Question

a residual plot is shown.
which statements are true about the residual plot and
the equation for the line of best fit for the data? select
two options..
the equation for the line of best fit is not a good
approximation for the data because the points have a
curved pattern.
the equation for the line of best fit is a good
approximation for the data because the points are
random, having no pattern.
the residual plot has a linear pattern.
the points of the residual plot are spread evenly above
and below the x - axis.
the residual plot has the pattern of a curve.

Explanation:

Step1: Analyze Residual Plot Pattern

A residual plot with a curved pattern (non - random) means the linear model (line of best fit) is not a good approximation. The given residual plot has points forming a curve (first, points above x - axis, then a point below, with a curved trend). So the statement "The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern" is true. Also, "The residual plot has the pattern of a curve" is true. The statement about points being random is false (since there is a curved pattern). The statement about points spread evenly is false (they follow a curve). The statement about linear pattern is false (it's a curve).

Step2: Identify True Statements

From the analysis, the two true statements are: "The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern" and "The residual plot has the pattern of a curve".

Answer:

1. The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
2. The residual plot has the pattern of a curve.