To determine the correlation between age and weight as shown in the table, we need to calculate the correlation coefficient. The correlation coefficient shows the strength and direction of the linear relationship between two variables. The possible types of correlation are positive, negative, none, or constant:
1. Positive Correlation: If the correlation coefficient is greater than 0, it implies that as one variable increases, the other variable also increases.
2. Negative Correlation: If the correlation coefficient is less than 0, it implies that as one variable increases, the other variable decreases.
3. No Correlation: If the correlation coefficient is 0, it means there is no linear relationship between the two variables.
4. Constant Correlation: This would imply that one variable remains unchanged regardless of the changes in the other variable. This is a hypothetical condition and not usually expressed through the correlation coefficient but rather through the variance.
Given the ages and weights of the babies at the hospital:
- Ages (in weeks): [tex]\(1, 2, 3, 3, 4, 4, 6, 8, 9, 9\)[/tex]
- Weights (in pounds): [tex]\(7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0\)[/tex]
After calculating the correlation coefficient for the provided data, we find that the correlation coefficient is approximately 0.8311. This correlation coefficient is positive and significantly greater than 0.
Thus, the correlation between age and weight as shown in the table is positive.
