Question

interpreting residual plots
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

• Pattern: Residuals show a curved (non - linear) pattern (e.g., starts low, rises, then falls).
• Matching Scatter Plot: Scatter Plot B has a non - linear (curved) relationship (points don’t follow a straight line). So Residual Plot 1 matches Scatter Plot B.
• Line of Best Fit: Since the relationship is non - linear, the line of best fit is not a good model (or “not appropriate” as the pattern is curved).

Residual Plot 2

• Pattern: Most residuals are near 0, except one outlier.
• Matching Scatter Plot: Scatter Plot C has a very strong linear (negative) relationship, with one possible outlier? Wait, no—Scatter Plot C has points almost perfectly on a line. Wait, Residual Plot 2 has most points on the x - axis (residual = 0) and one outlier. Wait, Scatter Plot C: points are almost collinear, so residuals should be small. Wait, maybe Scatter Plot C? Wait, no—Scatter Plot A: positive linear. Scatter Plot C: negative linear. Wait, Residual Plot 2: most residuals 0, one outlier. Let's re - check:
• Scatter Plot C: points are almost perfectly on a line, so residuals would be very small (close to 0) except maybe none. Wait, maybe Scatter Plot A? No, Scatter Plot A has a positive linear trend. Wait, maybe I made a mistake. Wait, Residual Plot 2: all points (except one) are on the x - axis (residual = 0). So the scatter plot has points almost exactly on the line, with one outlier. Scatter Plot C has points almost exactly on a line (negative slope), so Residual Plot 2 matches Scatter Plot C.
• Line of Best Fit: Since most points are on the line (residuals near 0), the line of best fit is a good model (e.g., “very good fit” or “appropriate” as the relationship is linear and residuals are small).

Residual Plot 3

• Pattern: Residuals are randomly scattered around 0 (no pattern: some positive, some negative, no trend).
• Matching Scatter Plot: Scatter Plot A has a positive linear trend, and residuals should be random (no pattern). So Residual Plot 3 matches Scatter Plot A.
• Line of Best Fit: The relationship is linear (positive), and residuals are random, so the line of best fit is a good model (e.g., “good fit” or “appropriate” as the relationship is linear and residuals are random).

Final Answers (Example, adjust based on exact options):

• Residual Plot 1: Scatter Plot B; Line of Best Fit: Not appropriate (or “poor fit”).
• Residual Plot 2: Scatter Plot C; Line of Best Fit: Very good fit (or “appropriate”).
• Residual Plot 3: Scatter Plot A; Line of Best Fit: Good fit (or “appropriate”).

(Note: The exact “line of best fit description” depends on the dropdown options, e.g., “good fit”, “poor fit”, “not appropriate”, etc.)

Answer:

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

Residual Plot 1

• Pattern: Residuals show a curved (non - linear) pattern (e.g., starts low, rises, then falls).
• Matching Scatter Plot: Scatter Plot B has a non - linear (curved) relationship (points don’t follow a straight line). So Residual Plot 1 matches Scatter Plot B.
• Line of Best Fit: Since the relationship is non - linear, the line of best fit is not a good model (or “not appropriate” as the pattern is curved).

Residual Plot 2

• Pattern: Most residuals are near 0, except one outlier.
• Matching Scatter Plot: Scatter Plot C has a very strong linear (negative) relationship, with one possible outlier? Wait, no—Scatter Plot C has points almost perfectly on a line. Wait, Residual Plot 2 has most points on the x - axis (residual = 0) and one outlier. Wait, Scatter Plot C: points are almost collinear, so residuals should be small. Wait, maybe Scatter Plot C? Wait, no—Scatter Plot A: positive linear. Scatter Plot C: negative linear. Wait, Residual Plot 2: most residuals 0, one outlier. Let's re - check:
• Scatter Plot C: points are almost perfectly on a line, so residuals would be very small (close to 0) except maybe none. Wait, maybe Scatter Plot A? No, Scatter Plot A has a positive linear trend. Wait, maybe I made a mistake. Wait, Residual Plot 2: all points (except one) are on the x - axis (residual = 0). So the scatter plot has points almost exactly on the line, with one outlier. Scatter Plot C has points almost exactly on a line (negative slope), so Residual Plot 2 matches Scatter Plot C.
• Line of Best Fit: Since most points are on the line (residuals near 0), the line of best fit is a good model (e.g., “very good fit” or “appropriate” as the relationship is linear and residuals are small).

Residual Plot 3

• Pattern: Residuals are randomly scattered around 0 (no pattern: some positive, some negative, no trend).
• Matching Scatter Plot: Scatter Plot A has a positive linear trend, and residuals should be random (no pattern). So Residual Plot 3 matches Scatter Plot A.
• Line of Best Fit: The relationship is linear (positive), and residuals are random, so the line of best fit is a good model (e.g., “good fit” or “appropriate” as the relationship is linear and residuals are random).

Final Answers (Example, adjust based on exact options):

• Residual Plot 1: Scatter Plot B; Line of Best Fit: Not appropriate (or “poor fit”).
• Residual Plot 2: Scatter Plot C; Line of Best Fit: Very good fit (or “appropriate”).
• Residual Plot 3: Scatter Plot A; Line of Best Fit: Good fit (or “appropriate”).

(Note: The exact “line of best fit description” depends on the dropdown options, e.g., “good fit”, “poor fit”, “not appropriate”, etc.)