Question

if the value of r is low, a linear model is not a good fit for the data. in that case, which is the best predicted value for the response variable?

what is the number written in words?
a. the smallest value listed in the data
b. a value calculated by using the prediction equation
c. the mean of the response variable
d. the median of the repsonse value

Explanation:

When the correlation coefficient \( r \) is low, a linear model isn't a good fit. In such cases, the best predicted value for the response variable is the mean of the response variable. Option A (smallest value) is not appropriate as it doesn't represent the central tendency. Option B (using prediction equation) is invalid since the linear model (which uses the prediction equation) is not a good fit. Option D has a typo ("repsonse") and the median is not the standard best prediction when the linear model fails; the mean of the response variable is used as the best prediction in this context.

Answer:

C. the mean of the response variable