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
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Using the first two points, we have:
[tex] m=\frac{10-15}{5-0}=\frac{-5}{5}=-1 [/tex]
Checking the next two points, we have:
[tex] m=\frac{5-10}{10-5}=\frac{-5}{5}=-1 [/tex]
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.
