What does a residual value of -4.5 mean in reference to the line of best fit?

A. The data point is 4.5 units above the line of best fit.
B. The data point is 4.5 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 -4.5.



Answer :

To understand the concept of residuals in the context of a line of best fit, we need to look at the meaning of a residual value. A residual is the difference between the observed value (the actual data point) and the predicted value (the corresponding point on the line of best fit).

Mathematically, it is calculated as:
[tex]\[ \text{Residual} = \text{Observed value} - \text{Predicted value} \][/tex]

If a residual value is negative, it means that the observed value is below the predicted value; hence, the data point is below the line of best fit.

In this particular case, the residual value is -4.5. This indicates that the actual data point is 4.5 units below what the line of best fit predicts.

Let's break this down step by step:
1. Residual Value: We are given a residual value of -4.5.
2. Interpreting the Sign: The negative sign in a residual suggests that the observation is less than the predicted value from the line of best fit.
3. Magnitude Interpretation: The magnitude of the residual, 4.5, tells us the distance between the observed data point and its predicted value on the line of best fit.

Given a residual of -4.5, we can conclude that:

- The data point is 4.5 units below the line of best fit.

Thus, the correct interpretation among the given options is:
- The data point is 4.5 units below the line of best fit.