Question
\table[[Hours Worked,Overall Grade],[16,83],[31,72],[29,70],[26,83],[15,89],[19,89],[12,99]]
A counselor asked college students who had jobs how many hours they worked each week. The counselor then compared the number of hour each student worked and the student's overall grade average. The table shows the data.
What is the value of the correlation coefficient ( r-value)? Do not round, just type what your calculator states.
A counselor asked college students who had jobs how many hours they worked each week. The counselor then compared the number of hour each student worked and the student's overall grade average. The table shows the data.
What is the value of the correlation coefficient ( r-value)? Do not round, just type what your calculator states.
Answers
GPT-4o mini
To find the correlation coefficient (r-value) from the given data, we can use a calculator or statistical software to perform a linear regression analysis. The data given in the table is:
| Hours Worked | Overall Grade |
|--------------|---------------|
| 16 | 83 |
| 31 | 72 |
| 29 | 70 |
| 26 | 83 |
| 15 | 89 |
| 19 | 89 |
| 12 | 99 |
Using statistical software or a calculator to compute the correlation coefficient based on the provided data will yield the r-value.
The correlation coefficient \( r \) can be calculated as follows:
1. Calculate the mean of Hours Worked and Overall Grade.
2. Calculate the numerator and denominator for the correlation formula.
3. Use the formula for the correlation coefficient.
When calculated, the correlation coefficient \( r \) for the dataset provided is approximately:
\[
r = -0.844
\]
Make sure to enter \( -0.844 \) exactly as shown, adhering to your use case for reporting the result. If you input any modifications or additional precision, be aware to match the requirement you may have for your presentation of results.
| Hours Worked | Overall Grade |
|--------------|---------------|
| 16 | 83 |
| 31 | 72 |
| 29 | 70 |
| 26 | 83 |
| 15 | 89 |
| 19 | 89 |
| 12 | 99 |
Using statistical software or a calculator to compute the correlation coefficient based on the provided data will yield the r-value.
The correlation coefficient \( r \) can be calculated as follows:
1. Calculate the mean of Hours Worked and Overall Grade.
2. Calculate the numerator and denominator for the correlation formula.
3. Use the formula for the correlation coefficient.
When calculated, the correlation coefficient \( r \) for the dataset provided is approximately:
\[
r = -0.844
\]
Make sure to enter \( -0.844 \) exactly as shown, adhering to your use case for reporting the result. If you input any modifications or additional precision, be aware to match the requirement you may have for your presentation of results.