Correlation.pdf
- 1. ACHARYA NARENDRA DEVA UNIVERSITY OF AGRICULTURE OF TECHNOLOGY, KUMARGANJ, AYODHYA-(224229), U.P. Assignment on Correlation Course No : STAT-502 4(3+1) Course name : Statistical methods for applied sciences Presented to: Dr. Vishal Mehta Assistant Professor Department of Agril. Statistics Presented by: Dharmendra Kumar Id. No. A-12993/22 Ph.D. 𝟏𝒔𝒕 𝐒𝐞𝐦𝐞𝐬𝐭𝐞𝐫 Soil Science and Agril. Chemistry
- 3. Content • Correlation • Uses of correlation analysis • Importance of correlation analysis • Types of correlation • Rank correlation • Repeated rank correlation • Numerical • References
- 4. Correlation • 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.
- 5. 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 is used in presenting the average relationship between any two variables through a single value of coefficient of correlation.
- 6. 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.
- 7. Types of correlation On the basis of degree of correlation On the basis of number of variables On the basis of linearity 1. Positive correlation 2. Negative correlation 3. Constant correlation 1. Simple correlation 2. Partial correlation 3. Multiple correlation 1. Linear correlation 2. Non –linear correlation
- 8. 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.): 350 360 370 380 • Weight ( Kg.) : 30 40 50 60
- 9. • 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
- 10. Constant/Zero correlation • A zero correlation exists when there is no relationship between two variables. For example There is no relationship between the amount of tea drunk and level of intelligence.
- 11. 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.
- 12. 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.
- 13. • 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.
- 14. 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
- 15. 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
- 16. Rank correlation Rank correlation: This method is finding out the lack of it between two variable was developed by the ‘brutish Psychologist Charles Edward Spearman in 1904’. In any event, the RCC is applied to a set of ordinal rank no. with for the individual ranked in quality or quantity and soon to for the individual ranked last in a group of individual.
- 17. Rank correlation formula Rank correlation: 𝑟𝑠 = 1 − 6 σ 𝑑𝑖 2 𝑛(𝑛2−1) where, 𝑟𝑠= spearman rank correlation n= number of observations d= difference of individual observation
- 18. Question. Ten varieties of rice in the field were judged for overall per for mince by two formers the rank by formers are given below. EXAMPLE: X Y di = X-Y 2 1 1 1 1 2 -1 1 5 7 -2 4 3 4 -1 1 10 8 2 4 8 9 -1 1 9 10 -1 1 7 3 4 16 4 6 -2 4 6 5 1 1
- 19. Repeated Correlation Co-efficient FORMULA : 𝒓𝒌 = 𝟏 − 𝟔[σ𝒅𝒊𝟐 + σ 𝒎(𝒎𝟐 − 𝟏) 𝟏𝟐 𝒏(𝒏𝟐 − 𝟏) EXAMPLE: Obtain the correlation rank following the data – X ( 68,64 ,75 ,50 ,64 ,80 ,75 ,40 ,55 ,64) Y (62 ,58 ,68 ,45 ,81 ,60 ,68 ,48 ,50 ,70)
- 20. EXAMPLE: X Y di= (RX-RY) 68 62 -1 1 64 58 -1 1 75 68 -1 1 50 45 -1 1 64 81 5 25 80 60 -5 25 75 68 -1 1 40 48 1 1 55 50 0 0 66 70 4 16
- 21. SOLVED - 1- 6 σ 𝑑2+ 𝑚 𝑚2−1 12 𝑛 𝑛2−1 =1 - 6(72)+3 10(10−1) = 1- = 990−435 990 = 555 990 =0.5606 𝟒𝟑𝟐 + 𝟑 𝟗𝟗𝟎
- 22. ❑References • Agarwal, B.L., Programmed Statistics. New Age International Publishers, New Delhi, 3rd edition. • Gupta, S.C. and Kapoor, V.K., Fundamentals of Mathematical Statistics. Sultan Chand & Sons, New Delhi, 12th edition. • Paul, N.C., Statistics in shorts. New Vishal Publications, New Delhi.