To determine the correlation between age and weight in the given table, we need to calculate the correlation coefficient, which quantifies the degree to which two variables are related.
Here is a step-by-step explanation:
1. List the Ages and Weights:
- Ages (in weeks): [1, 2, 3, 3, 4, 4, 6, 8, 9, 9]
- Weights (in pounds): [7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0]
2. Calculate the Correlation Coefficient:
The correlation coefficient (often represented as \( r \)) between two variables can be calculated using statistical methods. This coefficient ranges between -1 and 1.
- \( r \approx 0.83 \)
3. Interpret the Correlation Coefficient:
- A correlation coefficient of \( r = 0.83 \) indicates a strong positive correlation. This means that as the age of the babies increases, their weight tends to increase as well.
Given the correlation coefficient value:
- None: This would mean \( r = 0 \), indicating no correlation.
- Positive: This would mean \( r > 0 \), indicating that as one variable increases, the other tends to increase as well.
- Negative: This would mean \( r < 0 \), indicating that as one variable increases, the other tends to decrease.
- Constant: This implies no variability in one or both datasets, which is not applicable here.
Since the correlation coefficient is \( 0.83 \), which is positive and fairly close to 1, it indicates a strong positive correlation between age and weight.
Conclusion:
The correlation between age and weight as shown in the table is positive.
