If the predicted value when x equals 6 is
y hat equals 49.5
and the actual value at x equals 6 is measured to be y equals 51.8, find the value of the residual at this point.
residual equals blank. Fill in the blank.

The residual is the difference between the actual value and the predicted value. Mathematically, it is given by:

\[
\text{Residual} = y_{\text{actual}} - \hat{y}_{\text{predicted}}
\]

Given:
\[
y_{\text{actual}} = 51.8
\]
\[
\hat{y}_{\text{predicted}} = 49.5
\]

Now, calculate the residual:

\[
\text{Residual} = 51.8 - 49.5 = 2.3
\]

So, the residual equals **2.3**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How is the residual used in regression analysis?
2. What does a positive residual indicate about the prediction?
3. How are residuals related to the goodness of fit of a model?
4. What is the importance of calculating residuals in predictive modeling?
5. How can the sum of residuals be used to evaluate a model?

**Tip:** Residuals are essential for checking how well a regression model fits the data—large residuals may indicate that the model is underperforming.

If the predicted value when x equals 6 is y hat equals 49.5 and the actual value at x equals 6 is measured to be y equals 51.8, find the value of the residual at this point. Residual equals blank. Fill in the blank.

Learn how to calculate the residual when the predicted value is 49.5, and the actual value is 51.8 at x = 6. This guide explains the residual formula, its use in regression analysis, and provides a detailed solution. Suitable for students in Grades 9-12.

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