What values should be entered for [tex] x [/tex] and [tex] y [/tex] into a regression calculator to find the equation of the trend line?

[tex]
\begin{array}{l}
x: 3, 4, 6, 8, 9, 12 \\
y: 2, 5, 7, 10, 11, 15
\end{array}
[/tex]

Options:

1. [tex] x: 3, 4, 6, 8, 9, 15 [/tex], [tex] y: 2, 5, 7, 10, 11, 12 [/tex]

2. [tex] x: 2, 5, 7, 10, 11, 15 [/tex], [tex] y: 3, 4, 6, 8, 9, 12 [/tex]

3. [tex] x: 2, 5, 7, 10, 11, 12 [/tex], [tex] y: 3, 4, 6, 8, 9, 15 [/tex]

To solve this problem, we need to figure out the correct pairs of x and y values to calculate the equation of a trend line using regression. We are given several options, and our goal is to match the correct x values with their corresponding y values.

Let's break it down:

1. Identify the Data in the Table:
- Looking at the tabular data:
- When x is 3, y is 2.
- When x is 4, y is 5.
- When x is 6, y is 7.
- When x is 8, y is 10.
- When x is 9, y is 11.
- When x is 12, y is 15.

2. Determine the Correct x and y Pairs:
- The x values are: 3, 4, 6, 8, 9, 12
- The corresponding y values are: 2, 5, 7, 10, 11, 15

3. Review the Given Options:
- We need to match these pairs with the given options:
- Option 1:
- x: 3, 4, 6, 8, 9, 12
- y: 2, 5, 7, 10, 11, 15
- Option 2:
- x: 3, 4, 6, 8, 9, 15
- y: 2, 5, 7, 10, 11, 12
- The other options do not match both x and y with the required numbers.

4. Choose the Correct Option:
- The correct option must have x: 3, 4, 6, 8, 9, 12 and the corresponding y: 2, 5, 7, 10, 11, 15.
- Therefore, Option 1 is the correct choice, as it perfectly matches the values.

So, the correct values to enter into a regression calculator for finding the trend line are:
- x: 3, 4, 6, 8, 9, 12
- y: 2, 5, 7, 10, 11, 15