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 4 & 3 \\
\hline 6 & 4 \\
\hline 8 & 9 \\
\hline 11 & 12 \\
\hline 13 & 17 \\
\hline
\end{tabular}

A. [tex]$y=4.105 x-1.560$[/tex]
B. [tex]$y=-1.560 x+4.105$[/tex]
C. [tex]$y=-4.105 x+1.560$[/tex]
D. [tex]$y=1.560 x-4.105$[/tex]



Answer :

To find the equation of the line of best fit, we need to determine the slope and y-intercept that best represent the relationship between the given data points.

Given the data points:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 4 & 3 \\ \hline 6 & 4 \\ \hline 8 & 9 \\ \hline 11 & 12 \\ \hline 13 & 17 \\ \hline \end{array} \][/tex]

The line of best fit is given by the equation:

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

where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

For this dataset, after performing linear regression analysis, we find that the slope ([tex]\( m \)[/tex]) is 1.560 and the y-intercept ([tex]\( b \)[/tex]) is -4.105.

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

[tex]\[ y = 1.560x - 4.105 \][/tex]

Going through the options provided:

[tex]\[ \begin{array}{l} \text{A. } y = 4.105x - 1.560 \\ \text{B. } y = -1.560x + 4.105 \\ \text{C. } y = -4.105x + 1.560 \\ \text{D. } y = 1.560x - 4.105 \\ \end{array} \][/tex]

The correct answer is:

D. [tex]\( y = 1.560x - 4.105 \)[/tex]