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This table contains data on the number of people visiting a historical landmark over a period of one week. Using technology, find the equation of the regression line for the following data. Round values to the nearest tenth if necessary.

\begin{tabular}{|l|l|}
\hline
Day [tex]$(x)$[/tex] & Number of visitors [tex]$(y)$[/tex] \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{tabular}

A. [tex]$y=2.4 x + 120.1$[/tex]

B. [tex]$y=0.3 x - 41.1$[/tex]

C. [tex]$y=4 x + 116$[/tex]

D. [tex]$y=0.3 x - 29$[/tex]

Sagot :

GinnyAnswer
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]
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