To determine the residual when x = 4, we first need to clarify a few terms. In statistics and data analysis, a residual is defined as the difference between the observed value and the predicted value from a model. This is critical for understanding how well our model fits the data.
Assuming Melissa has a dataset that consists of pairs of (x, y) values, we need to perform the following steps:
- Find the observed value: Locate the value of y that corresponds to x = 4 from the data table Melissa collected.
- Predict the value: Use whatever model or equation Melissa is employing to find the predicted value of y when x = 4.
- Calculate the residual: Employ the formula for the residual:
Residual = Observed Value - Predicted Value
Substitute in the values you found in the previous steps.
For instance, let’s say the observed value from the data for x = 4 is 10, and from the model, the predicted value is 8. The calculation would be:
Residual = 10 - 8 = 2
This means there’s a positive residual of 2, indicating that the observed value is higher than what the model predicted, which suggests that the model underestimates the data at this point.
If more details about the specific dataset or model are available, we can refine this answer further for more accuracy. Remember, analyzing residuals is a vital step in improving models and ensuring they accurately represent the data.