If the two lines of regression are `3x+2y=26 and 6x+y=31`, then the coefficient of correlation between x and y is ……………..

Answer

To find the coefficient of correlation between x and y given the two lines of regression \(3x + 2y = 26\) and \(6x + y = 31\), we will follow these steps:

### Step 1: Convert the regression equations into slope-intercept form
1. **First Equation:** \(3x + 2y = 26\)
- Rearranging gives:
\[ 2y = -3x + 26 \]
- Dividing by 2:
\[ y = -\frac{3}{2}x + 13 \]
- Here, the slope \(b_{xy} = -\frac{3}{2}\).

2. **Second Equation:** \(6x + y = 31\)
- Rearranging gives:
\[ y = -6x + 31 \]
- Here, the slope \(b_{yx} = -6\).

### Step 2: Find the product of the slopes
Now, we need to find the product of the slopes \(b_{xy}\) and \(b_{yx}\):
\[ b_{xy} = -\frac{3}{2}, \quad b_{yx} = -6 \]
Calculating the product:
\[ b_{xy} \cdot b_{yx} = \left(-\frac{3}{2}\right) \cdot (-6) = \frac{3 \cdot 6}{2} = \frac{18}{2} = 9 \]

### Step 3: Calculate the coefficient of correlation
The coefficient of correlation \(r\) is given by:
\[ r = \sqrt{b_{xy} \cdot b_{yx}} \]
Substituting the product we found:
\[ r = \sqrt{9} = 3 \]

### Conclusion
Thus, the coefficient of correlation between x and y is:
\[ \boxed{3} \]