To determine the correlation between age and weight as shown in the table, we need to analyze the relationship between the two datasets: ages and weights.
Given the data:
| Age (weeks) | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 8 | 9 | 9 |
|----------------|---|----|----|----|----|----|----|----|-----|-----|
| Weight (lbs) |7.5|7.25|8.2 |7.95|8.0 |9.75|9.25|8.9 |9.85 |10.0 |
### Steps to Determine the Correlation:
1. Place the data in paired format:
Age (weeks): 1, 2, 3, 3, 4, 4, 6, 8, 9, 9
Weight (lbs): 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, denoted by [tex]\( r \)[/tex], measures the strength and direction of the linear relationship between two variables. The value of [tex]\( r \)[/tex] is always between -1 and 1:
- [tex]\( r > 0 \)[/tex] indicates a positive correlation.
- [tex]\( r < 0 \)[/tex] indicates a negative correlation.
- [tex]\( r = 0 \)[/tex] indicates no correlation.
- [tex]\( r = 1 \)[/tex] or [tex]\( r = -1 \)[/tex] indicates a perfect linear relationship.
Using the given data, the correlation coefficient [tex]\( r \)[/tex] is found to be approximately 0.8311.
### Interpretation of the Correlation Coefficient:
The computed correlation coefficient is [tex]\( 0.8311 \)[/tex].
- Since [tex]\( 0.8311 \)[/tex] is positive, it indicates a positive correlation.
- The value [tex]\( 0.8311 \)[/tex] is relatively close to 1, suggesting a strong linear relationship between age and weight.
Therefore, based on the correlation coefficient:
- The relationship between age and weight shown in the table is positive.
In conclusion, the correlation between age and weight as shown in the table is positive.
