example of a line of best fit

Question

What should be true about the line of best fit for any scatter plot? Check all that apply.

(2 points)
Responses

The line of best fit should be an exact representation of the data points.
The line of best fit should be an exact representation of the data points.

The line of best fit must have an equal number of points above and below the line.
The line of best fit must have an equal number of points above and below the line.

The line of best fit can, some times, be used as a prediction tool; showing a trend in the data.
The line of best fit can, some times, be used as a prediction tool; showing a trend in the data.

The line of best fit MUST cross through at least 2 points in the scatter plot.
The line of best fit MUST cross through at least 2 points in the scatter plot.

The line must represent the general relationship between the two variables.
The line must represent the general relationship between the two variables.

Answer 1

For a line of best fit in any scatter plot, the following statements are true:

• The line of best fit can sometimes be used as a prediction tool; showing a trend in the data.

• The line must represent the general relationship between the two variables.

The following statements are not generally true:

• The line of best fit should be an exact representation of the data points. (It typically provides a general trend rather than fitting all points exactly.)

• The line of best fit must have an equal number of points above and below the line. (This is not a requirement; it may not be the case depending on the data.)

• The line of best fit MUST cross through at least 2 points in the scatter plot. (While it is common for the line to pass through points, it does not have to pass through any points at all.)

In summary, the line of best fit aims to reflect the trend of the data, making it useful for predictions, without needing to adhere to the other conditions stated.