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

Pearson’s Correlation Calculations of Pearson Correlation

Pearson’s Correlation Example1: If you have the bellow data calculate Pearson’s correlation: NoYX

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

Pearson’s Correlation Where

Pearson’s Correlation Solution: YXY^2X^2XY Sum

Pearson’s Correlation Solution

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

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.

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:

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

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

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.

Pearson’s Correlation

Examples of scatter plot

Pearson’s Correlation Examples of scatter plot

Pearson’s Correlation Examples of scatter plot

Pearson’s Correlation Relation between linear regression and correlation