Correlation

Correlation

1. CORRELATION CHAPTER # 8 NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS

2. What is correlation ? Correlation is defined as “The Relationship which exists between two variables . OR Methods of measuring the degree of relationship existing between two variables

3. For example ; Increase in height of children is accompanied by increase in weight . Some more examples of correlation are defined as : 1-Income and Expenditure 2-Price and Demand

4. Types of correlation 1-Positive Correlation 2-Negative Correlation 3-Zero Correlation

5. Positive Correlation: If both the variables are moving in same direction (Increase OR Decrease) then correlation is said to be direct or Positive, the first example of Income and Expenditure related with positive correlation.

6. Common Examples of Positive Correlations The more time you spend running on a treadmill, the more calories you will burn. The longer your hair grows, the more shampoo you will need. As the temperature goes up, ice cream sales also go up.

7. The more petrol you put in your car, the farther it can go . As a child grows, so does his clothing size . The more it rains, the more sales for umbrellas go up . As more people go to the movies, the amount of money spent on tickets increases.

8. Negative Correlation : When the movements of the two variables are in opposite direction then this type of relation is called inversly proportion so in this case correlation is said to be negative , the second example of Price and Demand, if price increases the demand decreases

9. Common Examples of Negative  Correlation A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases. If a chicken increases in age, the amount of eggs it produces decreases.

10. Zero Correlation : If there is no association between the two variables the correlation is said to be zero correlation (It means Both the variables are independent).

11. Common Examples of Zero Correlation The number of cups of Tea consumed in an office each day in March and the number of inches of rainfall in Karachi on the same days. For example their is no relationship between the amount of tea drunk and level of intelligence.

12. The correlation may be studied by the following two methods. 1-Scatter Diagram 2-Coefficient of Correlation

13. Coefficient of Correlation :- Numerical Measure of correlation is called coefficient of correlation. It measured the degree of relationship between the variables. The formula is called Karl Pearson’s coefficient of correlation. There are different formulae for the calculation of Karl Pearson coefficient of correlation.

14. 1. r = 2. r = 3. r = 4. r = 5. r =  

15. Interpretation of coefficient of correlation:- The Limit of correlation is to be from negative one to positive one  

16. If r =1 the correlation is said to be perfect positive correlation . If r= -1 the correlation is said to be perfect negative c o rrelation . Coefficient of Correlation Strength 0.90---------0.99 Very strong 0.78---------0.89 Strong 0.64---------0.77 Moderate 0.46---------0.63 Low 0.10---------0.45 Very Low 0.00---------0.09 No

17. Example : An economist gives the following estimates: Calculate Karl Pearson’s coefficient of correlation and make Comments about the type of correlation exist. Price 1 2 3 4 5 Demand 9 7 6 3 1

18. Solution: X Price( Rs ) Y Demand(Kg) XY 1 9 9 1 81 2 7 14 4 49 3 6 18 9 36 4 3 12 16 9 5 1 5 25 1 =55 =176 X Price( Rs ) Y Demand(Kg) XY 1 9 9 1 81 2 7 14 4 49 3 6 18 9 36 4 3 12 16 9 5 1 5 25 1

19. Formula of Karl Pearson coefficient of correlation : r = r = r =  

20. r = r = r = r = - 0.99  

21. Comments : The Correlation between two variables is very high strong negative .

22. Do yourself following problems and make comments

23. Q1-A sample of 10 student was asked for distance and time required to reach the college on a particular day . Compute Karl Pearson’s coefficient of correlation between distance and time .(0.92) Distance 1 3 5 5 7 7 8 10 10 12 Time (Min) 5 10 15 20 15 25 20 25 35 35

24. Q2- For the paired observations (x, y) given below : Calculate coefficient of correlation .(0.07) X 12 13 16 18 21 22 Y 10 50 30 20 60 10

25. Q3- find coefficient of correlation . If N = 50 , (0)