1. The problem asks to identify which scatter diagrams correspond to specific types of linear correlations between variables $x$ and $y$. 2. Important concepts: - A positive linear correlation means as $x$ increases, $y$ also increases. - A negative linear correlation means as $x$ increases, $y$ decreases. - The strength of correlation is indicated by how closely points fit a straight line. 3. Given descriptions: - Graphs (a) and (b) show positive linear trends. - Graphs (c) and (d) show negative linear trends. 4. For (a) strongest positive linear correlation, choose the graph with points most tightly clustered along an upward line. Both (a) and (b) show positive trends, but the problem states (a) is strongest positive. 5. For (b) strongest negative linear correlation, choose the graph with points most tightly clustered along a downward line. Between (c) and (d), the problem states (d) is strongest negative. 6. For nearly perfect positive linear correlation, the graph must show points almost exactly on a straight line with positive slope. Based on the problem, this corresponds to graph (a). Final answers: - (a) strongest positive linear correlation: graph a - (b) strongest negative linear correlation: graph d - Nearly perfect positive linear correlation: graph a