Question

Your friend says that a line of fit must pass through at least one of the data points. Is your friend correct? A) Yes, a line of fit always passes through one data point. B) No, a line of fit may not necessarily pass through any data point.

Answer 1

The line of fit does not need to pass through any of the actual data points; its purpose is to minimize the residuals and show the data's trend, therefore the correct answer is B) No, a line of fit may not necessarily pass through any data point.

Step-by-step explanation:

The line of best fit, also known as a least-squares regression line, is a statistical tool used to model the relationship between two quantitative variables. When creating this line in a scatter plot, it may sometimes pass through one or more of the actual data points, but it is not required to. The line is calculated to minimize the sum of the squares of the vertical distances (residuals) between the observed values and the ones predicted by the line.

Thus, while a best-fit line can pass through actual data points, it is not a requirement for it to be considered accurate or useful. It is more important that the line reflects the central tendency of the data and provides a good estimate of the relationship between variables. The correct answer to this question is option B) No, a line of fit may not necessarily pass through any data point.