Question

shown below are three scatter plots and their lines of best fit. also shown are three residual plots. answer the questions that follow. scatter plot a scatter plot a image scatter plot b scatter plot b image scatter plot c scatter plot c image residual plot 1 residual plot 1 image which scatter plot matches this residual plot? select what best describes the line of best fit for the scatter plot? select residual plot 2 residual plot 2 image which scatter plot matches this residual plot? select what best describes the line of best fit for the scatter plot? select residual plot 3 residual plot 3 image which scatter plot matches this residual plot? select what best describes the line of best fit for the scatter plot? select

Explanation:

To solve this, we analyze each scatter plot and residual plot:

Residual Plot 1:

• Residuals (vertical distances from points to line of best fit) are randomly scattered around zero, with small magnitude.
• Scatter Plot A: Points lie exactly on a straight line (perfect linear relationship). Residuals should be zero (or extremely close). But Residual Plot 1 has small non - zero residuals. Wait, no—Scatter Plot A has a perfect linear fit, so residuals should be zero. Wait, maybe I mis - look. Wait, Scatter Plot B has some scatter, Scatter Plot A is perfect. Wait, Residual Plot 1: the residuals are small and randomly scattered. Wait, Scatter Plot B: points are close to the line but not perfect. Wait, no—Scatter Plot A: all points on the line, so residuals are zero. So Residual Plot 3: all residuals zero? Wait, Residual Plot 3 has all points on the x - axis (residual = 0). So Residual Plot 3 matches Scatter Plot A (since all points lie on the line, residuals are zero).

Residual Plot 2:

• Residuals show a pattern (e.g., curved trend), indicating the relationship is not linear (or the line of best fit is not appropriate for a non - linear relationship).
• Scatter Plot C: The points have a curved (non - linear) pattern around the horizontal line of best fit. So Residual Plot 2 matches Scatter Plot C (because the non - linear relationship creates a patterned residual plot).

Residual Plot 1:

• Residuals are randomly scattered (no pattern) with small magnitude, indicating a good linear fit (points close to the line but not perfect).
• Scatter Plot B: Points are close to the line of best fit but not perfectly on it, so residuals are small and random. Thus, Residual Plot 1 matches Scatter Plot B.

Line of Best Fit Descriptions:

• Scatter Plot A (matches Residual Plot 3): The line of best fit is a perfect linear fit (all points lie on the line, strong negative linear relationship).
• Scatter Plot B (matches Residual Plot 1): The line of best fit is a good linear fit (points are close to the line, negative linear relationship, residuals are random and small).
• Scatter Plot C (matches Residual Plot 2): The line of best fit (horizontal) is not appropriate (or the relationship is non - linear), as the residual plot shows a pattern (indicating the linear model is a poor fit for the non - linear data).

Final Matches:

• Residual Plot 1 ↔ Scatter Plot B
• Residual Plot 2 ↔ Scatter Plot C
• Residual Plot 3 ↔ Scatter Plot A

For the "line of best fit" questions:

• Scatter Plot A: Line of best fit is a strong negative linear fit (all points on the line).
• Scatter Plot B: Line of best fit is a good negative linear fit (points close to the line).
• Scatter Plot C: Line of best fit is a poor fit (or non - linear relationship, so the linear line of best fit is not appropriate).

Example Answers (depending on dropdown options, but typical):

• Residual Plot 1: Select Scatter Plot B
• Residual Plot 2: Select Scatter Plot C
• Residual Plot 3: Select Scatter Plot A

• Line of best fit for Scatter Plot A (Residual Plot 3): "Perfect negative linear fit" (or similar, depending on options)
• Line of best fit for Scatter Plot B (Residual Plot 1): "Good negative linear fit"
• Line of best fit for Scatter Plot C (Residual Plot 2): "Poor fit (non - linear relationship)"

Since the exact dropdown options are not fully visible, but based on the analysis:

Residual Plot 1:

Residual Plot 1 has small, random residuals (good linear fit). Scatter Plot B has points close to the line (not perfect), so they match.

Residual Plot 2 has a patterned (non - random) residual plot, indicating non - linear data. Scatter Plot C has a non - linear pattern, so they match.

Residual Plot 3 has all residuals = 0 (points on the line). Scatter Plot A has all points on the line, so they match.

Answer:

Scatter Plot B

Residual Plot 2: