Chapter 4, Problem 1CR

Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is $-1$ to $+1$. The values $-1$ and $+1$ of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.