To determine the relationship between "Height of People (cm)" and "Shoe Size," let's review the given data and consider the statistical measure used for determining relationships between two variables: the correlation coefficient.
The correlation coefficient measures the strength and direction of a linear relationship between two variables. The value of the correlation coefficient [tex]\( r \)[/tex] ranges from -1 to 1:
- [tex]\( r = 1 \)[/tex] indicates a perfect positive linear relationship.
- [tex]\( r = -1 \)[/tex] indicates a perfect negative linear relationship.
- [tex]\( r = 0 \)[/tex] indicates no linear relationship.
Given the correlation coefficient result of [tex]\( 0.9863939238321436 \)[/tex], we can interpret this value as follows:
1. The value is very close to 1, which suggests a strong positive linear relationship.
2. Since it is a correlation coefficient close to 1, there are virtually no significant deviations; the data points closely follow the linear trend.
This means that as the height of a person increases, their shoe size also tends to increase in a very consistent manner, indicating a positive linear relationship with almost no discrepancies.
Given the provided options, the most accurate description of this relationship is:
A. positive linear association with no deviations
