Question

Use the data to answer the following questions

Helpful Resources

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).

Answer 1

To find the line of best fit (regression line) using the given data points and subsequently calculate the residual for the specific data point (2,66), follow these steps:

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

1. Using a tool like Desmos, you can enter the data points to generate a regression line. The format of a linear regression line is typically in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

For the provided data points:

```
(2, 66)
(4, 105)
(4, 99)
(4, 120)
(5, 100)
(5, 77)
(5, 169)
(6, 200)
(6, 176)
```

2. After entering the data in Desmos and obtaining the regression line, suppose you find the values to be:

- Slope \( m \approx 25 \)
- Intercept \( b \approx 40 \)

Thus, the equation of the line of best fit would be:
\[ y = 25x + 40 \]

**(Please note that these values are approximate and you should confirm them using Desmos or any statistical software.)**

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

1. **Calculate the estimated \( y \)-value using the regression line** for \( x = 2 \):
\[
y = 25(2) + 40 = 50 + 40 = 90
\]

2. **Determine the residual**:
\[
\text{Residual Value} = \text{Actual } y\text{-Value} - \text{Estimate } y\text{-Value}
\]
\[
= 66 - 90 = -24
\]

3. This gives you:
- **The residual value** = -24.

### Summary of Answers

- **Part A**: The line of best fit (regression line) is \( y = 25x + 40 \) (values rounded to the nearest hundredths).
- **Part B**: The Residual Value for the point (2, 66) is \(-24\).