Question

a line that is used to represent the linear trend in the data is called the line of best fit. when finding the error of the line of best fit, which statement holds true?
a. if the error is less than one, the line of best fit is the linear equation of the data.
b. the smaller the error, the better the fit.
c. if the error is greater than one, there is no correlation to the line of best fit.
d. the larger the error, the better the fit.

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

• Option a: The line of best fit is an approximation, and error being less than one doesn't mean it's the exact linear equation of the data. So a is incorrect.
• Option b: The error in the line of best fit represents how well the line approximates the data. Smaller error means the line is closer to the actual data points, so the better the fit. This is correct.
• Option c: Error magnitude doesn't determine the existence of correlation. A large error just means a poor fit, not no correlation. So c is incorrect.
• Option d: Larger error means the line is less representative of the data, so it's a worse fit, not better. So d is incorrect.

Answer:

B. The smaller the error, the better the fit.