Question

objective 4-1: make and understand scatter plots.

1. what type of association does the scatter plot comparing elevation and mean annual temperature have?
2. describe the relationship between the discount and the number of items sold.
3. using the scatter plot, which of the following is the best prediction of x when y=32.

a. 6
b. 23
c. 38
d. 11

1. what does a cluster in a scatter plot represent?

what does a gap in a scatter plot represent?

Explanation:

Question 1

Step1: Analyze the scatter plot trend

The scatter plot for elevation (x - axis) and mean annual temperature (y - axis) has two distinct clusters. As elevation increases, the mean annual temperature does not follow a linear (constant rate of change) pattern. Instead, there are two separate groups of points, so the association is nonlinear.

Step2: Confirm the type of association

A linear association would have points roughly following a straight - line pattern. Here, the points are in two clusters, so it's a nonlinear association (specifically, a negative association in a nonlinear way as elevation increases, temperature decreases but in two clusters).

Step1: Observe the scatter plot pattern

The scatter plot for discount (x - axis) and number of items sold (y - axis) has points that do not follow a straight - line pattern. Initially, with low discounts, the number of items sold is low. Then, at certain discount levels, the number of items sold jumps. So the relationship is not linear.

Step2: Determine the association type

Since the points do not lie close to a straight line and the relationship between discount and items sold changes in a non - constant rate way, the relationship is a nonlinear association (it can also be described as having a nonlinear positive association in parts, but overall nonlinear).

Step1: Analyze the scatter plot for y = 32

Look at the scatter plot where y (vertical axis) is 32. Find the x - values (horizontal axis) corresponding to y = 32. The points around y = 32 have x - values around 30 - 40. Among the options, 38 (option c) is in this range. Option a (6) is too small, option b (23) is too small, and option d (11) is too small.

Step2: Select the best prediction

Based on the scatter plot, when y = 32, the x - value is best predicted as 38.

Answer:

Nonlinear association

Question 2