Question

consider the plot that was created from the residuals of a line of best fit for a set of data. does the residual plot show that the line of best fit is appropriate for the data? yes, the points are rising yes, the points are all above the x - axis no, it follows a pattern no, the points are falling

Explanation:

To determine if a line of best fit is appropriate, we analyze the residual plot. A good line of best fit should have residuals that are randomly scattered with no clear pattern. In this plot, the residuals (points) show a pattern of increasing as \( x \) increases (they form a rising trend). If residuals follow a pattern, the linear model (line of best fit) is not appropriate.

• "Yes, the points are rising" is incorrect because a rising pattern in residuals means the model is not appropriate.
• "Yes, the points are all above the x - axis" is incorrect as the position above the x - axis doesn't determine appropriateness; random scatter is key, and here there's a pattern.
• "No, it follows a pattern" is correct because the residuals have a clear increasing pattern, indicating the linear model isn't appropriate.
• "No, the points are falling" is incorrect as the points are rising, not falling.

Answer:

C. No, it follows a pattern