If `byx=-(1)/(4)`, mean of x = 3 and mean of y = 3, then regression equation y on x is

Options

A. `4x+y=15`
B. `x+4y=15`
C. `x+y=15`
D. none of the above

Answer

To find the regression equation of y on x given the information provided, we can follow these steps:

### Step 1: Write down the formula for the regression equation of y on x.
The regression equation of y on x can be expressed as:
\[ y - \bar{y} = b_{yx} (x - \bar{x}) \]
where:
- \( b_{yx} \) is the regression coefficient of y on x,
- \( \bar{y} \) is the mean of y,
- \( \bar{x} \) is the mean of x.

### Step 2: Substitute the given values into the equation.
From the question, we have:
- \( b_{yx} = -\frac{1}{4} \)
- \( \bar{x} = 3 \)
- \( \bar{y} = 3 \)

Substituting these values into the regression equation:
\[ y - 3 = -\frac{1}{4} (x - 3) \]

### Step 3: Simplify the equation.
Now, we will simplify the equation:
\[ y - 3 = -\frac{1}{4}x + \frac{3}{4} \]

### Step 4: Rearranging the equation.
To isolate y, we can add 3 to both sides:
\[ y = -\frac{1}{4}x + \frac{3}{4} + 3 \]
\[ y = -\frac{1}{4}x + \frac{3}{4} + \frac{12}{4} \]
\[ y = -\frac{1}{4}x + \frac{15}{4} \]

### Step 5: Multiply through by 4 to eliminate the fraction.
To make the equation neater, we can multiply the entire equation by 4:
\[ 4y = -x + 15 \]

### Step 6: Rearranging to standard form.
Rearranging gives us:
\[ 4y + x = 15 \]

### Final Equation:
Thus, the regression equation of y on x is:
\[ 4y + x = 15 \]