Variance Under Linear Transformation

When a linear transformation $$y = ax + b$$ is applied to data:
$$\text{Var}(y) = a^2 \cdot \text{Var}(x)$$

The constant term $$b$$ does not affect variance.

In the transformation $$y = 2x + 3$$:
- $$a = 2$$
- $$b = 3$$

Original variance: $$\text{Var}(x) = 4$$

New variance: $$\text{Var}(y) = 2^2 \cdot \text{Var}(x) = 4 \cdot 4 = 16$$