Question

shown below are the scatter plots for four data sets. answer the questions that follow. (a) which data set appears to show a negative linear relationship between its two variables? (b) which data set appears to show a positive 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:

• (a) In a negative linear relationship, as one variable increases, the other decreases. In Figure 3, the points follow a downward - sloping trend, indicating a negative linear relationship.
• (b) In a positive linear relationship, as one variable increases, the other also increases. In Figure 2, the points follow an upward - sloping trend, indicating a positive linear relationship.
• (c) A nonlinear relationship does not follow a straight - line pattern. In Figure 4, the points do not form a straight line but rather a curved pattern, indicating a nonlinear relationship.
• (d) No relationship means the points are scattered randomly. In Figure 1, the points are scattered without any discernible pattern (neither linear nor nonlinear), indicating no relationship.

Answer:

(a) The data set in Figure 3
(b) The data set in Figure 2
(c) The data set in Figure 4
(d) The data set in Figure 1