Question

For simple linear regression, suppose that we examine a residual plot and find that the residuals are generally more-dispersed at lower levels of the explanatory variable. True or False: This suggests that one of the assumptions for simple linear regression is violated.

Answer 1

TRUE

One of the assumptions of simple linear regression include homoscedasticity of the residuals. That means, variance of error is equal for all levels of explanatory variable. This can be checked by creating a scatterplot of the residuals against the explanatory variable, which should result in a random scatter(without any patterns).

Here in this case, residuals are more dispersed at lower level of the explanatory variable which implies variance is different at different level of explanatory variable. which violates one of the assumptions of simple linear regression, homoscedasticity. i.e, it is heteroscedastic.

other assumptions of simple linear regression includes

independent and dependent variable has linear relationship.

residuals should be uncorrelated(independent error).

normally distributed errors with mean 0.