To determine the strength and direction of the relationship between women's age and shoe size, we need to analyze the correlation between the two variables. Correlation coefficients range from -1 to 1 and can help us understand this relationship:
1. Positive Correlation: If the correlation coefficient is between 0 and 1, it indicates a positive relationship, where an increase in one variable tends to result in an increase in the other. The closer the value is to 1, the stronger the positive correlation.
2. Negative Correlation: If the correlation coefficient is between -1 and 0, it denotes a negative relationship, where an increase in one variable tends to result in a decrease in the other. The closer the value is to -1, the stronger the negative correlation.
3. Magnitude of Correlation Coefficient:
- Near 0: Indicates a weak correlation (whether positive or negative).
- Near ±1: Indicates a strong correlation (whether positive or negative).
Given the data:
- Ages: 18, 30, 52, 64
- Shoe Sizes: 7, 10, 6, 9
When examining these pairs, we calculate the correlation coefficient. Based on the correlation coefficient derived from the data:
- If the correlation coefficient is greater than 0.3 but less than or equal to 0.7, it indicates a weak positive correlation.
- If it is greater than 0.7, it would indicate a strong positive correlation.
- Conversely, if the coefficient is between -0.3 and -0.7, it would indicate a weak negative correlation.
- And if it is less than -0.7, it would indicate a strong negative correlation.
The result indicates a weak negative correlation.
Thus, the best description of the strength of the model based on the given data is:
a weak negative correlation
