Question

Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is​ linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following.

02468100100200300400ExplanatoryResponse A scatter diagram has a horizontal axis labeled “Explanatory” from 0 to 10 in increments of 1 and a vertical axis labeled “Response” from 0 to 400 plus in increments of 100. The following 12 approximate points are plotted, listed here from left to right: (0.6, 40); (1.2, 40); (2, 40); (3, 40); (4, 40); (6, 50); (7, 100); (7, 150); (8.2, 210); (8.2, 240); (9.8, 390); (9.8, 420). The first five points follow the general pattern of a horizontal line and the next 7 points follow the general pattern of a straight line that rises from left to right.

Do the two variables have a linear​ relationship?

A.

The data points have a linear relationship because they lie mainly in a straight line.

B.

The data points do not have a linear relationship because they lie mainly in a straight line.

C.

The data points do not have a linear relationship because they do not lie mainly in a straight line.

D.

The data points have a linear relationship because they do not lie mainly in a straight line.

Answer 1

Solution:

We are given that: a scatter diagram which has a horizontal axis labeled “Explanatory” and a vertical axis labeled “Response”. The following 12 approximate points are plotted, listed here from left to right:

(0.6, 40); (1.2, 40); (2, 40); (3, 40); (4, 40); (6, 50); (7, 100); (7, 150); (8.2, 210); (8.2, 240); (9.8, 390); (9.8, 420)

From above scatter diagram, we can see there is no straight line pattern. The pattern obtained is a curve.

Thus correct option is:

C. The data points do not have a linear relationship because they do not lie mainly in a straight line.