To solve this problem, we analyze the two scatterplots and the given answer choices.

• Plot A shows a clear nonlinear relationship; the points curve, indicating a parabolic shape, which is typical of a nonlinear relationship.
• Plot B shows a negative linear relationship, as the points appear to follow a downward sloping straight line.

Now, let's evaluate each option:

1. Option A: Plot A indicates a nonlinear relationship between the variables.

   • This is true since Plot A shows a curved (parabolic) pattern.

2. Option B: Plot B indicates a linear relationship between the variables.

   • This is true since Plot B shows points that follow a linear trend.

3. Option C: The correlation coefficient for the data in Plot B is close to 1.

   • This cannot be true. A correlation coefficient of 1 indicates a perfect positive linear relationship. However, Plot B shows a negative linear relationship, so the correlation should be close to -1, not 1.

4. Option D: The correlation coefficient for the data in Plot A is close to 0.

   • This is true. Since Plot A shows a nonlinear pattern, the correlation coefficient would not capture the relationship well and would likely be close to 0.

5. Option E: The $r^2$ value of the least-squares regression line for Plot B is greater than the $r^2$ value of the least-squares regression line for Plot A.

   • This is true. Plot B follows a strong linear trend, so the $r^2$ value would be high, while Plot A's $r^2$ value would be lower due to its nonlinear pattern.

Thus, the statement that cannot be true is Option C: The correlation coefficient for the data in Plot B is close to 1.

Would you like more details on the concepts of correlation and $r^2$ values?

Here are 5 related questions for deeper understanding:

1. What is the difference between correlation and $r^2$ in data analysis?
2. How is the correlation coefficient calculated, and what are its typical ranges?
3. Can a nonlinear relationship ever have a high $r^2$ value? If so, under what conditions?
4. What are some methods for detecting nonlinear relationships in scatterplots?
5. How does the least-squares regression line differ between linear and nonlinear models?

Tip: In scatterplot analysis, the correlation coefficient reflects the strength and direction of a linear relationship, while the $r^2$ value measures the proportion of variance explained by a model, which can apply to both linear and nonlinear fits.