Search Results

8 results for “variance”

Formulae (8)

\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2

Average squared deviation from the mean.

\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2}

Square root of the variance; typical spread.

\text{cov}(X,Y) = \frac{1}{n}\sum (x_i-\bar{x})(y_i-\bar{y})

Measures how two variables vary together.

s^2 = \frac{1}{n-1}\sum(x_i-\bar{x})^2

Unbiased estimate of population variance.

Var(X) = E[X^2] - (E[X])^2

Measures the spread of a random variable around its mean.

R^2 = 1 - \frac{\sum(y_i-\hat{y}_i)^2}{\sum(y_i-\bar{y})^2}

Proportion of variance in the target explained by the model.

z = \frac{x - \mu}{\sigma}

Standardizes features to zero mean and unit variance.

Error = Bias^2 + Variance + \sigma^2

Total expected error decomposes into bias, variance, and irreducible noise.