Regression analysis is a statistical technique used to determine the relationship between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The dependent variable is the variable being predicted, while the independent variables are what is used to make the predictions. Regression analysis helps establish functional relationships between variables and is used in business, economics, and other fields to model phenomena and make predictions.

2.  Regression analysis is used widely for
deriving an appropriate functional
relationship between variables.
 The variable predicted on the basis of
other variable is called the dependent
variable and the other variable is called the
independent variable.

3.  Theestimation or prediction of the
unknown value of one variable from the
known value of the other variable.

4.  “Regression analysis is a mathematical
measure of the average relationship
between two or more variables in terms of
the original units of data”
- M. M. Blair

5.  Itconsists of a mathematical device that is
used to measure the average relationship
between two or more closely related
variables.
 Used for estimating the unknown value of
some dependent variable with reference to
the known values of its related
independent variable.

6.  Helps in establishing a functional
relationship between two or more variable.
 Tool for solving many problems of
economic and business research.
 For prediction or estimation of future
production, price, sales, income, profits etc
which are of great importance to a
businessman or economist.

7.  Used in our day-to-day life and sociological
studies as well as to estimate the various
factors such as birth rate, death rate, yield
rate, etc.

8.  Simple
- the study of only two variables at a time
eg :
- the influence of rainfall on the yield of
a crop.
- the influence of advertisement on sales

9.  Multiple
- studying more than two variables at a
time
eg :
-yield of a crop depends on rainfall
and fertilizers.
- the turnover depends on advertising
and income of the people.

10.  Linear
• Amount of change in one variable bear a
constant change in the other variable.
• If the regression curve is a straight line, then
it is called linear regression.
 Non linear
• Amount of change in one variable doesn't
bear a constant change in the other
variable.
• If the curve of regression is not a straight
line, then it is called non linear regression.

11.  Total
in this case all the important
variables are considered. Normally they
take the form of a multiple relationship.
 Partial
study the effect of one or two relevant
variables on another variable.

12. Regression Line
Regression Equation
Regression Coefficient

13.  The regression line (known as the least
squares line) is a plot of the expected
value of the dependent variable for all
values of the independent variable.
Technically, it is the line that "minimizes
the squared residuals". The regression
line is the one that best fits the data on
a scatter plot.

14. y i     xi  
Error
Intercept
Dependent Independent
variable Independent
Regression
variable
coefficient
(explanatory
variable,
regressor…)
14

15. • We want to investigate if
there is a relationship
between cholesterol and age
on a sample of 18 people
• The dependent variable is
the cholesterol level
• The explanatory variable is
age
15

16. y 


C h o le s te ro l (m g /1 0 0 m l)
400 





 
300
 





200
20 30 40 50 60 x
Age
16