Join thousands of students who trust us to help them ace their exams!
Multiple Choice
Which of the following residual plots would indicate that a least squares regression line () is an appropriate model for the data?
A
A plot where the residuals are randomly scattered around the horizontal axis with no apparent pattern.
B
A plot where the residuals show a funnel shape, with increasing spread as the fitted values increase.
C
A plot where the residuals form a clear curved pattern.
D
A plot where the residuals increase or decrease systematically as the fitted values increase.
0 Comments
Verified step by step guidance
1
Understand that residuals are the differences between observed values and the values predicted by the regression model. They help us assess how well the model fits the data.
Recall that for a least squares regression line (LSRL) to be appropriate, the residuals should be randomly scattered around the horizontal axis (which represents zero residual) without any systematic pattern.
Recognize that if residuals show a funnel shape (increasing spread), it indicates heteroscedasticity, meaning the variance of errors is not constant, which violates regression assumptions.
Note that a clear curved pattern in the residual plot suggests that the relationship between variables is not linear, so a linear model like LSRL is not suitable.
Understand that residuals increasing or decreasing systematically indicate a trend in errors, meaning the model is missing some structure in the data, so LSRL is not appropriate.