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 should have no pattern (randomly scattered points) for a good - fit line of best fit. Here, the points are not randomly scattered. If we check the \(x\) - values \(1,2,3,4,5\) and the corresponding residual values \(0.86,-0.25,-1.66,-2.34,-4.1\), we can observe a linear pattern. As \(x\) increases, the residual values follow a linear trend (the difference between consecutive \(y\) - values of residuals is approximately constant: \(-0.25 - 0.86=-1.11\), \(-1.66+0.25 = - 1.41\), \(-2.34 + 1.66=-0.68\), \(-4.1+2.34=-1.76\), but the overall trend is linear - like). 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.