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

## 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.

Author: Nikitesh Somanthe