To determine the most accurate description of the residual plot based on the corresponding scatter plot of cost versus distance, it's essential to understand how residuals are calculated and what they represent.
In a residual plot:
- A dot above the residual=0 line indicates that the actual value is higher than the predicted value.
- A dot below the residual=0 line indicates that the actual value is lower than the predicted value.
- If the model fits the data perfectly, all points will lie on the residual=0 line.
- If there is some structure to the data (like a pattern), then there will be various points above and below.
Given the options provided:
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"There are three dots below the residual=0 line and three dots above." - This suggests that there is a fairly even balance of overestimations and underestimations, which may indicate that the scatter plot has some level of variability or pattern.
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"All of the dots would fall on the residual=0 line." - This would imply a perfect model fit, which is rare in real datasets.
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"There are five dots above the residual=0 line." - This suggests a significant bias in predictions being too low.
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"There are two dots that will fall on or close to the residual=0 line." - This would suggest that some predictions are fairly accurate, but doesn’t indicate a balanced distribution.
If the scatter plot shows that there is variability around a linear trend (e.g., points scattered above and below), the first option (three dots below and three dots above) would likely be the most accurate residual plot description as it indicates some level of consistency and variability in the predictions.
So the most accurate answer is:
"There are three dots below the residual=0 line and three dots above."