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# PPT - Regression analysis B Com Notes | EduRev

## B Com : PPT - Regression analysis B Com Notes | EduRev

``` 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
```

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