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]
