The regression equation of y on x is 2x-5y +60 =0.
Mean of x = 18
`:. bary=square`
`sigma_x:sigma_y=3:2`
`:. b_(yx)= (square)/(square)`
`:. r = square`

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Identify the regression equation
The regression equation of \( y \) on \( x \) is given as:
\[ 2x - 5y + 60 = 0 \]

### Step 2: Find the mean of \( y \) using the mean of \( x \)
We know that the mean of \( x \) (denoted as \( \bar{x} \)) is 18. We can substitute this value into the regression equation to find the mean of \( y \) (denoted as \( \bar{y} \)).

Substituting \( \bar{x} = 18 \) into the regression equation:
\[ 2(18) - 5\bar{y} + 60 = 0 \]
Calculating this gives:
\[ 36 - 5\bar{y} + 60 = 0 \\ 96 - 5\bar{y} = 0 \\ 5\bar{y} = 96 \\ \bar{y} = \frac{96}{5} = 19.2 \]

### Step 3: Find the slope of the regression line \( b_{yx} \)
The regression equation can be rearranged to express \( y \) in terms of \( x \):
\[ 5y = 2x + 60 \\ y = \frac{2}{5}x + 12 \]
From this, we can see that the slope \( b_{yx} \) is:
\[ b_{yx} = \frac{2}{5} \]

### Step 4: Determine the ratio of standard deviations \( \sigma_x : \sigma_y \)
We are given that:
\[ \sigma_x : \sigma_y = 3 : 2 \]
This implies:
\[ \frac{\sigma_x}{\sigma_y} = \frac{3}{2} \quad \text{or} \quad \frac{\sigma_y}{\sigma_x} = \frac{2}{3} \]

### Step 5: Find the correlation coefficient \( r \)
The relationship between the slope \( b_{yx} \) and the correlation coefficient \( r \) is given by:
\[ b_{yx} = r \cdot \frac{\sigma_y}{\sigma_x} \]
Substituting the known values:
\[ \frac{2}{5} = r \cdot \frac{2}{3} \]
To find \( r \), we rearrange this equation:
\[ r = \frac{2}{5} \cdot \frac{3}{2} \]
Calculating this gives:
\[ r = \frac{3}{5} = 0.6 \]

### Final Answers
- \( \bar{y} = 19.2 \)
- \( b_{yx} = \frac{2}{5} \)
- \( r = 0.6 \)