Question

For a better linear fit, we want the r (correlation coefficient) to be

O Higher
O Unable to tell with info given
O Lower
O zero (or close)

Answer 1

For a better linear fit, we desire a higher correlation coefficient (r). A high r-value close to +1 or -1 indicates a strong linear relationship between two variables. The increase in r-value from 0.6631 to 0.9121 after removing an outlier suggests a better linear fit and prediction model.

Step-by-step explanation:

For a better linear fit, we want the correlation coefficient (r) to be higher. A high r-value, which is close to +1 or -1, indicates a strong linear relationship between the variables. If the question refers to a positive linear relationship, then an r-value close to +1 is desirable.

The correlation coefficient helps in analyzing the strength and direction of the linear association between an independent variable x and a dependent variable y. When r is positive and closer to +1, as in the new line with r = 0.9121, it suggests that as x increases, y tends to increase as well, indicating a strong positive correlation and a better prediction model.

It's also important to note that a significant change in the r-value, such as from 0.6631 to 0.9121, suggests that an influential point, such as an outlier, has been removed, providing a more reliable linear fit and thus a more accurate prediction ability for the final exam score based on the third exam score.