In a blvariate data `sum x=30, sumy=400, sumx^(2)=196, sumxy=850 and n=10`. Find the regression coefficient of y on x.

Answer

To find the regression coefficient of y on x, we can use the formula:

\[ b_{yx} = \frac{\sum xy - \frac{1}{n} \sum x \sum y}{\sum x^2 - \frac{1}{n} (\sum x)^2} \]

Given:
- \(\sum x = 30\)
- \(\sum y = 400\)
- \(\sum x^2 = 196\)
- \(\sum xy = 850\)
- \(n = 10\)

### Step 1: Substitute the values into the formula

\[ b_{yx} = \frac{850 - \frac{1}{10} \cdot 30 \cdot 400}{196 - \frac{1}{10} \cdot (30)^2} \]

### Step 2: Calculate \(\frac{1}{n} \sum x \sum y\)

\[ \frac{1}{10} \cdot 30 \cdot 400 = \frac{12000}{10} = 1200 \]

### Step 3: Calculate \(\frac{1}{n} (\sum x)^2\)

\[ \frac{1}{10} \cdot (30)^2 = \frac{900}{10} = 90 \]

### Step 4: Substitute these results back into the formula

\[ b_{yx} = \frac{850 - 1200}{196 - 90} \]

### Step 5: Simplify the numerator and denominator

Numerator:
\[ 850 - 1200 = -350 \]

Denominator:
\[ 196 - 90 = 106 \]

### Step 6: Calculate \(b_{yx}\)

\[ b_{yx} = \frac{-350}{106} \approx -3.30 \]

### Conclusion

The regression coefficient of y on x is approximately \(-3.30\).

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