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:

$$\begin{array}{r}(2,66)(4,105)(4,99)(4,120)(5,100)(5,77)(5,169)(6,200)(6,176)\end{array}$$

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 $-10.16$.