The question you're asking involves finding the residual for a linear regression equation, $y = -3x + 2$, when $x = 3$ and the actual value of $y$ is provided.

To calculate the residual, follow these steps:

1. Find the predicted $y$: Using the equation of the line, substitute $x = 3$ into the regression equation to calculate the predicted value of $y$.

$y_{\text{pred}} = -3(3) + 2 = -9 + 2 = -7$

2. Use the given actual value of $y$: The actual value of $y$ will be provided in the problem statement. For this example, if the actual $y = -4$, we can now calculate the residual.

3. Calculate the residual: The residual is the difference between the actual value and the predicted value of $y$:

$\text{Residual} = y_{\text{actual}} - y_{\text{pred}} = -4 - (-7) = -4 + 7 = 3$

Thus, the residual is $3$.

If you'd like, you can let me know the actual value of $y$ to complete the calculation or if you'd like further clarification.

Here are five related questions to consider:

1. How does a residual help assess the fit of a regression model?
2. What are some other ways to visualize residuals in linear regression?
3. How would the residual change if the predicted value were off by a larger margin?
4. What is the difference between a residual and an error in regression analysis?
5. How can you use residuals to detect outliers in regression data?

Tip: Always check for any data points that produce large residuals—they could indicate outliers or points where the model doesn't fit well!