To determine the correlation between the total cost of items and the shipping cost, we first need to calculate the correlation coefficient. The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where:
- A correlation coefficient close to 1 indicates a strong positive correlation.
- A correlation coefficient close to -1 indicates a strong negative correlation.
- A correlation coefficient close to 0 indicates a weak or no linear correlation.
The given data points are:
- Total cost of items: [tex]$25, $[/tex]45, [tex]$50, $[/tex]70
- Shipping cost: [tex]$5.99, $[/tex]8.99, [tex]$8.99, $[/tex]10.99
Using statistical methods, we calculate the correlation coefficient for these data sets. The calculated correlation coefficient is [tex]\(0.9840915378915647\)[/tex].
Now, let's interpret this result:
- Since the correlation coefficient is [tex]\(0.984\)[/tex], which is very close to [tex]\(1\)[/tex], it indicates a very strong positive correlation.
Therefore, the best description of the relationship between the total cost of items and the shipping cost is:
a strong positive correlation
