Question

shown below are the scatter plots for four data sets. answer the questions that follow. (a) which data set appears to show a positive linear relationship between its two variables? (b) which data set appears to show a negative linear relationship between its two variables? (c) which data set appears to show a nonlinear relationship between its two variables? (d) which data set appears to show no relationship between its two variables?

Explanation:

Step1: Understand positive linear relationship

A positive linear relationship has points that generally go up - as the x - value increases, the y - value increases in a linear fashion. In Figure 2, as x increases, y also increases in a somewhat straight - line pattern.

Step2: Understand negative linear relationship

A negative linear relationship has points such that as the x - value increases, the y - value decreases in a linear way. In Figure 1, as x increases, y decreases in a fairly linear manner.

Step3: Understand nonlinear relationship

A nonlinear relationship has a curved pattern. In Figure 3, the points form a U - shaped (curved) pattern, indicating a nonlinear relationship.

Step4: Understand no relationship

A data set with no relationship has points that are randomly scattered with no discernible pattern. In Figure 4, the points are randomly placed with no clear trend.

Answer:

(a) Figure 2
(b) Figure 1
(c) Figure 3
(d) Figure 4