Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.