Let's analyze the data provided to determine the strength of the correlation between the total cost of items and their shipping costs. The data points are as follows:
- For a total cost of \[tex]$25, the shipping cost is \$[/tex]5.99.
- For a total cost of \[tex]$45, the shipping cost is \$[/tex]8.99.
- For a total cost of \[tex]$50, the shipping cost is \$[/tex]8.99.
- For a total cost of \[tex]$70, the shipping cost is \$[/tex]10.99.
We need to determine the correlation between the total cost of items and their respective shipping costs. The correlation coefficient measures the strength and direction of a linear relationship between two variables:
- [tex]\( \text{Correlation coefficient} (r)= 1 \)[/tex] implies a perfect positive correlation.
- [tex]\( r = -1 \)[/tex] implies a perfect negative correlation.
- [tex]\( r = 0 \)[/tex] implies no correlation.
For our data, after calculating the correlation coefficient, we obtain a value of approximately [tex]\( r = 0.984 \)[/tex].
This value indicates the following:
1. Correlation coefficient (r) is close to +1:
- An [tex]\( r \)[/tex] value of 0.984 suggests a very strong positive correlation between the total cost of the items and the shipping costs.
2. Strength of the correlation:
- Since the correlation coefficient is greater than 0.7, we classify this as a strong positive correlation.
Therefore, based on the data provided and the calculated correlation coefficient, the strength of the model is best described as:
a strong positive correlation.
