Question

The line of best fit (regression line) is y =

x +
(Round your values to the nearest hundredths).

Part B: Determine the residual data point (2,66)
. (Use the rounded regression line you found above)

Recall that Residual Value = Actual Y-Value - Estimate Y-Value

The Residual Value =
−
=
(Round your values to the nearest hundredths).

Answer 1

y=28.49x-6.24

Answer 2

To assist with your problem, I need the equation of the regression line you found. The equation usually looks something like this:

\[ y = mx + b \]

Where \( m \) is the slope and \( b \) is the y-intercept.

Once you provide the slope and intercept values or the full equation of the line, I can help you find the estimated Y-value for the given data point (2, 66) and calculate the residual value.

The formula for residual value you mentioned is:

\[ \text{Residual Value} = \text{Actual Y-Value} - \text{Estimated Y-Value} \]

Just provide the regression equation, and we'll continue from there!

Answer 3

Great, you provided the regression equation:

\[ y = 28.49x - 6.24 \]

Part B requires us to determine the residual for the data point (2, 66).

1. **Calculate the estimated Y-value using the regression line:**

Substitute \( x = 2 \) into the regression equation:

\[
y = 28.49(2) - 6.24
\]

\[
y = 56.98 - 6.24 = 50.74
\]

So, the estimated Y-value at \( x = 2 \) is \( 50.74 \).

2. **Calculate the residual:**

The actual Y-value is \( 66 \). We can use the residual formula:

\[
\text{Residual Value} = \text{Actual Y-Value} - \text{Estimated Y-Value}
\]

\[
\text{Residual Value} = 66 - 50.74 = 15.26
\]

### Summary:
- The estimated Y-value is \( 50.74 \).
- The residual value is \( 15.26 \).

If you have any further questions or need assistance with anything else, feel free to ask!