To analyze what best describes the strength of the model between the total cost of items and their corresponding shipping costs, we need to calculate the correlation coefficient. The correlation coefficient (denoted as [tex]\( r \)[/tex]) quantifies the degree to which two variables are linearly related.
Given the provided data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Total cost of items} & \text{Shipping costs} \\
\hline
\$ 25 & \$ 5.99 \\
\hline
\$ 45 & \$ 8.99 \\
\hline
\$ 50 & \$ 8.99 \\
\hline
\$ 70 & \$ 10.99 \\
\hline
\end{array}
\][/tex]
We calculate the correlation coefficient between the total costs of items and the shipping costs. The result of this calculation is:
[tex]\[
\text{Correlation coefficient} \approx 0.984
\][/tex]
Now, let's interpret this coefficient:
1. The value of 0.984 is very close to 1, indicating a very strong relationship.
2. The fact that the correlation coefficient is positive (greater than zero) tells us that as the total cost of items increases, the shipping cost also tends to increase.
To determine the strength of the correlation:
- A correlation coefficient of [tex]\(0.7 \leq |r| \leq 1\)[/tex] indicates a strong correlation.
- Because our calculated correlation coefficient is 0.984, which falls within this range, we classify it as a strong correlation.
Therefore, considering both the strength and the direction of the correlation coefficient, the best description of the relationship between the total cost of items and the shipping costs is:
a strong positive correlation.
Thus, the correct answer is:
a strong positive correlation.
