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What is the equation of the line of best fit for the following data? Round the slope and [tex]$y$[/tex]-intercept of the line to three decimal places.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline \hline
5 & 4 \\
\hline
6 & 6 \\
\hline
9 & 9 \\
\hline
10 & 11 \\
\hline
14 & 12 \\
\hline \hline
\end{tabular}

A. [tex]$y = -0.535 x + 0.894$[/tex]

B. [tex]$y = -0.894 x + 0.535$[/tex]

C. [tex]$y = 0.894 x + 0.535$[/tex]

D. [tex]$y = 0.535 x + 0.894$[/tex]



Answer :

GinnyAnswer
To find the equation of the line of best fit, we need to determine the slope (m) and the y-intercept (b) of the line [tex]\( y = mx + b \)[/tex].

Given the data points:
- [tex]\( (5, 4) \)[/tex]
- [tex]\( (6, 6) \)[/tex]
- [tex]\( (9, 9) \)[/tex]
- [tex]\( (10, 11) \)[/tex]
- [tex]\( (14, 12) \)[/tex]

By performing a linear regression analysis, we calculate the slope (m) and the y-intercept (b). After a detailed calculation, the slope is found to be:

[tex]\[ m = 0.894 \][/tex]

and the y-intercept is:

[tex]\[ b = 0.535 \][/tex]

Thus, the equation of the line of best fit, rounded to three decimal places, is:

[tex]\[ y = 0.894x + 0.535 \][/tex]

So the correct option is:

C. [tex]\( y = 0.894x + 0.535 \)[/tex]

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