Correlation and regression analysis are statistical techniques used to analyze relationships between variables. Correlation determines the strength and direction of relationships, while regression allows for predicting values of one variable based on the other. There are different types of correlation (positive, negative, simple, multiple) and regression (linear, non-linear). Karl Pearson developed a widely used method for calculating correlation coefficients based on means, standard deviations, and covariance. Regression analysis has various uses including prediction, estimating relationships, and testing hypotheses, but relies on assumptions like linear relationships between variables.

1. CORRELATION ANALYSIS
1- definition :
"Correlation is an analysis of the co-variation Between two or more variables ."
According to Croxton & Cowden, " when the relationship is of a quantitative nature, the
Appropriate statistical tool for discovering & measuring the relationship & expressing
it in a brief formula is known as correlation."
2- USES OR SIGNIFICANCE OF CORRELATION
ANALYSIS
Points....,
(A) - The correlation coefficient helps us in measuring the extent of relationship
Between two or more than two variables .The degree & extent of the relationship between
Two variables is, of course, one of the most important problems in statistics.
(B)- It is through correlation that we can predict about the future. For instance, If there
Are good monsoons, we can expect better food supply & hence can expect fall in price of
Food grains & other products.
(C)- If the value of a variable is given, we can know the value of another variable.
It is of course, done with the help of regression analysis.
(D)- Correlation contributes to economic behavior. It helps us in knowing the important
Variables on which others depend .
(E)- The technique of ratio of variation & regression analysis depends totally
On the findings of coefficient of correlation .
(F)- In the field of commerce & industry, the technique of correlation coefficient
Helps to make estimates like sales, price or costs .
(G)- The predictions made on the basis of correlation analysis are considered to beNearer to
reality & hence reliable.
3- TYPES OF CORRELATION
There are three important types of correlation:
(1)- Positive & Negative correlation:
Correlation between two variables, positive or negative depends on the direction
In which the variables move.
(A)- Positive or direct correlation.
If the two variables move in the same direction that's mean with an increase in one variable,
The other variable also increases or with a fall in one variable, the other variable Also falls, the
correlation is said to be positive. For example, price & supply are positively related.
It means if price goes up, the supply goes up & vice versa. It can be shown with the help of "arrows".
(B)- Negative or inverse correlation.
If two variables move in opposite direction that's mean with the increase in one variable,
The other variable falls or with the fall in one variable, the other variable rises, The correlation is said
to be negative or inverse.

2. (2)-SIMPLE & MULTIPLE
CORRELATION.
(A)- Simple Correlation.
When there are only two variables & he relationship is studied between those two variable ,
it is a case of simple correlation .
Relationships between height & weight, price & demand or income & consumption etc. Are examples
of simple correlation .
(B)- Multiple Correlation .
When there are more than two variables & we study the relationship between one variable
& all the other variables taken together then it is a case of multiple correlation.
(3)- LINEAR & NON-LINEAR
CORRELATION.
(A)- Linear Correlation.
The correlation between two variables will be linear if corresponding to a unit change
in one variable, there is a constant change in the other variable over the entire range of the values.
(B)- NON-LINEAR CORRELATION.
The relationship between two variables will be NON-LINEAR or curvi-linear, if Corresponding to a unit
change in one variable, the other variables change at a different rate .
If such data is plotted, we don't get a straight line but a curve type figure.
CHPTER
9
CORRELATION ANALYSIS
Karl Person's Method 6.3.1
Karl Person, a reputed statistician, in 1890, has constructed a well set formula based
.on mathematical treatment for determining the coefficient of correlation
The formula is named after his name as Karl Pearson's formula and is popularly
known as' Karl Person's coefficient of correlation'. it is also named as "Product
.'moment coefficient
.Based on Arithmetic Mean and Standard Deviation .1
The formula is based upon arithmetic mean and standard deviation. The products of
the corresponding values of the two series i.e. o-variance is divided by the product of
.standard deviations of the series to determine the formula
determines the direction of relationship. Karl Pearson's method establishes the .2
.direction of relationship of variables viz., Positive orNegative
Establishes the size of relationship. Karl person's method also between +1 and -1. .3
+1 means perfect positive correlation and -1 mean perfect negative relationship. In
.case the value is'0', then it means no relationship between the variables
4. Ideal Measure. Karl Person's method is considered to be an ideal method of
calculation of correlation coefficient. It is because of the covariance which is most
reliable as a standard statistical tool.

3. CHAPTER
10
REGRESSION ANALYSIS
1. INTRODUCTION
The analysis of coefficient of correlation between tow variables : examines the
extent and degree of cor-relationship between two variables co-vary in a given
period of study. The statistical technique of estimating or predicting the
unknown value of a dependent variable from the known value of an
independent variable is called regression analysis.
Regression is more useful for business planning and forecasting.
Definitions:
According to Morris M. Blair “Regression is the measure of the average
relationship between two or more variables in terms of the original units of
the data."
2. CLASSIFICATION OF REGRESSION ANALYSIS
The regression analysis can be classified on the following bases:-
2.1. Change in Proportion; and
2.2. Number of variables.
2.1.1. Linear Regression Analysis Model
When dependent variable moves in a fixed proportion of the unit movement of the
unit movement of independent variable, it is called a linear regression.
Linear regression, when plotted on a graph paper, forms a straight line.
Mathematically the relation between X and Y variables can be expressed by a
simple linear regression equation as under-
Yi = a + bxi + ei
Where a and b are known as regression parameters.
2.1.2. Non-linear regression Analysis
Contrary to the liner regression model, in non-linear regression, the value of
dependent variable say 'y' dose not change by a constant absolute amount for unit
change in the value of the independent variable, say 'x'. If the data are plotted on
graph, it would form a curve, rather than a straight line. This is called curvi-linear
regression.

4. 9. UTILITY/UES OF REGRESSION ANALYSIS
Prediction of Unknown Value: The regression analysis technique is very useful in .1
predicting the probable value of an unknown variable in response to some known
.related variable
Nature of Relationship: The regression device is useful in establishing the nature .2
.of the relationship between two variables
Estimation of Relationship: Regression analysis is extensively used for the .3
.measurement and estimation of the relationship among variables
Calculation of Co-efficient of determination: The regression analysis.3
provides regression co-efficient which are generally used in calculation of
Co-efficient of Correlation. The square of co-efficient of correlation
.r ) is called the co-efficient of determination ) .4
.5
Helpful in calculation of error: Regression analysis is very helpful in estimating .5
.the error involved in using the regression line as a basis for estimation
Police formulation: The predictions made on the basis of estimated inter- .6
relationship through the techniques of regression analysis provide sound basis for
.police formulation in socio- economic fields
Touch stone of hypothesis: The regression tool is considered to be a pertinent .7
.testing tool in statistical methodology
10. LIMITATION OF REGRESSION ANALYSIS
1. Assumption of liner relationship: Regression analysis is based on the assumption
that there always exists liner relationship between related variables.
2. Assumption of static condition: while calculating the regression equation a static
condition of relationship between the variables is presumed.
3. Study of relationship in prescribed limits: The linear relationship between the
variables can only be ascertained within limits.