What does a residual value of -0.8 mean in reference to the line of best fit?
A. The given point is 0.8 units above the line of best fit.
B. The given point is 0.8 units below the line of best fit.
C. The line of best fit is not appropriate to the data.
D. The line of best fit has a slope of 0.8.
Answer (1)
A residual value indicates the difference between an observed value and the value predicted by the line of best fit.
A negative residual means the observed value is below the line of best fit.
The magnitude of the residual indicates the distance between the point and the line.
A residual of -0.8 means the data point is 0.8 units below the line of best fit. $\boxed{The given point is 0.8 units below the line of best fit.}
Explanation
Understanding Residuals A residual value represents the difference between the actual observed value of a data point and the value predicted by the line of best fit. In simpler terms, it tells us how far off the line of best fit is from the actual data point.
Interpreting Negative Residuals A negative residual indicates that the actual data point lies below the line of best fit. The magnitude of the residual (0.8 in this case) tells us the vertical distance between the point and the line.
Conclusion Therefore, a residual value of -0.8 means that the given data point is 0.8 units below the line of best fit.
Examples
Imagine you're predicting the height of a plant based on the amount of sunlight it receives. If the actual plant height is 10 cm, but your prediction (based on the line of best fit) is 10.8 cm, the residual is -0.8 cm. This means your prediction overestimated the plant's height by 0.8 cm. Understanding residuals helps refine your prediction models and understand the accuracy of your estimations.
