Why variance of error are assumed to be costant in homoscedasticity
In homoscedasticity, the variance of errors is assumed to be constant because it ensures that the errors have the same level of variability across all levels of the independent variable. This means that the errors have an equal amount of spread or dispersion around the regression line, regardless of the values of the predictors.
Assuming constant variance helps to avoid biased estimates of the regression coefficients and improves the accuracy of prediction intervals. It also simplifies the interpretation of the regression results since the relationship between the independent and dependent variables can be described in a consistent manner across the range of the predictor values.
On the other hand, violating the assumption of homoscedasticity leads to heteroscedasticity, where the variance of errors varies across levels of the independent variable. This can cause problems in regression analysis such as biased coefficient estimates and too narrow or too wide prediction intervals.