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 thats 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 thats 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)-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 dont get a straight line but a curve type figure. CHPTER 9 CORRELATION ANALYSIS Karl Persons 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 Pearsons formula and is popularly known as Karl Persons 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 ofthe 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 Pearsons method establishes the .2 .direction of relationship of variables viz., Positive orNegativeEstablishes the size of relationship. Karl persons method also between +1 and -1. .3 +1 means perfect positive correlation and -1 mean perfect negative relationship. In .case the value is0, then it means no relationship between the variables 4. Ideal Measure. Karl Persons 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.
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 AnalysisContrary to the liner regression model, in non-linear regression, the value ofdependent variable say y dose not change by a constant absolute amount for unitchange in the value of the independent variable, say x. If the data are plotted ongraph, it would form a curve, rather than a straight line. This is called curvi-linearregression.
9. UTILITY/UES OF REGRESSION ANALYSISPrediction of Unknown Value: The regression analysis technique is very useful in .1predicting the probable value of an unknown variable in response to some known.related variableNature of Relationship: The regression device is useful in establishing the nature .2.of the relationship between two variablesEstimation 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 .5Helpful in calculation of error: Regression analysis is very helpful in estimating .5.the error involved in using the regression line as a basis for estimationPolice formulation: The predictions made on the basis of estimated inter- .6relationship through the techniques of regression analysis provide sound basis for.police formulation in socio- economic fieldsTouch stone of hypothesis: The regression tool is considered to be a pertinent .7.testing tool in statistical methodology 10. LIMITATION OF REGRESSION ANALYSIS1. Assumption of liner relationship: Regression analysis is based on the assumptionthat there always exists liner relationship between related variables.2. Assumption of static condition: while calculating the regression equation a staticcondition of relationship between the variables is presumed.3. Study of relationship in prescribed limits: The linear relationship between thevariables can only be ascertained within limits.