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 residual plot and match it to the scatter plot, then describe the line of best fit:

Residual Plot 1

• Match Scatter Plot: Residual Plot 1 has residuals (errors) with no clear pattern but some spread, matching Scatter Plot B (since B’s points are more scattered around a horizontal line).
• Line of Best Fit: For Scatter Plot B, the line is horizontal (no upward/downward trend), so the line of best fit is a horizontal line (or weak/no trend, but visually horizontal).

Residual Plot 2

• Match Scatter Plot: Residual Plot 2 has almost no residual (all points near 0), matching Scatter Plot A (since A’s points lie almost perfectly on a straight line, so residuals are minimal).
• Line of Best Fit: Scatter Plot A has a strong positive linear trend, so the line of best fit is a strong positive linear line.

Residual Plot 3

• Match Scatter Plot: Residual Plot 3 has residuals with a pattern (curved or spread indicating a negative trend), matching Scatter Plot C (since C’s points follow a negative linear trend).
• Line of Best Fit: Scatter Plot C has a strong negative linear trend, so the line of best fit is a strong negative linear line.

Final Answers (Example Selections):

• Residual Plot 1:
• Scatter Plot: B
• Line of Best Fit: Horizontal line (or “No strong trend, horizontal”)

• Residual Plot 2:
• Scatter Plot: A
• Line of Best Fit: Strong positive linear

• Residual Plot 3:
• Scatter Plot: C
• Line of Best Fit: Strong negative linear

(Note: Exact options depend on the dropdown choices, but the reasoning is based on residual plot interpretation: residuals near 0 = perfect fit (A), scattered with no trend = B, residuals matching negative trend = C.)

Answer:

To solve this, we analyze each residual plot and match it to the scatter plot, then describe the line of best fit:

Residual Plot 1

• Match Scatter Plot: Residual Plot 1 has residuals (errors) with no clear pattern but some spread, matching Scatter Plot B (since B’s points are more scattered around a horizontal line).
• Line of Best Fit: For Scatter Plot B, the line is horizontal (no upward/downward trend), so the line of best fit is a horizontal line (or weak/no trend, but visually horizontal).

Residual Plot 2

• Match Scatter Plot: Residual Plot 2 has almost no residual (all points near 0), matching Scatter Plot A (since A’s points lie almost perfectly on a straight line, so residuals are minimal).
• Line of Best Fit: Scatter Plot A has a strong positive linear trend, so the line of best fit is a strong positive linear line.

Residual Plot 3

• Match Scatter Plot: Residual Plot 3 has residuals with a pattern (curved or spread indicating a negative trend), matching Scatter Plot C (since C’s points follow a negative linear trend).
• Line of Best Fit: Scatter Plot C has a strong negative linear trend, so the line of best fit is a strong negative linear line.

Final Answers (Example Selections):

• Residual Plot 1:
• Scatter Plot: B
• Line of Best Fit: Horizontal line (or “No strong trend, horizontal”)

• Residual Plot 2:
• Scatter Plot: A
• Line of Best Fit: Strong positive linear

• Residual Plot 3:
• Scatter Plot: C
• Line of Best Fit: Strong negative linear

(Note: Exact options depend on the dropdown choices, but the reasoning is based on residual plot interpretation: residuals near 0 = perfect fit (A), scattered with no trend = B, residuals matching negative trend = C.)