If `u = (x-20)/5` and `v = (y-30)/4` then `b_(yx)=`

Answer

To find \( b_{yx} \) given \( u = \frac{x-20}{5} \) and \( v = \frac{y-30}{4} \), we can follow these steps:

### Step 1: Understand the relationship between \( u \), \( v \), \( x \), and \( y \)

We start with the definitions:
- \( u = \frac{x - 20}{5} \)
- \( v = \frac{y - 30}{4} \)

From these equations, we can express \( x \) and \( y \) in terms of \( u \) and \( v \):
- Rearranging \( u \):
\[ x = 5u + 20 \]
- Rearranging \( v \):
\[ y = 4v + 30 \]

### Step 2: Identify the coefficients of \( u \) and \( v \)

From the equations, we can identify:
- The coefficient \( b \) for \( u \) is 5 (from \( x = 5u + 20 \)).
- The coefficient \( d \) for \( v \) is 4 (from \( y = 4v + 30 \)).

### Step 3: Use the formula for \( b_{yx} \)

The relationship between the regression coefficients is given by:
\[ b_{yx} = r_{uv} \cdot \frac{d}{b} \]
Where:
- \( r_{uv} \) is the correlation coefficient between \( u \) and \( v \).
- \( d \) is the coefficient of \( v \) (which is 4).
- \( b \) is the coefficient of \( u \) (which is 5).

### Step 4: Substitute the values into the formula

Since we know that the correlation coefficient \( r_{xy} = r_{uv} \), we can write:
\[ b_{yx} = r_{uv} \cdot \frac{4}{5} \]

### Step 5: Conclusion

Thus, the final expression for \( b_{yx} \) in terms of \( r_{uv} \) is:
\[ b_{yx} = \frac{4}{5} \cdot b_{vu} \]
Where \( b_{vu} \) is the regression coefficient of \( v \) on \( u \).