Financial Risk Manager Part 1

Explanation

Under OLS (Ordinary Least Squares) estimation:

• The regression equation is: $y_i = \alpha + \beta x_i$
• Where Y is the dependent variable (foetal weight)
• X is the independent variable (gestation period)
• $\alpha$ = the y-intercept
• $\beta$ = the slope

Calculating the slope ($\beta$):

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

Calculating the y-intercept ($\alpha$):

First, we need the means:

• Mean of Y ($\bar{y}$): $\bar{y} = \frac{(1.6 + 1.7 + 2.5 + 2.8 + 3.2 + 3.5)}{6} = 2.55$
• Mean of X ($\bar{x}$): $\bar{x} = \frac{(30 + 32 + 34 + 36 + 38 + 40)}{6} = 35$

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

Therefore, the correct values are:

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

This corresponds to option A.