This document discusses correlation and linear regression. It defines correlation as the statistical relationship between two variables, ranging from -1 to 1. Positive correlation means the variables increase or decrease together, while negative correlation means they deviate in opposite directions. Linear regression analyzes the linear relationship between a dependent and independent variable to predict future outcomes. It allows executives to forecast sales, understand how variables influence each other, and prepare budgets based on regression equations.

2.  It is a technique of statistically measuring the
strength of linear association between the two sets
of data.
 Basically it is the process of establishing a
relationship or connection between two or more
things . As if the change in one variable affects the
change in another variable, the variables are said to
be correlated.
 It ranges from -1 to 1.

3.  Correlation can be positive and negative.
 If the two variables deviate in the same
direction i.e., if the increase(or decrease)in one
results in a corresponding increase(or decrease)
in 0ther,correlation is said to be positive.
 E.g.-height and weight of group of persons
 But if they constantly deviate in the opposite
directions i.e. if increase(or decrease) in one
results in corresponding decrease(or increase)
in the other, the correlation is said to be
negative.
 E.g.-price and demand of a commodity

4.  Spurious /non-sense correlation-there is
absence of relationship between the correlation
or you can say there is zero correlation.
 E.g.-relationship between increase in the
demand of salt and increase in the demand of
TV.
 Causation-it is the relationship between cause
and effect.
 When there is a causation, the correlation also
exists but not vice versa.

5.  COVARIANCE-the mean value of the product of
the deviations of two variates from their respective
means.

6. 1)Scatter diagram
2)Karl Pearson's coefficient of correlation
3)Rank coefficient of correlation
4)Concurrent deviation method

7.  It is a simple graphic way of understanding
association between the two discrete data sets.
 Scatter of dots indicates the extent and
direction of association between the two data
sets.
 Greater scatter – less correlation
 Close scatter – high correlation
 Types: positive, perfect positive, negative,
perfect negative & no correlation

8.  r= covariance/σx σy
 If the means of two series is not in integers then
the above mentioned formula becomes very
clumsy, thus then r is calculated using:

9.  When the sample size is large and the values
have frequencies, the problem is presented in
the form of grouped data.

10.  It is also denoted by r and the formula is:

11. HISTORY
The earliest form of regression was the method of
least squares which was published by Legendre in
1805,and by Gauss In 1809. Legendre and Gauss
both applied the method to the problem of
determining, from astronomical observations, the
orbits of bodies about the Sun (mostly comets, but
also later the then newly discovered minor
planets).
LINEAR REGRESSION ANALYSIS

12.  It is a procedure of functional relationship used for
prediction.
 It can be simple or multiple.
 Two types of variables: dependent and independent
variables.
 Regression equations can be of two types:
deterministic and probabilistic.

13. • Functional relationship between two
variables.
• Basic purpose is forecasting and
prediction.
• Influencing dependent variable in terms
of independent variable.

14. The product of the two regression coefficient will
never exceed one.
r=√(byx*bxy)
Both regression coefficients will have same
algebric signs.
Regression coefficient are independent of origin
but not of scale.
Mean of byx and bxy will be more than or equal to
r.

16. 2
)x-(x
)y-(y)x-(x
b

yx
 Y on X
Y= a+ bx
Here b is known as regression coefficient
regression Y on X

17. Executive can arrive at sales forecasts for a
company.
Describe relationship between two or more
variables.
Find out what the future holds before a
decision can be made.
Predict revenues before a budget can be
prepared.
Change in the price of a product and
consumer demand for the product.

18.  The dependence of personal consumption
expenditure on after-tax, will help executive in
estimating the marginal propensity to consume,
a dollar’s worth of change in real income.