Question

Residuals
A residual is the difference between the actual value and the
Answer value.
Steps to finding a residual:
1. Substitute the point's
Answer
into the equation to find the
Answer
' value of y.
2. Subtract the
Answer
value of y from the point's
Answer
value of y.
Example: Suppose the regression line modeling ticket sales is y = -5.9x + 170.85, where x represents ticket price
and y represents attendance.
What is the predicted attendance when the ticket price is $5? Answer The actual attendance was 160 when the ticket price was $5.
Find the residual:
1 Answer
:: predicted
:: predicted
:: 160-141.3 = 18.7
:: predicted
÷ actual
:: x-value
:: 141.3

Answer 1

Let's go through the process of finding the residual step by step based on the example given.

1. **Substitute the point's x-value (ticket price) into the equation to find the predicted value of y (attendance).**

The regression line modeling ticket sales is given by the equation:
\[
y = -5.9x + 170.85
\]
For a ticket price of $5 (where \(x = 5\)):
\[
y = -5.9(5) + 170.85
\]
\[
y = -29.5 + 170.85
\]
\[
y = 141.35
\]

So, the predicted attendance when the ticket price is $5 is **141.35**.

2. **Subtract the predicted value of y from the actual value of y to find the residual.**

The actual attendance is given as 160.

To find the residual:
\[
\text{Residual} = \text{Actual attendance} - \text{Predicted attendance}
\]
\[
\text{Residual} = 160 - 141.35
\]
\[
\text{Residual} = 18.65
\]

So, the residual is **18.65**.

### Summary:
- **Predicted attendance when ticket price is $5:** 141.35
- **Actual attendance:** 160
- **Residual:** 18.65