In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed.
Find the regressions coefficient of y on x from
{(x, y)} = {(5, 15), (10, 12), (15, 6), (20, 9), (10, 5)}

Answer

To find the regression coefficient of \( y \) on \( x \) from the given points \((5, 15), (10, 12), (15, 6), (20, 9), (10, 5)\), we will follow these steps:

### Step 1: Create a table of values
We will list the values of \( x \), \( y \), \( xy \), and \( x^2 \).

| \( x \) | \( y \) | \( xy \) | \( x^2 \) |
|---------|---------|----------|-----------|
| 5 | 15 | 75 | 25 |
| 10 | 12 | 120 | 100 |
| 15 | 6 | 90 | 225 |
| 20 | 9 | 180 | 400 |
| 10 | 5 | 50 | 100 |

### Step 2: Calculate the summations
Now, we will calculate the required summations:

- \( \Sigma x = 5 + 10 + 15 + 20 + 10 = 70 \)
- \( \Sigma y = 15 + 12 + 6 + 9 + 5 = 47 \)
- \( \Sigma xy = 75 + 120 + 90 + 180 + 50 = 515 \)
- \( \Sigma x^2 = 25 + 100 + 225 + 400 + 100 = 850 \)
- Number of points \( n = 5 \)

### Step 3: Use the formula for the regression coefficient
The regression coefficient of \( y \) on \( x \) is given by the formula:

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

### Step 4: Substitute the values into the formula
Substituting the values we calculated:

\[ b_{yx} = \frac{5 \times 515 - 70 \times 47}{5 \times 850 - 70^2} \]

### Step 5: Calculate the numerator and denominator
Calculating the numerator:

\[ 5 \times 515 = 2575 \]
\[ 70 \times 47 = 3290 \]
So, the numerator is:

\[ 2575 - 3290 = -715 \]

Calculating the denominator:

\[ 5 \times 850 = 4250 \]
\[ 70^2 = 4900 \]
So, the denominator is:

\[ 4250 - 4900 = -650 \]

### Step 6: Calculate the regression coefficient
Now, substituting back into the formula:

\[ b_{yx} = \frac{-715}{-650} \approx 1.100 \]

### Final Answer
The regression coefficient of \( y \) on \( x \) is approximately \( 1.100 \).