Question

• Explain in your words how homoscedasticity affects the results of a regression test?

Answer 1

The assumption of homoscedasticity means the different sample have same variance, even they are came from different population. Homoscedasticity gives the error term is the same across all values of the independent variable or predictor variable.  
If Homoscedasticity is violated then the size of the error term differs across values of an independent variable.The standard errors are biased. Standard error are used to calculating confidence interval, biased stai errors give incorrect conclusion about significance of the regression coefficient.
Homoscedasticity is check by residual plot.
If residual plot shows pattern then we conclude that there is unequal variation in independent variable. To overcome this problem transform the dependent variable using one of the variance stabilizing transformations.A logarithmic transformation can be applied to highly skewed variables, while count variables can be transformed using a square root transformation.
The error term is usually denoted as ε, or epsilon, and you often see regression equations written:

Regression equation
Y = a + bx + ε

The distribution of ε must be normal, and the distributions of ε for all the locations must have the same variance this is known as Homoscedasticity.