Question

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

R =

Answer 1

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!

Answer 2

The correct answer is:

-1.

Step-by-step 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=(y_2-y_1)/(x_2-x_1)`

Using the first two points, we have:

`m=(10-15)/(5-0)=(-5)/(5)=-1`

Checking the next two points, we have:

`m=(5-10)/(10-5)=(-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.