To find the equation of the regression line for the given data, we proceed as follows:
1. Organize the Data:
We have the following data from the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Day} (x) & \text{Number of visitors} (y) \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{array}
\][/tex]
2. Calculate the Regression Line:
To determine the regression line [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept, we use statistical methods to calculate:
- Slope ([tex]$m$[/tex])
- Intercept ([tex]$b$[/tex])
3. Resulting Calculation:
After performing the linear regression calculation:
[tex]\[
m \approx 2.4 \quad \text{(slope)}
\][/tex]
[tex]\[
b \approx 120.1 \quad \text{(intercept)}
\][/tex]
Hence, the equation of the regression line, rounded to the nearest tenth, is:
[tex]\[
y = 2.4x + 120.1
\][/tex]
4. Checking with Given Options:
Compare the derived equation with the given options:
A. [tex]\(y = 0.3x - 41.1\)[/tex]
B. [tex]\(y = 4x + 116\)[/tex]
C. [tex]\(y = 0.3x - 29\)[/tex]
D. [tex]\(y = 2.4x + 120.1\)[/tex]
The correct option matching our calculated regression line is:
[tex]\[
\boxed{D. \; y = 2.4x + 120.1}
\][/tex]
Thus, the equation of the regression line for the data is [tex]\(\boxed{y = 2.4x + 120.1}\)[/tex].
