Question

which characteristic of a data set makes a linear regression model unreasonable?
○ a slope close to 0
○ a correlation coefficient close to 0
○ a slope close to −1
○ a correlation coefficient close to −1

Explanation:

To determine which characteristic makes a linear regression model unreasonable, we analyze each option:

• A slope close to 0 means a weak positive/negative linear trend but doesn't make the model unreasonable (e.g., a flat line can still be a valid linear model if the relationship is truly linear with little change).
• A correlation coefficient close to 0 indicates a very weak or no linear relationship between the variables. Linear regression is used to model linear relationships, so if the correlation is near 0, the data doesn't have a linear pattern, making the linear regression model unreasonable.
• A slope close to -1 indicates a strong negative linear relationship, which is suitable for linear regression.
• A correlation coefficient close to -1 indicates a strong negative linear relationship, which is suitable for linear regression.

Answer:

B. a correlation coefficient close to 0