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1. Presented By :
Vijay

2. Introduction
• Father of Regression Analysis
Carl F. Gauss (1777-1855).
• contributions to physics, Mathematics & astronomy.
• The term “Regression” was first used in 1877 by Francis Galton.

3. Regression Analysis. . .
• It is the study of the relationship between variables.
• It is one of the most commonly used tools for business analysis.
• It is easy to use and applies to many situations.

4. Why Regression ?
For Example.
Last 30 days data for a KFC shop in a Mall. Number of visitors v.s burgers sold

5. Definition
Regression analysis is a branch of statistical theory that is widely used in almost all the scientific
disciplines. In economics it is basic technique for measuring or estimating the relationship among
economics variables that constitute the essence of economics theory and economic variables.

6. Properties
i. Coefficient of correlation is the Geometric mean of regression coefficient.
ii. Both the regression coefficient of the same algebraic sine.
iii. Coefficient of correlation will have the same sign(+,-) as the regression coefficient.
iv. Both the regression coefficient can not be greater than unitary
v. Arithmetic mean of the regression coefficient is either ,equal or greater than the correlation coefficient.

7. Regression types. . .
• Simple Regression: single explanatory variable
• Multiple Regression: includes any number of explanatory variables.

8. Simple Linear Regression Model
A simple linear regression model is based on a single independent variable and its general form is:
Here
Y = dependent variable
a = Intercept
b = Slope of the line
x= independent variable
Y =a+bx

9. i) X = Independent Variable (we provide this)
ii) Y = Dependent Variable (we observe this)
Variables:
Regression coefficient of Y on X
Regression coefficient of X on Y
𝑏𝑦𝑥 = 𝑟.
𝜎𝑦
𝜎𝑥
𝑏𝑥𝑦 = 𝑟.
𝜎𝑥
𝜎𝑦