What is homoscedasticity?

What is homoscedasticity?

• A. for every value of x, variances on y should be equal.
• B. means of y are equal across x.
• C. y has constant correlation with x.
• D. residuals are normally distributed.

Answer: (A)

Homoscedasticity means the spread of the outcome is the same across all levels of the predictor. In regression, this translates to the residuals (the differences between observed and predicted y) having constant variance regardless of the x value. When this holds, the residuals form a roughly uniform band around the regression line across the entire range of x. If the spread changes with x, that’s heteroscedasticity. The statement that variances on y are equal for every value of x captures this idea. The other options refer to equal means, constant correlation, or normality of residuals, which are different properties.

Homoscedasticity means the spread of the outcome is the same across all levels of the predictor. In regression, this translates to the residuals (the differences between observed and predicted y) having constant variance regardless of the x value. When this holds, the residuals form a roughly uniform band around the regression line across the entire range of x. If the spread changes with x, that’s heteroscedasticity. The statement that variances on y are equal for every value of x captures this idea. The other options refer to equal means, constant correlation, or normality of residuals, which are different properties.