GEA1000 chapt 3 correlation coefficient and its limitations

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what is correlation coefficient

• a measure of linear association

• summarises direction and strength of linear association

• ranges between -1 and 1

what are the different interpretations of r-value

r > 0 → positive linear association

r < 0 → negative linear association

r = 1 → perfect positive linear association

r = -1 → perfect negative linear association 

r = 0 → no linear association 

what does the magnitude of the r-value mean

• strength of linear association

• closer value of r to -1 or 1 → stronger the linear association

• closer value of r to 0 → weaker the linear association

what is the formula for correlation coefficient

1. convert each data point to Standard Unit (SUx, SUy, Sx is s.d of X and Sy is s.d of Y)

SUx = [X - avg(X)] / Sx

SUy = [Y - avg(Y)] / Sy

2. r value is the sum of product of X and Y in standard unit divided by (n-1)

• n is no. of data points

what is the properties of r

r is not affected by:

• interchange of 2 variables

• adding a number to all values of a variable

• multiplying a positive number to all values of a variable

what are some limitations of correlation coefficient 

• correlation DOES NOT imply causation 

• a third variable might affect the outcome 

how can a quadratic scatter plot have a r = 0

• r only measures the linear association between 2 variables

• quadratic scatter plot is not a linear association

what are outliers

observations that fall far from the main cluster of points

how can they affect correlation

decrease of increase the strength of the correlation, depending on where the outlier is with respect to the other points