3. the correlation (r) between x and y, with the relationship displayed in the following scatterplot, is…

3. the correlation (r) between x and y, with the relationship displayed in the following scatterplot, is 0.969. lewis is an ap stats student who says that the best regression model for this data must be linear because the correlation is so close to 1. do you agree? explain.

3. the correlation (r) between x and y, with the relationship displayed in the following scatterplot, is 0.969. lewis is an ap stats student who says that the best regression model for this data must be linear because the correlation is so close to 1. do you agree? explain.

Answer

Brief Explanations:

The correlation coefficient ($r$) measures the strength and direction of a linear relationship. However, a high $r$ - value (close to 1 or - 1) does not necessarily mean the relationship is linear. There could be a non - linear relationship that still has a high correlation due to the nature of how $r$ is calculated. For example, a quadratic relationship with a particular set of data points can have a high $r$ value. Just looking at the scatter - plot, the points do not seem to form a perfect straight line.

Answer:

No, I do not agree. A high correlation value close to 1 only indicates a strong linear - like association, but does not prove that the relationship is linear. There could be a non - linear relationship underlying the data.