Answered

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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 & 11 \\
\hline
2 & 8 \\
\hline
3 & 4 \\
\hline
4 & 1 \\
\hline
5 & 0 \\
\hline
\end{tabular}

\begin{array}{l}
\text{LinReg} \\
y = a x + b \\
a = -2.9 \\
b = 13.5 \\
r^2 = .9688940092 \\
r = -.9843241383
\end{array}

What is the line of best fit?

A. [tex]$y = 13.5 x - 2.9$[/tex]

B. [tex]$y = -2.9 x + 13.5$[/tex]

C. [tex]$y = -0.984 x + 13.5$[/tex]

D. [tex]$-0.984 = -2.9 x + 13.5$[/tex]

Sagot :

GinnyAnswer
To determine the correct line of best fit from the given options, let's use the provided values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

The equation of the line of best fit is usually expressed as:
[tex]\[ y = ax + b \][/tex]

Here, the values provided are:
[tex]\[ a = -2.9 \][/tex]
[tex]\[ b = 13.5 \][/tex]

Plugging these values into the standard linear equation form [tex]\( y = ax + b \)[/tex], we get:
[tex]\[ y = -2.9x + 13.5 \][/tex]

Now, let's compare this derived equation with the given options:

A. [tex]\( y = 13.5x - 2.9 \)[/tex]

B. [tex]\( y = -2.9x + 13.5 \)[/tex]

C. [tex]\( y = -0.984x + 13.5 \)[/tex]

D. [tex]\( -0.984 = -2.9x + 13.5 \)[/tex]

Clearly, the correct equation matches option B:

[tex]\[ y = -2.9x + 13.5 \][/tex]

Thus, the line of best fit is:

B. [tex]\( y = -2.9x + 13.5 \)[/tex]
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