Question

which statement it true regarding their claims? adele is correct because only lines may have a negative slope. adele is correct because the y values increase as the x values decrease in graph a, so it shows a positive correlation. monte is correct because both graphs show a strong correlation. monte is correct because in both scatterplots, the y values decrease as the x values increase so both have a negative correlation.

Explanation:

Step1: Analyze the concept of correlation

In a scatter - plot, if \(y\) values decrease as \(x\) values increase, it is a negative correlation. It is not restricted to lines.

Step2: Check each option

• Option 1: Non - linear relationships (like the first scatter - plot which is a curve) can also have a negative correlation (since \(y\) decreases as \(x\) increases). So, the statement “only lines may have a negative slope (correlation)” is wrong.
• Option 2: In graph A, as \(x\) increases, \(y\) decreases. So, it is a negative correlation, not a positive correlation.
• Option 3: The first graph (a curve) has a non - linear relationship. But correlation (linear or non - linear trend) is about the general direction of the relationship. The second graph is a line. Just saying “strong correlation” without considering the direction is incorrect.
• Option 4: In both scatter - plots, as \(x\) values increase, \(y\) values decrease. So, both have a negative correlation.

Answer:

Monte is correct because in both scatterplots, the \(y\) values decrease as the \(x\) values increase so both have a negative correlation.