1. Pearson’s Correlation The Pearson correlation coefficient is the most widely used for summarizing the relation ship between two variables that have a straight line or linear ship with each other. The possible value of range from -1 to +1 only

2. Pearson’s Correlation Calculations of Pearson Correlation

3. Pearson’s Correlation Example1: If you have the bellow data calculate Pearson’s correlation: NoYX 11610 21712 31815 4 8 51820 62217 71912 82215 91812 101510 11188 121610

4. Pearson’s Correlation 1. We can easiest the above calculation as

5. Pearson’s Correlation Where

6. Pearson’s Correlation Solution: YXY^2X^2XY 1610256100160 1712289144204 1815324225270 15822564120 1820324400360 2217484289374 1912361144228 2215484225330 1812324144216 1510225100150 18832464144 1610256100160 Sum214149387619992716

7. Pearson’s Correlation Solution

8. Pearson’s Correlation This indicates a relatively large positive relationship between the two variables.

9. Pearson’s Correlation Test of coefficient When computing a correlation coefficient, it is also useful to test the correlation coefficient for significance. This provides the researcher with some idea of how large a correlation coefficient must be before considering it to demonstrate that there really is a relationship between two variables. It may be that two variables are related by chance.

10. Pearson’s Correlation The sampling distribution of Pearson correlation is approximately t distribution with Degree of freedom = n - 2 And t can be calculated as:

11. Pearson’s Correlation At alpha = 0.05 test if there is a positive relation between Y and X in previous example Tabulated t at df = 12 – 2 = 10

12. Pearson’s Correlation Then we reject the null hypothesis so that there is a positive relation between Y and X.

13. Pearson’s Correlation Scatter diagram: A scatter diagram is a diagram that shows the values of two variables X and Y, from this scatter diagram we can conclude the relation between these variables. In the bellow diagram we can see the relation between Y and X variable.

14. Pearson’s Correlation

15. Examples of scatter plot

16. Pearson’s Correlation Examples of scatter plot

17. Pearson’s Correlation Examples of scatter plot

18. Pearson’s Correlation Relation between linear regression and correlation