The assumption of regression which requires that the variance of the errors is constant for all values of the independent variable(s) is:

The assumption of regression which requires that the variance of the errors is constant for all values of the independent variable(s) is known as Homoscedasticity.

Here are the steps to understand this:

1. In regression analysis, we have a dependent variable and one or more independent variables. We build a model to explain the relationship between these variables.

2. The difference between the observed value of the dependent variable and the value predicted by the regression model is known as the error term, or residual.

3. Homoscedasticity is an assumption in regression analysis that states that the variance, or spread, of the residuals is constant across all levels of the independent variables. This means that the spread of the residuals should be roughly the same for all predicted values.

4. If this assumption is violated, we have what's known as heteroscedasticity. This can lead to inefficient estimates of the coefficients in the regression model and can affect hypothesis testing.

5. To check for homoscedasticity, we can plot the residuals against the predicted values. If the plot shows a random pattern, the assumption of homoscedasticity is likely met. If the plot shows a funnel shape or any other systematic pattern, it suggests heteroscedasticity.