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 image scatter plot b scatter plot image scatter plot c scatter plot image residual plot 1 residual plot 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 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 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 the scatter plots and their corresponding residual plots:

Residual Plot 1

• Match Scatter Plot: Residual Plot 1 has residuals with no clear pattern (random scatter) but some spread. Scatter Plot C has a linear trend but with some deviation (not perfect like Plot B). So Residual Plot 1 matches Scatter Plot C.
• Line of Best Fit: Since the residual plot is random (no pattern), the line of best fit is a good model (linear, appropriate).

Residual Plot 2

• Match Scatter Plot: Residual Plot 2 has residuals close to zero (very small spread), indicating a nearly perfect linear fit. Scatter Plot B has points very close to the line of best fit. So Residual Plot 2 matches Scatter Plot B.
• Line of Best Fit: The residual plot shows minimal error, so the line of best fit is an excellent model (linear, very appropriate).

Residual Plot 3

• Match Scatter Plot: Residual Plot 3 has a curved pattern (residuals form a curve), indicating a non - linear trend. Scatter Plot A has a horizontal line of best fit, but the points suggest a non - linear (maybe curved) relationship. So Residual Plot 3 matches Scatter Plot A.
• Line of Best Fit: The residual plot has a pattern (curved), so the linear line of best fit is not appropriate (a non - linear model would be better).

Final Answers (for each residual plot):

Residual Plot 1

• Matches: Scatter Plot C
• Line of Best Fit: Appropriate (linear model is good)

Residual Plot 2

• Matches: Scatter Plot B
• Line of Best Fit: Excellent (linear model is very good)

Residual Plot 3

• Matches: Scatter Plot A
• Line of Best Fit: Not Appropriate (linear model is bad, non - linear needed)

(Note: If the question expects dropdown selections, the matches are:

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

For the line of best fit:

• Residual Plot 1: Appropriate (or “Good linear fit”)
• Residual Plot 2: Excellent (or “Very good linear fit”)
• Residual Plot 3: Not appropriate (or “Poor linear fit, non - linear needed”))

Answer:

To solve this, we analyze the scatter plots and their corresponding residual plots:

Residual Plot 1

• Match Scatter Plot: Residual Plot 1 has residuals with no clear pattern (random scatter) but some spread. Scatter Plot C has a linear trend but with some deviation (not perfect like Plot B). So Residual Plot 1 matches Scatter Plot C.
• Line of Best Fit: Since the residual plot is random (no pattern), the line of best fit is a good model (linear, appropriate).

Residual Plot 2

• Match Scatter Plot: Residual Plot 2 has residuals close to zero (very small spread), indicating a nearly perfect linear fit. Scatter Plot B has points very close to the line of best fit. So Residual Plot 2 matches Scatter Plot B.
• Line of Best Fit: The residual plot shows minimal error, so the line of best fit is an excellent model (linear, very appropriate).

Residual Plot 3

• Match Scatter Plot: Residual Plot 3 has a curved pattern (residuals form a curve), indicating a non - linear trend. Scatter Plot A has a horizontal line of best fit, but the points suggest a non - linear (maybe curved) relationship. So Residual Plot 3 matches Scatter Plot A.
• Line of Best Fit: The residual plot has a pattern (curved), so the linear line of best fit is not appropriate (a non - linear model would be better).

Final Answers (for each residual plot):

Residual Plot 1

• Matches: Scatter Plot C
• Line of Best Fit: Appropriate (linear model is good)

Residual Plot 2

• Matches: Scatter Plot B
• Line of Best Fit: Excellent (linear model is very good)

Residual Plot 3

• Matches: Scatter Plot A
• Line of Best Fit: Not Appropriate (linear model is bad, non - linear needed)

(Note: If the question expects dropdown selections, the matches are:

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

For the line of best fit:

• Residual Plot 1: Appropriate (or “Good linear fit”)
• Residual Plot 2: Excellent (or “Very good linear fit”)
• Residual Plot 3: Not appropriate (or “Poor linear fit, non - linear needed”))