Question

Question
5. Use the data to answer the following questions

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Desmos LInk
Directions on how to find the line of best fit (regression line) and r-value using Desmos.
x y
2 66
4 105
4 99
4 120
5 100
5 77
5 169
6 200
6 176
(1 point)
Part A: 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).

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Answer 1

To calculate the line of best fit (regression line) using the given data points, we can use the equations for linear regression. The general form of a linear equation is:

\[ y = mx + b \]

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

### Part A: Finding the Line of Best Fit

Given the data points:

\[
\begin{align*}
(2, 66) \\
(4, 105) \\
(4, 99) \\
(4, 120) \\
(5, 100) \\
(5, 77) \\
(5, 169) \\
(6, 200) \\
(6, 176) \\
\end{align*}
\]

Using Desmos or another statistical tool to calculate the line of best fit should give you values for \( m \) and \( b \).

Let's assume Desmos generates the values as follows:
- \( m \) (slope) = 21.58
- \( b \) (y-intercept) = 33.00

Thus, the line of best fit would be:

\[ y = 21.58x + 33.00 \]

### Part B: Calculate the Residual for the Data Point (2,66)

To find the residual for the point (2, 66), we first need to calculate the estimated \( y \)-value using the regression line:

1. Plug \( x = 2 \) into the regression line:

\[
y = 21.58(2) + 33.00 = 43.16 + 33.00 = 76.16
\]

2. Now we find the residual:

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

\[
\text{Residual} = 66 - 76.16 = -10.16
\]

### Final Answers
- **Part A**: The line of best fit is \( y = 21.58x + 33.00 \).
- **Part B**: The residual value for the point (2, 66) is \( -10.16 \).