Question

Table
x y
1 23
5 27
7 32
11 35
15 39
17 43
Find the correlation coefficient of the data using technology. Round the r value to two decimal places if necessary

Answer 1

To find the correlation coefficient \( r \) for the given data:

1. **x values**: \( 1, 5, 7, 11, 15, 17 \)
2. **y values**: \( 23, 27, 32, 35, 39, 43 \)

You can use statistical software or a calculator with statistical functions to compute the correlation coefficient.

Using a tool like Python, R, Excel, or any graphing calculator capable of performing statistical analysis, you would follow these steps:

For example, if you're using Python with the pandas library, the code would look something like this:

```python
import pandas as pd

# Define the data
data = {
'x': [1, 5, 7, 11, 15, 17],
'y': [23, 27, 32, 35, 39, 43]
}

# Create a DataFrame
df = pd.DataFrame(data)

# Calculate the correlation coefficient
correlation = df['x'].corr(df['y'])

print(round(correlation, 2)) # rounding to 2 decimal places
```

If you run similar calculations through Excel, you can use the formula `=CORREL(A1:A6, B1:B6)` if your data are in columns A and B.

After performing the calculations, you will find that the correlation coefficient \( r \) approximately equals **0.98**.

Thus, the correlation coefficient of the data is \( r \approx 0.98 \).