Question

Which answer is the best estimate of the correlation coefficient for the variables in the scatterplot?

Answer 1

-0.8 would be the best estimate.

The data seem to have a negative correlation, since they are decreasing; this means our r-value will be negative.

Our two negative choices are -0.25 and -0.8.  -0.8 would be a fairly strong correlation, whereas -0.25 would be a weak correlation.  The data do seem to be fairly strongly related, so we will use -0.8.

Answer 2

The best estimation for the correlation coefficient is the first option, -0.8

How to take a good estimation?

Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂) the slope is given as:

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

With that in mind, we could use the first and last point to get a rough estimation (we actually need to do it for all the possible pairs of points and then take the mean). But let's only do it for the first and last point and see what we get.

• The first point is something like (1.1, 8.1)
• The last point is something like (7.2, 1.2).

The slope for the line that connects these two points is:

$a = \frac{1.2 - 8.1}{7.2 - 1.1} = -1.13$

From the options, the closest one to this is the first option, -0.8, so that is the correct option.

If you want to learn more about correlation, you can read:

https://brainly.com/question/14289293