To determine the equation of the line of best fit for the given data points, we will need to perform a linear regression analysis.
Given data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
4 & 5 \\
7 & 7 \\
10 & 12 \\
12 & 14 \\
13 & 18 \\
\hline
\end{array}
\][/tex]
### Steps:
1. Compute the slope (m) and y-intercept (b) for the line:
We use the least squares method to find the best fit line. The formulas for the slope [tex]\( m \)[/tex] and y-intercept [tex]\( b \)[/tex] are:
[tex]\[
m = \frac{N\sum{xy} - \sum{x} \sum{y}}{N\sum{x^2} - (\sum{x})^2}
\][/tex]
[tex]\[
b = \frac{\sum{y} - m \sum{x}}{N}
\][/tex]
Where [tex]\( N \)[/tex] is the number of data points.
2. Round the slope [tex]\((m)\)[/tex] and y-intercept [tex]\((b)\)[/tex] to three decimal places:
After calculating, we round the results to three decimal places for precision.
3. Identify the correct equation from the given options:
[tex]\( \text{A. } y = 1.383 x + 1.526 \)[/tex]
[tex]\( \text{B. } y = -1.526 x + 1.383 \)[/tex]
[tex]\( \text{C. } y = -1.526 x - 1.383 \)[/tex]
[tex]\( \text{D. } y = 1.383 x - 1.526 \)[/tex]
### Results:
After following the detailed calculations, we find:
- The slope of the line [tex]\( m = 1.383 \)[/tex].
- The y-intercept of the line [tex]\( b = -1.526 \)[/tex].
### Conclusion:
The equation of the line of best fit is:
[tex]\[ y = 1.383 x - 1.526 \][/tex]
Thus, the correct choice is:
[tex]\[ \text{D. } y = 1.383 x - 1.526 \][/tex]
