation, is conventionally called the independent variable and the 
variable whose value is to be estimated+ is called the dependent 
variable.
• In general, it is used to model a response variable (Y) as a function of 
one or more driver variables (X
1
, X
2
, ..., X
p
).
• The functional form used is:
Y
i
 = ?
0
 + ?
1
X
1i
 + ?
2
X
2i
 + ... + ?
p
X
pi
 + ?
•
The dependent variable is variously known as  explained 
variables, predictand, response and endogenous variables.
•
While the independent  variable is known as explanatory, 
regressor and exogenous variable.
Introduction to Regression Analysis
Page 5


PRESENTATION
 ON 
REGRESSION ANALYSIS
Definition
 The Regression Analysis  is a technique of studying the dependence of one variable (called 
dependant variable), on one or more variables (called explanatory variable), with a view to 
estimate or predict the average value of the dependent variables in terms of the known or 
fixed values of the independent variables.
THE REGRESSION TECHNIQUE IS PRIMARILY USED TO :
• Estimate the relationship that exists, on the average, between the dependent variable and the 
explanatory variable
• Determine the effect of each of the explanatory variables on the dependent variable, 
controlling the effects of all other explanatory variables
• Predict the value of dependent variable for a given value of the explanatory variable
Assumptions of the Linear Regression 
Model
1. Linear Functional form
2. Fixed independent variables
3. Independent observations
4. Representative sample and proper specification of the model 
(no omitted variables)
5. Normality of the residuals or errors
6. Equality of variance of the errors (homogeneity of residual 
variance)
7. No multicollinearity
8. No autocorrelation of the errors
9. No outlier distortion
•
Regression analysis is the most often applied technique of statistical 
analysis and modeling.  
• If two variables are involved, the variable that is the basis of the 
estimation, is conventionally called the independent variable and the 
variable whose value is to be estimated+ is called the dependent 
variable.
• In general, it is used to model a response variable (Y) as a function of 
one or more driver variables (X
1
, X
2
, ..., X
p
).
• The functional form used is:
Y
i
 = ?
0
 + ?
1
X
1i
 + ?
2
X
2i
 + ... + ?
p
X
pi
 + ?
•
The dependent variable is variously known as  explained 
variables, predictand, response and endogenous variables.
•
While the independent  variable is known as explanatory, 
regressor and exogenous variable.
Introduction to Regression Analysis
Derivation of the Intercept
n n n
i i i
i i i
n n n n
i i i i
i i i i
n
i
i
n n n
i i i
i i i
a y b x
n n
i i
i i
y a bx e
e y a bx
e y a b x
Because by definition e
y a b x
na y b x
a y bx
= = =
= = = =
=
= = =
= - = =
= + +
= - - = - - =
= - - ?? ?
= - = - ? ?? ?
?
?? ?
? ?
1 1 1
1 1 1 1
1
1 1 1
1 1
0
0