Residual Analysis in Linear Regression

The video tutorial explores checking model assumptions in simple linear regression using residual plots. It discusses the assumptions of normal distribution, homoscedasticity, and independence of error terms. The tutorial explains how to plot residuals and interpret them, highlighting common issues like increasing variance and systematic curvature. Real-world examples are used to demonstrate how residual plots can indicate problems with the assumed model and suggest improvements.

What is the primary purpose of using residual plots in simple linear regression?

• To calculate the mean of the residuals

• To determine the correlation between variables

• To check the accuracy of the predicted values

• To verify the assumptions of the linear regression model

In a simple linear regression model, what does the error term epsilon represent?

• The predicted value of Y

• The slope of the regression line

• The intercept of the regression line

• The random error component

Which of the following is NOT an assumption about the error terms in linear regression?

• They are normally distributed

• They have constant variance

• They are independent of one another

• They are dependent on each other

What should the observed residuals indicate if the model assumptions are true?

• They should be exactly zero

• They should be normally distributed with constant variance

• They should increase with X

• They should decrease with X

Why should residuals not be plotted against the observed values of Y?

• Because it is not a common practice

• Because it is difficult to interpret

• Because it would give a misleading picture

• Because they are unrelated

What is a key characteristic of residuals in simple linear regression?

• They always sum to the mean of Y

• They always sum to a positive value

• They always sum to a negative value

• They always sum to zero

What does a good residual plot typically show?

• A clear pattern

• A parabolic curve

• A random scattering of points

• A linear trend

In an experiment with controlled X levels, what should a residual plot ideally show?

• Systematic curvature

• Increasing variance

• Decreasing variance

• Random scattering of points

What does increasing variance in a residual plot indicate?

• A violation of the normality assumption

• A violation of the constant variance assumption

• A violation of the linearity assumption

• A violation of the independence assumption

What does systematic curvature in residuals suggest about the relationship between Y and X?

• It is a perfect non-linear relationship

• It is not a reasonable linear relationship

• It is a perfect linear relationship

• It is a random relationship