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Use the image to answer the question.

A coordinate plane for cost versus distance.

Based on the scatterplot, connect the shape of the scatterplot to the accurate description of the shape of a residual plot. Which residual plot description is the most accurate?

(1 point)
Responses

There are three dots below the residual=0 line and three dots above.
There are three dots below the residual=0 line and three dots above.

There are five dots above the residual=0 line.
There are five dots above the residual=0 line.

All of the dots would fall on the residual=0 line.
All of the dots would fall on the residual=0 line.

There are two dots that will fall on or close to the residual=0 line.

1 answer

To determine the most accurate description of the residual plot based on the scatterplot of cost versus distance, it’s important to understand the relationship between the scatterplot and the residuals.

  1. If the scatterplot indicates a clear linear trend, we would expect the residuals to be distributed evenly around the residual=0 line, potentially showing some dots both above and below the line.

  2. If the scatterplot has a strong positive or negative slope with no clear deviations from a trend, we might see more points clustered consistently above or below the line.

  3. If the scatterplot shows random scatter around the regression line, the residuals would vary widely above and below the residual=0 line.

Based on the description provided:

  • The first option indicates a balanced number of residual points above and below the line.
  • The second option suggests that all residuals are above the line, indicating a possible systematic error.
  • The third option suggests no deviation from the line, which is not typical in real-world data.
  • The fourth option indicates a small number of residuals close to the line, suggesting that the model fits the data closely in some areas but not consistently.

Without seeing the scatterplot, I recommend choosing the first option: "There are three dots below the residual=0 line and three dots above." This typically suggests a reasonable fit for the model with some variance, which is often reflected in real data. However, if the shape of the scatterplot suggests a clear trend, the last option might also be relevant depending on how closely the points deviate.