Select the correct answer.

This table contains data on the number of people visiting a historical landmark over a period of one week.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Day & Number of Visitors \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{tabular}
\][/tex]

Sketch a scatter plot. Which of these values comes closest to the correlation coefficient for this data?

A. 0.0
B. 0.3
C. 0.9
D. -0.3
E. -0.9



Answer :

To determine which of the given values comes closest to the correlation coefficient for the provided data, follow these steps:

### Step-by-Step Solution:

1. Understanding the Data:
We have data points representing the number of visitors to a historical landmark over the course of a week.

| Day | Number of Visitors |
|----|----------------------|
| 1 | 120 |
| 2 | 124 |
| 3 | 130 |
| 4 | 131 |
| 5 | 135 |
| 6 | 132 |
| 7 | 135 |

2. Convert Data into Coordinate Points:
Each day's visitors count forms a pair of coordinates [tex]\((x, y)\)[/tex], where [tex]\(x\)[/tex] is the day and [tex]\(y\)[/tex] is the number of visitors.
- (1, 120)
- (2, 124)
- (3, 130)
- (4, 131)
- (5, 135)
- (6, 132)
- (7, 135)

3. Scatter Plot:
To visualize the data, we would plot each pair of coordinates on a graph with "Day" on the x-axis and "Number of Visitors" on the y-axis. The scatter plot will show that as the days progress, the number of visitors generally increases.

4. Calculate the Correlation Coefficient:
The correlation coefficient (often denoted as [tex]\( r \)[/tex] or [tex]\( \rho \)[/tex]) quantifies the degree of linear relationship between two variables. Here are some values of [tex]\( r \)[/tex]:
- [tex]\( r = 1 \)[/tex] implies a perfect positive linear relationship.
- [tex]\( r = -1 \)[/tex] implies a perfect negative linear relationship.
- [tex]\( r = 0 \)[/tex] means no linear relationship.
Intermediate values indicate the strength and direction of the relationship.

Given the data points, we observe a fairly strong positive trend—visitor count increases as days progress (with slight fluctuation).

5. Select the Closest Value:
The correlation coefficient for this data is approximately [tex]\(0.9055551449149456\)[/tex].

Comparing with the provided choices:
- A. 0.0 (no correlation)
- B. 0.3 (weak positive correlation)
- C. 0.9 (strong positive correlation)
- D. -0.3 (weak negative correlation)
- E. -0.9 (strong negative correlation)

As our calculated value is close to 0.9, the correct answer is:

### Answer:
C. 0.9