Question

Answer the following questions:

Describe the range of values for the correlation coefficient.

Discuss the difference between "r" and "p".

In your own words, what does it mean to say "correlation does not imply causation?"

Answer 1

The range of correlation coefficient ( r ) is from -1 to 1

If r = -1 then there is perfect negative correlation between the two varables. That is increase in one variable implies that the decrease in other variables with same rate and vice versa.

Note that the value of r represent only linear relationship between the two variables. It is not usefull for nonlinear relationship.

If r is closeto -1 then there is strong negative correlation between the variables. That is increase in the value of one variable leads the decrease in the value of other variable and vice versa. Here all the point (x, y) are very closed to the line with negative slope.

If r is not very close to -1 but greater than -0.4 then we say that there is moderate negative correlation between the two variables. In this case the points ( x , y ) scatter from the line with negatiive slope ( that is they are not very close to the line with negative slope).

If r = 0 then there is no correlation ( no relationship ) between the variables.

If r is lies between ( 0.4 to 0.6) then there is  moderate positive correlation between the two variables. In this case the points ( x , y ) scatter from the line with positive slope ( that is they are not very close to the line with positive slope).

If r is lies between ( 0.6 to 0.8) then there is  strong positive correlation between the two variables. In this case the points ( x , y ) closed from the line with positive slope ( that is they are not very close to the line with positive slope). Also if the one variable is increases then other is also increase and decrease in the one variable result in decrease in the other variable.

If r is lies between ( 0.8 to 1) then there is very strong positive correlation between the two variables. In this case the points ( x , y ) very closed from the line with positive slope. Also if the one variable is increases then other is also increase and decrease in the one variable result in decrease in the other variable.

If r = 1 then there is perfect correlation between the two variables.

So that, if the one variable is increases then other is also increase with same rate and decrease in the one variable result in decrease in the other variable with same rate.

If there is correlation between the two variables then we cannot conclude that one of the variable is affect the other variable value. That is we cannot say that there is cause-and-effect relationship is present.

For example: If we want to find the correlation between the number of tempes in a cities and the number of crimes of the cities and suppose we get r = 0.98. Which is very strong correlation. So we cannot conclude that the large number of temples lead more crimes happen in the city.

This result may be from the fact that "large area of the city leads more population and so number of temples and number of crime rates also large.