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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).

3 answers

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!

y=28.49x-6.24

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 \( 50.74 \).

  1. 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!