To find the equation of the regression line for the given data, follow these steps:
1. Observe the data:
- Days [tex]\( (x) \)[/tex]: 1, 2, 3, 4, 5, 6, 7
- Number of visitors [tex]\( (y) \)[/tex]: 120, 124, 130, 131, 135, 132, 135
2. Determine the linear relationship:
- We want to determine the best fit line [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Calculate the slope and intercept:
- Using the given data and applying statistical methods, like linear regression, the slope ([tex]\( m \)[/tex]) and intercept ([tex]\( b \)[/tex]) are calculated.
4. Result after calculation:
- The calculated slope [tex]\( m \)[/tex] is 2.4.
- The calculated intercept [tex]\( b \)[/tex] is 120.1.
5. Equation of the regression line:
- The equation of the regression line is [tex]\( y = 2.4x + 120.1 \)[/tex].
6. Verification with given options:
- Option A is [tex]\( y = 2.4x + 120.1 \)[/tex]
- Option B is [tex]\( y = 0.3x - 41.1 \)[/tex]
- Option C is [tex]\( y = 4x + 116 \)[/tex]
- Option D is [tex]\( y = 0.3x - 29 \)[/tex]
7. Matching the calculated equation:
- The correct equation that matches our calculation is given in Option A.
Therefore, the equation of the regression line for the given data is:
[tex]\[ \boxed{A.\; y = 2.4x + 120.1} \][/tex]
