Question

Serena says that if a regression line is drawn correctly in a scatterplot, there will always be the same number of points above the line as there are below the line. Which of these must be a counterexample to her claim?

Answer 1

a scatterplot with an odd number of points in which the correct regression line passes directly through 0 of the points

Explanation:

i took the test

Answer 2

Options are;

1) a scatterplot with an odd number of points in which the correct regression line passes directly through 0 of the points

2) a scatterplot with an even number of points in which the correct regression line passes directly through 0 of the points

3) a scatterplot with an odd number of points in which the correct regression line passes directly through 1 of the points

4) a scatterplot with an even number of points in which the correct regression line passes directly through 2 of the points

Answer:

Option 1: a scatterplot with an odd number of points in which the correct regression line passes directly through 0 of the points

Explanation:

From what Serena said about regression line drawn correctly in a scatter plot, looking at the options, the correct answer is option 1. This is due to the fact that If there is an odd number, and the regression line touches none of them, then there must at least be one more point located on one side of the line when compared to the point on the other side of the line.