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

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

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

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

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

Answer :

To find the equation of the trend line from the data in the table, you need to enter pairs of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values into a regression calculator. The table shows pairs of numbers that form the data points you will use. Each row in the table represents a pair:

```
\begin{tabular}{|c|c|}
\hline
3 & 2 \\
\hline
4 & 5 \\
\hline
6 & 7 \\
\hline
8 & 10 \\
\hline
9 & 11 \\
\hline
12 & 15 \\
\hline
\end{tabular}
```

To find the correct pairs for the regression analysis, you need to ensure each [tex]\(x\)[/tex] value correctly matches its corresponding [tex]\(y\)[/tex] value. From the table, the pairs are:

- When [tex]\(x = 3\)[/tex], [tex]\(y = 2\)[/tex]
- When [tex]\(x = 4\)[/tex], [tex]\(y = 5\)[/tex]
- When [tex]\(x = 6\)[/tex], [tex]\(y = 7\)[/tex]
- When [tex]\(x = 8\)[/tex], [tex]\(y = 10\)[/tex]
- When [tex]\(x = 9\)[/tex], [tex]\(y = 11\)[/tex]
- When [tex]\(x = 12\)[/tex], [tex]\(y = 15\)[/tex]

Thus, the [tex]\((x, y)\)[/tex] pairs to input into the regression calculator are:
- [tex]\(x\)[/tex] values: [3, 4, 6, 8, 9, 12]
- [tex]\(y\)[/tex] values: [2, 5, 7, 10, 11, 15]

By using these pairs, you can calculate the trend line, which represents the best fit line through the given points. This trend line will show you how [tex]\(y\)[/tex] changes with [tex]\(x\)[/tex].

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