To determine the equation of the line that best fits the given data using linear regression, we need to find the slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(b\)[/tex]) of the line.
Given the following data points:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
y & 87 & 106 & 125 & 155 & 164 & 180 \\
\hline
\end{array}
\][/tex]
The slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(b\)[/tex]) for the best-fitting line have been calculated, and they are:
- Slope: [tex]\(m = 19.11\)[/tex]
- Y-intercept: [tex]\(b = 69.27\)[/tex]
Thus, the equation of the line that best fits the data is:
[tex]\[
y = 19.11x + 69.27
\][/tex]
This equation represents the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] based on the given data points, where [tex]\(x\)[/tex] is the independent variable and [tex]\(y\)[/tex] is the dependent variable.
