Answer: Least square estimator: 0.2043; Y-intercept: -4.6

## 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.

Author: Tanishq Prabhu