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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 = ax + b \\
a = -2.9 \\
b = 13.5 \\
r^2 = 0.9688940092 \\
r = -0.9843241383 \\
\end{array}

What is the line of best fit?

A. [tex]$-0.984 = -2.9x + 13.5$[/tex] \\
B. [tex]$y = -2.9x + 13.5$[/tex] \\
C. [tex]$y = 13.5x - 2.9$[/tex] \\
D. [tex]$y = -0.984x + 13.5$[/tex]



Answer :

GinnyAnswer
To determine the appropriate line of best fit from the given choices, let's interpret the results of the linear regression analysis shown in the table.

The standard form of a linear equation is given by [tex]\(y = ax + b\)[/tex], where:
- [tex]\(a\)[/tex] is the slope of the line,
- [tex]\(b\)[/tex] is the y-intercept (the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex]).

From the results of the linear regression:
- The slope ([tex]\(a\)[/tex]) is -2.9.
- The y-intercept ([tex]\(b\)[/tex]) is 13.5.

Using these values, the equation of the line of best fit can be written as:
[tex]\[ y = -2.9x + 13.5 \][/tex]

Now let's match this equation with the provided options:
A. [tex]\(-0.984 = -2.9x + 13.5\)[/tex] (This does not match the form [tex]\(y = ax + b\)[/tex])
B. [tex]\(y = -2.9x + 13.5\)[/tex] (This matches the form [tex]\(y = ax + b\)[/tex])
C. [tex]\(y = 13.5x - 2.9\)[/tex] (This has the slope and y-intercept reversed)
D. [tex]\(y = -0.984x + 13.5\)[/tex] (This has an incorrect slope)

The correct equation of the line of best fit is given by option B:
[tex]\[ y = -2.9x + 13.5 \][/tex]

So, the line of best fit is:
[tex]\[ \boxed{y = -2.9x + 13.5} \][/tex]

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