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:

To determine if the line of best fit is appropriate, we analyze the residual plot pattern. Residuals should have no pattern (random scatter) for a good linear fit. The given residuals: at \( x = 1 \), residual is \( 0.88 \); \( x = 2 \), \( -0.25 \); \( x = 3 \), \( -1.66 \); \( x = 4 \), \( -2.34 \); \( x = 5 \), \( -4.1 \). As \( x \) increases, the residuals are decreasing in a roughly linear way (forming a linear pattern downward). A linear pattern in residuals means the linear model is not appropriate (since residuals should be random). So we check the options:

• "Yes, the points have no pattern" is wrong (there is a pattern).
• "Yes, the points are evenly distributed about the x - axis" is wrong (they are not evenly distributed; they show a downward trend).
• "No, the points are in a linear pattern" matches our analysis (the residuals show a linear trend as \( x \) increases).
• "No, the points are in a curved pattern" is wrong (the pattern is linear, not curved).

Answer:

C. No, the points are in a linear pattern