x: 1,2,3,4,9,10
y: 12,2,3,5,9,11
What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between x and y in most of the observations?
x: 1,2,3,4,9,10
y: 12,2,3,5,9,11
What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between x and y in most of the observations?
This is due to the first pair $(x_1,y_1)=(1,12)$. If you exclude this observation the correlation is $99\%$. If you include it, then the correlation reduces indeed to about 0.4133.
Correlation is a measurement of the strength of the linear relationship between the two variables and this observation affects a lot the straigh-line relationship that is between the rest of the observations.