12. Regression

Residuals

12. Regression

Residuals

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Multiple Choice

Which of the following residual plots suggest that a linear regression model is appropriate?

Scatter plot with red dots representing residuals, indicating potential appropriateness of a linear regression model.

Red dots on a grid represent a residual plot, indicating a potential linear relationship in the data.

A grid plot showing red dots representing residuals, indicating potential linear regression model appropriateness.

Residual plot with red dots representing data points, indicating the appropriateness of a linear regression model.

Verified step by step guidance

Step 1: Understand the purpose of residual plots. Residual plots are used to assess the appropriateness of a linear regression model. A good residual plot for linear regression should show no discernible pattern, with residuals randomly scattered around zero.

Step 2: Analyze the first residual plot. Check if the residuals are randomly scattered around the horizontal axis (zero line) without forming any systematic pattern.

Step 3: Analyze the second residual plot. Look for any trends or systematic patterns, such as a curve or increasing/decreasing residuals, which would indicate that a linear model is not appropriate.

Step 4: Analyze the third residual plot. Again, check for randomness in the distribution of residuals around the zero line. If the residuals are evenly scattered, this suggests a linear model may be appropriate.

Step 5: Analyze the fourth residual plot. Look for any systematic patterns, such as clusters or trends, which would suggest that a linear model is not suitable. Random scatter indicates appropriateness for linear regression.

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