1. **Problem Statement:** We are given four bivariate data sets and asked to identify the nature of the relationships between the variables in each set. 2. **Understanding Relationships:** - A **strong nonlinear relationship** means the data points follow a clear pattern but not a straight line. - A **perfect negative linear relationship** means the points lie exactly on a line with a negative slope. - The **strongest positive linear relationship** means the points closely follow a line with a positive slope. - An **apparent positive but not perfect linear relationship** means the points generally increase but with some variability. 3. **Analyzing Each Data Set:** - Data set (w,t) shows points scattered without a clear linear trend, indicating a strong nonlinear relationship. - Data set (u,v) shows a perfect decreasing linear trend, indicating a perfect negative linear relationship. - Data set (m,n) shows a generally increasing trend with some variability, indicating a positive but not perfect linear relationship. - Data set (x,y) shows a generally downward trend but not perfect, so it is not the strongest positive. 4. **Final Answers:** (a) Strong nonlinear relationship: **(w,t)** (b) Perfect negative linear relationship: **(u,v)** (c) Strongest positive linear relationship: **Figure 4 data set (7.0,5.7), (8.0,6.6), (9.0,8.8), (10.0,7.5)** (d) Apparent positive but not perfect linear relationship: **(m,n)**