To determine the relationship between the number of calories in a meal and the cost of the meal, we need to calculate the correlation coefficient and examine its magnitude and direction. Here is the step-by-step solution:
1. Data Collection
- Number of calories in meals: 550, 1250, 780, 650
- Cost of meals: \[tex]$12, \$[/tex]11, \[tex]$13, \$[/tex]10
2. Calculate the Correlation Coefficient
The correlation coefficient quantifies the degree to which two variables are related. Based on calculations, the correlation coefficient turns out to be -0.129.
3. Interpret the Correlation Coefficient
- Magnitude and Strength: The absolute value of the correlation coefficient (0.129) is less than 0.7, indicating a weak correlation.
- Direction: The sign of the correlation coefficient is negative (-0.129), indicating that as the number of calories increases, the cost of the meal tends to decrease, albeit very slightly.
4. Conclusion
The best description for the strength of the model, considering the data provided, is that there is a weak negative correlation.
Therefore, the correct answer is:
a weak negative correlation.
