To determine the strength of the relationship between the total cost of items and the shipping costs, we calculate the Pearson correlation coefficient. The Pearson correlation coefficient measures the linear relationship between two sets of data, providing a value between -1 and 1. Here is a step-by-step solution to interpret the strength of the model:
1. List the data points:
- Total cost of items: [tex]$25, $[/tex]45, [tex]$50, $[/tex]70
- Shipping costs: [tex]$5.99, $[/tex]8.99, [tex]$8.99, $[/tex]10.99
2. Compute the Pearson correlation coefficient:
The Pearson correlation coefficient for the given data is calculated based on the given values. The result of this calculation is approximately 0.9841.
3. Interpret the correlation coefficient:
The Pearson correlation coefficient (0.9841) is very close to 1. This indicates a very high degree of positive linear relationship between the total cost of items and their corresponding shipping costs.
4. Determine the strength of the model:
- If the correlation coefficient is greater than 0.7, it signifies a strong positive correlation.
- If it falls between 0 and 0.7, it indicates a weak positive correlation.
- A value between -0.7 and 0 suggests a weak negative correlation.
- If the value is less than -0.7, it represents a strong negative correlation.
Given that our computed correlation coefficient is approximately 0.9841, it clearly falls into the category of a strong positive correlation.
Conclusion:
The best description of the strength of the model is:
- a strong positive correlation
