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# Correlation analysis

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### Correlation analysis

1. 1. Correlation Analysis Shivani Sharma M.Com Sem. 1 3014
2. 2. Meaning of Correlation Analysis Correlation is the degree of inter-relatedness among the two or more variables. Correlation analysis is a process to find out the degree of relationship between two or more variables by applying various statistical tools and techniques. According to Conner “if two or more quantities vary in sympathy, so that movement in one tend to be accompanied by corresponding movements in the other , then they said to be correlated.”
3. 3. Three Stages to solve correlation problem :  Determination of relationship, if yes, measure it.  Significance of correlation.  Establishing the cause and effect relationship, if any.
4. 4. Uses of Correlation Analysis  It is used in deriving the degree and direction of relationship within the variables.  It is used in reducing the range of uncertainty in matter of prediction.  It I used in presenting the average relationship between any two variables through a single value of coefficient of correlation.
5. 5. Uses of Correlation Analysis  In the field of science and philosophy these methods are used for making progressive conclusions.  In the field of nature also, it is used in observing the multiplicity of the inter related forces.
6. 6. Types of correlation On the basis of degree of correlation On the basis of number of variables On the basis of linearity •Positive correlation •Negative correlation •Simple correlation •Partial correlation •Multiple correlation •Linear correlation •Non – linear correlation
7. 7. Correlation : On the basis of degree  Positive Correlation if one variable is increasing and with its impact on average other variable is also increasing that will be positive correlation. For example : Income ( Rs.) : 350360 370 380 Weight ( Kg.) : 30 40 50 60
8. 8. Correlation : On the basis of degree  Negative correlation if one variable is increasing and with its impact on average other variable is also decreasing that will be positive correlation. For example : Income ( Rs.) : 350 360 370 380 Weight ( Kg.) : 80 70 60 50
9. 9. Correlation : On the basis of number of variables  Simple correlation Correlation is said to be simple when only two variables are analyzed. For example : Correlation is said to be simple when it is done between demand and supply or we can say income and expenditure etc.
10. 10. Correlation : On the basis of number of variables  Partial correlation : When three or more variables are considered for analysis but only two influencing variables are studied and rest influencing variables are kept constant. For example : Correlation analysis is done with demand, supply and income. Where income is kept constant.
11. 11. Correlation : On the basis of number of variables  Multiple correlation : In case of multiple correlation three or more variables are studied simultaneously. For example : Rainfall, production of rice and price of rice are studied simultaneously will be known are multiple correlation.
12. 12. Correlation : On the basis of linearity  Linear correlation : If the change in amount of one variable tends to make changes in amount of other variable bearing constant changing ratio it is said to be linear correlation. For example : Income ( Rs.) : 350 360 370 380 Weight ( Kg.) : 30 40 50 60
13. 13. Correlation : On the basis of linearity  Non - Linear correlation : If the change in amount of one variable tends to make changes in amount of other variable but not bearing constant changing ratio it is said to be non - linear correlation. For example : Income ( Rs.) : 320 360 410 490 Weight ( Kg.) : 21 33 49 56
14. 14. Importance of correlation analysis :  Measures the degree of relation i.e. whether it is positive or negative.  Estimating values of variables i.e. if variables are highly correlated then we can find value of variable with the help of gives value of variable.  Helps in understanding economic behavior.
15. 15. Correlation and Causation  The correlation may be due to pure chance, especially in a small sample.  Both the correlated variables may be influenced by one or more other variables.  Both the variables may be mutually influencing each other so that neither an be designed as the cause and other as
16. 16. Probable Error : Probable error determine the reliability of the value of the coefficient in so far as it depends on the conditions of random sampling. It helps in interpreting its value. P.E.r = 0.6745 (1-r2)/√n r = coefficient of correlation. n = number of pairs of observation.
17. 17. Conditions under Probable error :  if the value of r is less than the probable error there is no evidence of correlation, i.e. the value of r is not at all significant. If the value of r is more than six times the probable error, the coefficient of correlation is practically certain i.e. the value of r is significant.
18. 18. Conditions under Probable error  By adding and subtracting the value of probable error from the coefficient of correlation we get the upper and lower limits, between correlation lies. P = r+ P.E. ( upper limit ) P = r- P.E. ( lower limit )
19. 19. Coefficient of Determination : Coefficient of determination also helps in interpreting the value of coefficient of correlation. Square of value of correlation is used to find out the proportionate relationship or dependence of dependent variable on independent variable. For e.g. r= 0.9 then r2 = .81 or 81% dependence of dependent variable on independent variable.Coefficient of Determination = Explained variation Total variance
20. 20. Thank you
21. 21. References :  S. P. Gupta  S. C. Gupta  www.wikipedia.org  Mr. Kohli  Mr. D. Patri