Question

What is the correlation coefficient for the data shown in the table? R =

Answer 1

The correct answer is:

-1.

Explanation:

When we graph this data, we can see it seems to form a straight line. To check this, we find the slope of the data using the formula

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the first two points, we have:

$m=\frac{10-15}{5-0}=\frac{-5}{5}=-1$

Checking the next two points, we have:

$m=\frac{5-10}{10-5}=\frac{-5}{5}=-1$

Since the slope is the same between successive pairs of points, this is a linear data set.

This means the linear regression will go through every point, and will be a perfect fit. The correlation coefficient, r, of a data set is 1 if it is a perfect positive fit and -1 if it is a perfect negative fit; since the slope is decreasing, this is a negative correlation, and since it fits perfectly, it is -1.

Answer 2

As the data makes a linear function, y = -x + 15, the correlation coefficient would be r = -1, as the function is negative.

Hope this helps!