PPT - Regression analysis

# PPT - Regression analysis - Business Mathematics and Statistics - B Com

``` 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
```

115 videos|142 docs

## FAQs on PPT - Regression analysis - Business Mathematics and Statistics - B Com

 1. What is regression analysis? Ans. Regression analysis is a statistical technique used to study the relationship between a dependent variable and one or more independent variables. It helps in understanding how the dependent variable changes when the independent variables are varied.
 2. How is regression analysis used in research? Ans. Regression analysis is commonly used in research to examine the strength and direction of the relationship between variables. It helps researchers understand the impact of independent variables on the dependent variable and can be used to make predictions and test hypotheses.
 3. What are the different types of regression analysis? Ans. There are several types of regression analysis, including linear regression, logistic regression, polynomial regression, and multiple regression. Linear regression is used when the relationship between variables is linear, logistic regression is used when the dependent variable is categorical, polynomial regression is used when the relationship is curvilinear, and multiple regression is used when there are multiple independent variables.
 4. How is regression analysis different from correlation analysis? Ans. Regression analysis and correlation analysis are similar, but there are key differences. Correlation analysis examines the strength and direction of the relationship between variables without considering causation. Regression analysis, on the other hand, not only examines the relationship but also helps in understanding the effect of independent variables on the dependent variable.
 5. What are the limitations of regression analysis? Ans. Regression analysis has certain limitations that researchers should be aware of. These include assumptions of linearity, independence of errors, homoscedasticity, and absence of multicollinearity. Violation of these assumptions can impact the accuracy and reliability of the regression results. Additionally, regression analysis assumes that the relationship between variables is constant and does not account for nonlinear relationships.

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