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.
