To determine the relationship between the two variables, we will use the correlation coefficient. The steps involved in this process are:
1. List the data points:
- Height of People (cm): 170, 172, 174, 176, 178
- Shoe Size: 8.5, 9, 9.5, 10, 11
2. Calculate the Correlation Coefficient:
The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. It ranges between -1 and 1.
3. Interpret the Correlation Coefficient:
- A correlation coefficient close to 1 indicates a strong positive linear relationship.
- A correlation coefficient close to -1 indicates a strong negative linear relationship.
- A correlation coefficient close to 0 indicates no linear relationship.
In this case, the correlation coefficient is approximately 0.986. This value is very close to 1, indicating a very strong positive linear relationship between the height of people and their shoe sizes.
4. Determine the Relationship:
- Option A: A positive linear association with no deviations. This would typically be represented by a correlation coefficient very close to 1.
- Option B: Exponential relationship. This is not determined by a correlation coefficient.
- Option C: Negative linear association. This corresponds to a correlation coefficient close to -1.
- Option D: No relationship. This would suggest a correlation coefficient close to 0.
- Option E: Positive linear association with one deviation. This would typically suggest a high, but not extremely high, correlation coefficient.
Since the correlation coefficient is very close to 1 (0.986), it strongly indicates a positive linear association with no deviations.
Therefore, the relationship between the height of people and their shoe size as given in the table is:
A. positive linear association with no deviations.
