Week 4 understanding Correlation through Covariance and Standard Deviation.

[Yogendra Shakya]

Would like to have some clarification on what is the difference between covariance and standard deviation.

we divide Covariance between 2 items with sd of them and received the proportional difference as the correlation, but it seems we are doing the operations on the numbers (multiplying x-xbar.y-ybar and summing them for covariance; and for standard deviation, squaring thex-xbar x y-ybar multiplying their sum and finally again square rooting them. doing the same operation slightly different way..

just to understand same, i created a simple data sheet (with 2 values for x and y) to test same and it always gives me any correlation as r =1 always..    

i would like to understand what is the mathematical difference that occurs between these two items when we do similar operations on both the items. (my data sheet shows no difference, but i know we generally get proportional difference which is the correlation r.) 

Please find the link to my document below.

please help understand.

https://docs.google.com/spreadsheets/d/1o4ifknFA6CK7uN7PznW6n8iXcAJoFzwQ590qBrntf1Q/edit?usp=sharing

[statistics-1]

When we talk about covariance, we are talking about the spread of both variables from their mean. That is why we multiply the (x-x bar)*(y-y bar). 

Standard deviation is spread of one variable.  Since covariance has units and thereby different numbers. To scale it we are dividing it by deviations of two variables. 

In the sheet, if you change the data then you won't get the same value. 

Best regards,
Ram,

Statistics-1 Course Support Team