Financial Risk Manager Part 1

Explanation

Under OLS (Ordinary Least Squares) estimation, the regression equation is of the form: $y_i = \alpha + \beta x_i$

Where:

• $Y$ is the dependent variable (foetal weight)
• $X$ is the independent variable (gestation period)
• $\alpha$ = the y-intercept
• $\beta$ = the slope

Step 1: Calculate the slope ($\beta$)

The slope is calculated as:

$\beta = \frac{S_{XY}}{S_{XX}} = \frac{14.3}{70} = 0.2043$

Step 2: Calculate the means

• Mean of Y (foetal weight): $\bar{y} = \frac{1.6 + 1.7 + 2.5 + 2.8 + 3.2 + 3.5}{6} = 2.55$

• Mean of X (gestation period): $\bar{x} = \frac{30 + 32 + 34 + 36 + 38 + 40}{6} = 35$

Step 3: Calculate the y-intercept ($\alpha$)

The y-intercept is calculated as:

$\alpha = \bar{y} - \beta \bar{x} = 2.55 - 0.2043 \times 35 = -4.60$

Step 4: Verify the calculation

• $0.2043 \times 35 = 7.1505$
• $2.55 - 7.1505 = -4.6005 \approx -4.60$

Therefore, the correct answer is:

• Least square estimator (slope): 0.2043
• Y-intercept: -4.6

This matches option A.