Under OLS estimation,
The regression equation is of the form: $y_i = \alpha + \beta x_i$

Where Y is the dependent variable (height), X is the independent variable (age), $\alpha =$ the y-intercept, and $\beta =$ the slope.

$$\beta = \sum \frac{(x_i - \bar{x}) - (y_i - \bar{y})}{(x_i - \bar{x})^2} = \frac{S_{xy}}{S_{xx}} = \frac{11.3}{66} = 0.1712$$ $$\alpha = \bar{y} - \beta \bar{x}$$ $$\bar{y} = \frac{144 + 150 + 157}{3} = 150.33$$ $$\bar{x} = \frac{11 + 12 + 13}{3} = 12$$

Therefore, $\alpha = 150.33 - 0.1712 \times 12 = 148.27$

Chapter: Linear Regression
Learning objectives:

• Interpret the results of an ordinary least squares (OLS) regression with a single explanatory variable.
• Describe the key assumptions of OLS parameter estimation.