CORRELATION AND

REGRESSION

CORRELATION

Meaning

Correlation is the statistical tool with the help of which the

relationship between two or mare variable are studied

Definition

According to Croxton and cowdon,’when the relationship

between two variable is of quantitative nature , the appropriate statistical tool, for discovering and

measuring the relationship and expressing in a brief formula is

known as correlation.’

SIGNIFICANCE OF CORRELATION

Correlation coefficient help in measuring the relationship of two variables in one single figureWith the help of correlation we can estimate the future value of variableCorrelation coefficient helps in measuring the extent of co-variance between the two variableCorrelation analysis enables the business manager two estimate cost sales prices and other criteria to the given variable

Conclusion

Correlation is a statistical technique which measures the strength, degree and direction of relationship or co-variance between two

or more variable

Types of correlation Positive correlation: on the basis of direction in which variables move ,correlation maybe positive or negative. If both the variable moves I the same

direction is said to be positiveNegative correlation: if the two variable move

in opposite direction is said to be inverse or negative correlation

Simple correlation: it is used to study only two variables that is correlation between income and

consumption, height and weight etc. .......

Multiple correlation: it is the study of relationship between more than two variables Partial correlation: if there is an existence of multiple variables, under such circumstances

only two variable are studied.Linear correlation: this type of correlation is based on the consistency of the ratio of change

between variable.Logical correlation: when the relationship between two variable studied logically and

mathematically defined is termed as logically correlation

Probable error

It is a statistical measure which provides 2 limits within which all the measure are obtained from different of population.

In simple, probable error is a difference resulting due to taking samples from the

mass population

Rank correlation

Under this method, an independent variable [x,y] are arranged in order of their marks. This method is applicable only to individual observation and it

is not used for frequency distribution.

MERITSIt is easy to calculateIt is simple to understandIt can be applied to any type of data qualitative or quantitative. Hence correction with quantitative data such as honesty, beauty can be found.Suitable for data with two attributes

DEMERITSIt is not accurate as only appropriate value is takenNot suitable for large dataCombination of different series cannot be obtained as I case of S.D and mean Not suitable for further mathematical calculation.

Regression analysis

Meaning: It is the theory of estimation of unknown values of a variable with the help of known values of a variable.Ex: Finding the sales for a given adv expenditure.Regression equation:

They are the algebraic expressions of the regression lines. there are two regression equation1. x on y -> x dependent on y.It is used to estimate x values.2. y on x->y dependent on x.it is used to estimate y values.Regression co-efficient:

The constant in the regression equation is known as Regression co-efficient. Since there are two regression equation there two Regression co-efficient also i.e co-efficient of x on y and y on x.

INTERPOLATION AND

EXTRAPOLATION

Interpolation:

It refers to the insertion of an intermediate value in a given series of values. It is the process of finding values of a quantity between some of its known values. In short, drawing conclusions about missing information is termed as Interpolation.Ex: estimation of population figures for any year in 10 years gap

Extrapolation:

Estimating the values for the future when a given set of values for the known period. In simple, extrapolation refers to projecting a value for the future.Ex: Predicting the sales for the year 2017 based on the data up to 2015.

Definition:According to W.M.Harper ,’ Interpolation consists of reading values which lies between two extreme points. Extrapolation means reading values that lies outside the two extreme points

Thus Interpolation supplies us the missing link where as extrapolation helps in forecasting.

ASSUMPTIONS:There are no sudden jumps in the series from one period to another, where extrapolation assumed as, there will not be any chance of sudden changes in the that in the future.

The rate of change in value in uniform.

Methods

1. Binomial expansion method2. Newton's advancing difference

method

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