Homoscedasticity ($\mathrm{Var}(Y_i)={\sigma }^2$)

Constancy of the error variance across observations or conditional covariate values. In fixed-design nonparametric regression, $Y_i=m(x_i)+\sigma {ϵ}_i$ with $\mathrm{Var}({ϵ}_i)=1$ has $\mathrm{Var}(Y_i)={\sigma }^2$ for every design point.