To determine the regression line for the given data, we'll follow these steps.
1. Collect the Data:
We have the following pairs of [tex]\( x \)[/tex] (Day) and [tex]\( y \)[/tex] (Number of visitors):
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{array}
\][/tex]
2. Fit a Linear Regression Line:
A linear regression line can be expressed in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. Using statistical methods, we can determine these coefficients.
3. Interpret the Results:
After performing the calculations, we get the following coefficients:
- Slope ([tex]\( m \)[/tex]): [tex]\( 2.4 \)[/tex]
- Intercept ([tex]\( b \)[/tex]): [tex]\( 120.1 \)[/tex]
4. Express the Regression Line:
With [tex]\( m = 2.4 \)[/tex] and [tex]\( b = 120.1 \)[/tex], the equation of the regression line is:
[tex]\[
y = 2.4x + 120.1
\][/tex]
5. Choose the Correct Option:
Comparing our result with the given choices:
- A: [tex]\( y = 0.3x - 41.1 \)[/tex]
- B: [tex]\( y = 2.4x + 120.1 \)[/tex]
- C: [tex]\( y = 0.3x - 29 \)[/tex]
- D: [tex]\( y = 4x + 116 \)[/tex]
The correct option that matches our regression line equation is:
[tex]\[
\boxed{B: \, y = 2.4x + 120.1}
\][/tex]
