We first calculate the variance of $Y_h$:

The variance of $Y_h$ is calculated using the formula:

$$\text{Var}(Y_h) = \frac{\sum (Y_h - \bar{Y}_h)^2}{n - 1}$$

Mean: $\bar{Y}_h = \frac{2.0 + 2.5 + 1.5 + 3.0}{4} = 2.25$

Now, $\text{Var}(Y_h) = \frac{(2.0 - 2.25)^2 + (2.5 - 2.25)^2 + (1.5 - 2.25)^2 + (3.0 - 2.25)^2}{4 - 1} = 0.4167$

Now,

$$\beta = \frac{\text{Cov}(Y_h, Y_p)}{\text{Var}(Y_h)} = \frac{0.273}{0.4167} = 0.6551 \approx 0.66$$