If for 5 observations of pairs (x,y), `Sigmax=15,Sigmay=25,Sigmay^(2)=135 and Sigmaxy=83`, then the value of `b_(xy)` is

Options

A. 0.8
B. 1.25
C. -0.8
D. 1

Answer

To find the value of \( b_{xy} \) using the given data, we will apply the formula for the slope of the regression line \( b_{xy} \):

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

Where:
- \( n \) = number of observations
- \( \Sigma x \) = sum of x values
- \( \Sigma y \) = sum of y values
- \( \Sigma y^2 \) = sum of squares of y values
- \( \Sigma xy \) = sum of the product of x and y values

Given:
- \( n = 5 \)
- \( \Sigma x = 15 \)
- \( \Sigma y = 25 \)
- \( \Sigma y^2 = 135 \)
- \( \Sigma xy = 83 \)

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

Substituting the known values into the formula:

\[ b_{xy} = \frac{5 \cdot 83 - 15 \cdot 25}{5 \cdot 135 - 25^2} \]

### Step 2: Calculate the numerator

Calculating the numerator:

\[ 5 \cdot 83 = 415 \]
\[ 15 \cdot 25 = 375 \]
\[ \text{Numerator} = 415 - 375 = 40 \]

### Step 3: Calculate the denominator

Calculating the denominator:

\[ 5 \cdot 135 = 675 \]
\[ 25^2 = 625 \]
\[ \text{Denominator} = 675 - 625 = 50 \]

### Step 4: Calculate \( b_{xy} \)

Now, substituting the calculated numerator and denominator back into the formula:

\[ b_{xy} = \frac{40}{50} = 0.8 \]

### Final Answer

Thus, the value of \( b_{xy} \) is:

\[ \boxed{0.8} \]

---