Find the regression coefficient of x on y from the following data:
`sumx=15, sumy=15, sumy^(2)=49, sumxy=44, n=5`, Also find the value of x when y = 7.

Answer

To find the regression coefficient of x on y and the value of x when y = 7, we will follow these steps:

### Step 1: Write down the formula for the regression coefficient of x on y (bxy)

The formula for the regression coefficient of x on y is given by:

\[ b_{xy} = \frac{n \cdot \sum xy - \sum x \cdot \sum y}{n \cdot \sum y^2 - (\sum y)^2} \]

### Step 2: Substitute the given values into the formula

We have the following values:
- \( n = 5 \)
- \( \sum x = 15 \)
- \( \sum y = 15 \)
- \( \sum y^2 = 49 \)
- \( \sum xy = 44 \)

Now substituting these values into the formula:

\[ b_{xy} = \frac{5 \cdot 44 - 15 \cdot 15}{5 \cdot 49 - 15^2} \]

### Step 3: Calculate the numerator

Calculating the numerator:

\[ 5 \cdot 44 = 220 \]
\[ 15 \cdot 15 = 225 \]
\[ \text{Numerator} = 220 - 225 = -5 \]

### Step 4: Calculate the denominator

Calculating the denominator:

\[ 5 \cdot 49 = 245 \]
\[ 15^2 = 225 \]
\[ \text{Denominator} = 245 - 225 = 20 \]

### Step 5: Calculate the regression coefficient

Now substituting the values of the numerator and denominator back into the formula:

\[ b_{xy} = \frac{-5}{20} = -0.25 \]

### Step 6: Find the regression equation of x on y

The regression equation can be expressed as:

\[ x - \bar{x} = b_{xy} (y - \bar{y}) \]

### Step 7: Calculate \(\bar{x}\) and \(\bar{y}\)

\[ \bar{x} = \frac{\sum x}{n} = \frac{15}{5} = 3 \]
\[ \bar{y} = \frac{\sum y}{n} = \frac{15}{5} = 3 \]

### Step 8: Substitute \(\bar{x}\), \(\bar{y}\), and \(b_{xy}\) into the regression equation

Substituting these values into the regression equation:

\[ x - 3 = -0.25 (y - 3) \]

### Step 9: Rearranging the equation

Rearranging gives:

\[ x - 3 = -0.25y + 0.75 \]
\[ x = -0.25y + 3.75 \]

### Step 10: Find the value of x when y = 7

Substituting \(y = 7\) into the equation:

\[ x = -0.25(7) + 3.75 \]
\[ x = -1.75 + 3.75 \]
\[ x = 2 \]

### Final Answers
- The regression coefficient of x on y is \(-0.25\).
- The value of x when y = 7 is \(2\).