Question

1. What is the difference between Pearson’s correlation coefficient, r, and the coefficient of determination, r²? What does each statistic tell us about the relationship between two variables? What do these statistics NOT tell us about the relationship between two variables?

Answer 1

Difference between Pearson's correlation coefficient (r) and coefficient of determination (r2)

The pearson's correlation coefficient tells us about the degree and direction of relationship between the two variables.

The value of r range from -1 to 1.

The coefficent of determination (r2) explains the variation caused in one variable due to other related variables.

What does each statistic tells about the relationship between two variables?

Pearson Correlation Coefficient (r)

if r - value is 0 , then we say that there is no relation between variables

if r value is more than 0 , then we say there is positive relation between two variables, which means than if one variables increases then other will also increase

if r value is less than 0, then we say there is negative relationship between

Coefficient of Determination (r2):

The less the value of r2, there will be less variation in the data and all data points will be more closer to the mean value and vice versa.

What does each statistic not tell about the relationship between two variables?

The pearson correlation coefficient does not able to prove the causation which means that the r value just tells the relationship between two variables but can not work if there are more than 2 variables

The coefficient of determination can not tell us whether the data is biased or not.