Question
The table shows the heights and the lengths of several rectangles.
Height (in.)417021341092542410354266Length (in.)212532121645402345352114
What does the correlation coefficient for the data indicate about the strength of the linear association between the height and the length of these rectangles?
A.
Weak negative correlation
B.
Strong negative correlation
C.
Weak positive correlation
D.
Strong positive correlation
Height (in.)417021341092542410354266Length (in.)212532121645402345352114
What does the correlation coefficient for the data indicate about the strength of the linear association between the height and the length of these rectangles?
A.
Weak negative correlation
B.
Strong negative correlation
C.
Weak positive correlation
D.
Strong positive correlation
Answers
GPT-4o mini
To determine the correlation coefficient between the height and length of the rectangles, we would typically compute the correlation coefficient (often denoted as \( r \)) using statistical software or a calculator. However, since you have not provided the correlation coefficient directly, I can help interpret the options based on general knowledge of correlation.
1. **Weak negative correlation**: Values close to -1, but not significantly so, suggesting a slight downward trend.
2. **Strong negative correlation**: Values closer to -1 indicate a strong downward trend.
3. **Weak positive correlation**: Values close to 0, but positive, suggesting a slight upward trend.
4. **Strong positive correlation**: Values close to 1 indicate a strong upward trend.
Given the context of the problem, it seems you are looking for the strength and direction of the linear association between the height and length of the rectangles.
Without the exact value of the correlation coefficient, you can look at the data trends visually (if you have a scatter plot) to assess if there's a positive or negative relationship, and how strong that relationship seems to be based on the plotted points.
If you have calculated the correlation coefficient and it's positive and strong (close to 1), then you would choose option D. If it's negative and strong (close to -1), then option B would be appropriate. For a weak correlation, either A or C would be applicable depending on whether it's positive or negative.
In conclusion, the correct answer would depend on the actual correlation coefficient you calculated from the data provided. If you have a specific value or visual observation, we can help you interpret that directly.
1. **Weak negative correlation**: Values close to -1, but not significantly so, suggesting a slight downward trend.
2. **Strong negative correlation**: Values closer to -1 indicate a strong downward trend.
3. **Weak positive correlation**: Values close to 0, but positive, suggesting a slight upward trend.
4. **Strong positive correlation**: Values close to 1 indicate a strong upward trend.
Given the context of the problem, it seems you are looking for the strength and direction of the linear association between the height and length of the rectangles.
Without the exact value of the correlation coefficient, you can look at the data trends visually (if you have a scatter plot) to assess if there's a positive or negative relationship, and how strong that relationship seems to be based on the plotted points.
If you have calculated the correlation coefficient and it's positive and strong (close to 1), then you would choose option D. If it's negative and strong (close to -1), then option B would be appropriate. For a weak correlation, either A or C would be applicable depending on whether it's positive or negative.
In conclusion, the correct answer would depend on the actual correlation coefficient you calculated from the data provided. If you have a specific value or visual observation, we can help you interpret that directly.