Question

Suppose a linear model with a positive slope is moderately appropriate for a dataset. What might its correlation coefficient and residuals look like?(1 point)
Responses

Its correlation coefficient would be close to 0.5
0.5
, and its residuals would be relatively small.
Its correlation coefficient would be close to 0 point 5, and its residuals would be relatively small.

Its correlation coefficient would be close to −0.5
−
0.5
, and its residuals would widely vary.
Its correlation coefficient would be close to negative 0 point 5, and its residuals would widely vary.

Its correlation coefficient would be close to −0.5
−
0.5
, and its residuals would have some variation.
Its correlation coefficient would be close to negative 0 point 5, and its residuals would have some variation.

Its correlation coefficient would be close to 0.5, and its residuals would have some variation.

Answer 1

Given that a linear model with a positive slope is moderately appropriate for a dataset, the correlation coefficient would likely indicate a moderate positive relationship between the variables. A correlation coefficient close to 0.5 suggests a moderate positive correlation, meaning the relationship is present but not particularly strong.

Regarding the residuals, since the model is only moderately appropriate, the residuals would show some variation but would not be extremely large, as a well-fitting model would keep residuals smaller and more uniform.

Therefore, the most fitting response would be:

**Its correlation coefficient would be close to 0.5, and its residuals would have some variation.**