CORRELATION & REGRESSION

CORRELATION

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.

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

CONT..

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.

COMPUTATION

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

Measures of coefficient of correlation:

1)Scatter diagram

2)Karl Pearson's coefficient of correlation

3)Rank coefficient of correlation

4)Concurrent deviation method

SCATTER DIAGRAM

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

Karl pearson’s coefficient of correlation

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:

Grouped data

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

SPEARMAN’S RANK COEFFICIENT OF

CORRELATION

It is also denoted by r and the formula is:

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

INTRODUCTION

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.

FOR UNDERSTANDING

•Functional relationship between two variables.

•Basic purpose is forecasting and prediction.

•Influencing dependent variable in terms of independent variable.

PROPERTIES OF REGRESSION COEFFCIENT

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.

2)x-(x

)y-(y)x-(x b

yx

Y on X

Y= a+ bxHere b i s known as reg ress ion coeff ic ien t

reg ress ion Y on X

For Computation:

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.

Regression in corporate field

CONT..

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.

PRESENTED BY: SMITA DIVYA DIVYASHIUTSAVGAURAVTEJASV