To determine the strength and direction of the correlation between the number of calories and the cost of the meals, we first calculate the correlation coefficient. The correlation coefficient ranges from -1 to 1:
- A value near 1 indicates a strong positive correlation.
- A value near -1 indicates a strong negative correlation.
- A value near 0 indicates no correlation.
Given the calculated correlation coefficient, \(-0.1292396089051281\), we can analyze its strength and direction:
1. Direction:
- The correlation coefficient is negative \(-0.1292396089051281 < 0\), indicating a negative correlation between the number of calories in the meal and the cost of the meal.
2. Strength:
- We determine the strength of correlation with the following thresholds:
- If the absolute value of the correlation coefficient \(|r|\) is between 0.7 and 1.0, the correlation is strong.
- If \(|r|\) is between 0.3 and 0.7, the correlation is moderate.
- If \(|r|\) is between 0 and 0.3, the correlation is weak.
The absolute value of our correlation coefficient is \( | -0.1292396089051281 | \approx 0.129 \). This value falls within the range of [0, 0.3], indicating a weak correlation.
Therefore, the best description based on the correlation coefficient \(-0.1292396089051281\) is a weak negative correlation.
The correct answer is:
- a weak negative correlation
