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 \( \text{Cov}(x, y) \) given the regression equation of \( y \) on \( x \) and the standard deviation of \( x \), we can follow these steps:

### Step 1: Rearranging the Regression Equation
The given regression equation is:
\[ 8x - 10y + 66 = 0 \]
Rearranging this equation to express \( y \) in terms of \( x \):
\[ 10y = 8x + 66 \implies y = \frac{8}{10}x + \frac{66}{10} \]
This simplifies to:
\[ y = 0.8x + 6.6 \]

### Step 2: Identifying the Slope
From the equation \( y = 0.8x + 6.6 \), we can identify the slope \( b_{yx} \) as:
\[ b_{yx} = 0.8 \]

### Step 3: Using the Formula for Covariance
The formula for covariance in terms of the slope of the regression line and the standard deviation of \( x \) is given by:
\[ \text{Cov}(x, y) = b_{yx} \cdot \sigma_x^2 \]
Where \( \sigma_x \) is the standard deviation of \( x \).

### Step 4: Calculating the Variance of \( x \)
Given that \( \sigma_x = 3 \), we can calculate the variance of \( x \):
\[ \sigma_x^2 = 3^2 = 9 \]

### Step 5: Calculating Covariance
Now substituting the values into the covariance formula:
\[ \text{Cov}(x, y) = 0.8 \cdot 9 = 7.2 \]

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

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