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Sagot :
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
### 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
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