If the regression coefficients be given `b_(yx)=1.6 and b_(xy)=0.4` then find the sum of the slopes of the two regression lines.

Answer

To find the sum of the slopes of the two regression lines given the regression coefficients \( b_{yx} = 1.6 \) and \( b_{xy} = 0.4 \), we can follow these steps:

### Step 1: Identify the slopes of the regression lines
Let:
- \( M_1 \) be the slope of the regression line of \( y \) on \( x \), which is given by \( b_{yx} \).
- \( M_2 \) be the slope of the regression line of \( x \) on \( y \), which is given by \( \frac{1}{b_{xy}} \).

### Step 2: Calculate \( M_1 \)
From the given information:
\[ M_1 = b_{yx} = 1.6 \]

### Step 3: Calculate \( M_2 \)
Using the formula for \( M_2 \):
\[ M_2 = \frac{1}{b_{xy}} = \frac{1}{0.4} \]
Calculating \( M_2 \):
\[ M_2 = 2.5 \]

### Step 4: Find the sum of the slopes
Now, we can find the sum of the slopes \( M_1 + M_2 \):
\[ M_1 + M_2 = 1.6 + 2.5 \]
Calculating the sum:
\[ M_1 + M_2 = 4.1 \]

### Final Answer
The sum of the slopes of the two regression lines is \( 4.1 \).

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