Question

use the graphing calculator tool to plot the residual points.
(1, 0.86), (2, -0.25), (3, -1.66), (4, -2.34), (5, -4.1)
does the residual plot show that the line of best fit is appropriate for the data?
yes, the points have no pattern.
yes, the points are evenly distributed about the x - axis.
no, the points are in a linear pattern.
no, the points are in a curved pattern.

Explanation:

A residual plot is used to assess the goodness - of - fit of a regression line. If the line of best fit is appropriate, the residual plot should show no pattern (random scatter). In this case, we need to check the pattern of the given residual points \((1, 0.86),(2, - 0.25),(3, - 1.66),(4, - 2.34),(5, - 4.1)\).
When we observe the \(y\) - values (residuals) as \(x\) (independent variable) increases: as \(x\) goes from \(1\) to \(5\), the \(y\) - values (\(0.86,-0.25,-1.66,-2.34,-4.1\)) show a decreasing trend. This is a linear - like (negative linear) pattern. A non - random (linear in this case) pattern in the residual plot indicates that the line of best fit is not appropriate.

Answer:

No, the points are in a linear pattern.