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 good residual plot for a linear model should have random, unpatterned points. Here, the points show a curved (non - random) pattern. So, if there's a pattern (like curved), the linear model (line of best fit) is not a good approximation. Also, the points do have a curved pattern, not linear. And they aren't spread evenly (since there's a curve), but the curved pattern means the line of best fit isn't good, and the residual plot has a curved pattern.

Step2: Evaluate Each Statement

• Statement 1: "The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern." - True, as a curved pattern in residuals means the linear model is inappropriate.
• Statement 2: "The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern." - False, since points have a curved (patterned) distribution.
• Statement 3: "The residual plot has a linear pattern." - False, the pattern is curved.
• Statement 4: "The points of the residual plot are spread evenly above and below the x - axis." - False, the curved pattern shows uneven spread.
• Statement 5: "The residual plot has the pattern of a curve." - True, from the plot, the points form a curve.

Answer:

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