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? select (b) which data set appears to show a negative linear relationship between its two variables? select (c) which data set appears to show no relationship between its two variables? select (d) which data set appears to show a nonlinear relationship between its two variables? select

Explanation:

Step1: Understand positive linear relationship

A positive linear relationship means as one variable increases, the other variable also increases in a linear - like fashion. In Figure 2, as the x - values increase, the y - values generally increase in a somewhat straight - line pattern.

Step2: Understand negative linear relationship

A negative linear relationship means as one variable increases, the other variable decreases in a linear - like fashion. In Figure 4, as the x - values increase, the y - values generally decrease in a somewhat straight - line pattern.

Step3: Understand no relationship

In Figure 3, the points are scattered randomly and there is no clear pattern (neither increasing nor decreasing in a linear or non - linear way) as the x - values change. So, there appears to be no relationship.

Step4: Understand non - linear relationship

A non - linear relationship means the relationship between the two variables is not in a straight - line form. In Figure 1, the points form a U - shaped pattern, which is a non - linear relationship.

Answer:

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