Regression equation of yon is 8x-10y+66=0 `sigmax=3`. Hence cov(x,y) is equal to

Options

A. 11,25
B. 7.2
C. 2,4
D. None of these

Answer

To find the covariance of \( x \) and \( y \) given the regression equation of \( y \) on \( x \) and the standard deviation of \( x \), we can follow these steps:

### Step 1: Rewrite the Regression Equation
The given regression equation is:
\[ 8x - 10y + 66 = 0 \]
Rearranging this equation to express \( y \) in terms of \( x \):
\[ 10y = 8x + 66 \implies y = \frac{8}{10}x + \frac{66}{10} \]
Thus, we have:
\[ y = 0.8x + 6.6 \]
Here, the coefficient \( b_{yx} = 0.8 \).

### Step 2: Identify the Standard Deviation of \( x \)
We are given that the standard deviation of \( x \) is:
\[ \sigma_x = 3 \]
The variance of \( x \) can be calculated as:
\[ \text{Variance}(x) = \sigma_x^2 = 3^2 = 9 \]

### Step 3: Use the Relationship Between Covariance and Regression Coefficient
The relationship between the covariance of \( x \) and \( y \) and the regression coefficient is given by:
\[ b_{yx} = \frac{\text{Cov}(x, y)}{\text{Var}(x)} \]
Rearranging this formula to find the covariance:
\[ \text{Cov}(x, y) = b_{yx} \times \text{Var}(x) \]

### Step 4: Substitute the Values
Now substituting the values we have:
\[ \text{Cov}(x, y) = 0.8 \times 9 = 7.2 \]

### Conclusion
Thus, the covariance of \( x \) and \( y \) is:
\[ \text{Cov}(x, y) = 7.2 \]