To determine the correlation coefficient for the provided data, we first need to understand what the correlation coefficient represents. It measures the strength and direction of the linear relationship between two variables, which in this scenario are the days and the number of visitors.
Given the data:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Day} & \text{Number of Visitors} \\
\hline 1 & 120 \\
\hline 2 & 124 \\
\hline 3 & 130 \\
\hline 4 & 131 \\
\hline 5 & 135 \\
\hline 6 & 132 \\
\hline 7 & 135 \\
\hline
\end{array}
\][/tex]
Step 1: Sketch a Scatter Plot
We plot each pair (Day, Number of Visitors) on a graph where the x-axis represents the day and the y-axis represents the number of visitors.
- Day 1, Visitors 120
- Day 2, Visitors 124
- Day 3, Visitors 130
- Day 4, Visitors 131
- Day 5, Visitors 135
- Day 6, Visitors 132
- Day 7, Visitors 135
When you plot these points, you'll observe that they lie fairly close to a straight line that slopes upwards, indicating a positive correlation.
Step 2: Estimate the Correlation Coefficient
Next, we estimate the correlation coefficient. Given that the data points form a pattern that suggests a strong positive linear relationship, we can infer that the correlation coefficient will be a positive value close to 1.
Step 3: Choose the Closest Value
From the possible options:
A. 0.0
B. 0.3
C. 0.9
D. -0.3
E. -0.9
Since the scatter plot suggests a strong positive correlation, the correct answer should be a value close to 1. Therefore, the value that comes closest to the correlation coefficient for this data is:
C. 0.9
