A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
1 & 9 \\
\hline
2 & 6 \\
\hline
3 & 2 \\
\hline
4 & -2 \\
\hline
5 & -5 \\
\hline
\end{tabular}

[tex]\[
\text{LinReg}
\begin{array}{l}
y = ax + b \\
a = -3.6 \\
b = 12.8 \\
r^2 = .9969230769 \\
r = -.9984603532
\end{array}
\][/tex]

What is the line of best fit?

A. [tex]$y = -0.998x + 12.8$[/tex]

B. [tex]$y = 12.8x - 3.6$[/tex]

C. [tex]$y = -3.6x + 12.8$[/tex]

D. [tex]$-0.998 = -3.6x + 12.8$[/tex]

Question

21-07-2024
Mathematics

Answered

A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
1 & 9 \\
\hline
2 & 6 \\
\hline
3 & 2 \\
\hline
4 & -2 \\
\hline
5 & -5 \\
\hline
\end{tabular}

[tex]\[
\text{LinReg}
\begin{array}{l}
y = ax + b \\
a = -3.6 \\
b = 12.8 \\
r^2 = .9969230769 \\
r = -.9984603532
\end{array}
\][/tex]

What is the line of best fit?

A. [tex]$y = -0.998x + 12.8$[/tex]

B. [tex]$y = 12.8x - 3.6$[/tex]

C. [tex]$y = -3.6x + 12.8$[/tex]

D. [tex]$-0.998 = -3.6x + 12.8$[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-21T17:24:22-04:00

To determine the line of best fit from linear regression, we use the equation provided by the regression analysis:

[tex]\[ y = ax + b \][/tex]

From the results:
- [tex]$ a = -3.6 $[/tex]
- [tex]$ b = 12.8 $[/tex]

We substitute these values into the equation:

[tex]\[ y = -3.6x + 12.8 \][/tex]

Therefore, the line of best fit is:

[tex]\[ y = -3.6x + 12.8 \][/tex]

Among the given options:

A. [tex]$ y = -0.998x + 12.8 $[/tex]
B. [tex]$ y = 12.8x - 3.6 $[/tex]
C. [tex]$ y = -3.6x + 12.8 $[/tex]
D. [tex]$ -0.998 = -3.6x + 12.8 $[/tex]

The correct answer is C. [tex]$ y = -3.6x + 12.8 $[/tex].