Residual Analysis in Regression Models

The video tutorial discusses checking model assumptions in simple linear regression using residual plots. It explains the assumptions of normal distribution, homoscedasticity, and independence of error terms. The tutorial demonstrates how to plot residuals and interpret them, highlighting the importance of random scattering and mean zero. It identifies common issues in residual plots, such as increasing variance and systematic curvature, and suggests solutions like weighted regression and model transformation. Real-world examples illustrate these concepts, emphasizing the need for accurate model assumptions for valid statistical inference.

What is one of the key assumptions about the error term epsilon in simple linear regression?

• It is uniformly distributed.

• It is normally distributed.

• It has a mean of one.

• It is dependent on X.

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

• Because it is not a common practice.

• Because it would give a misleading picture.

• Because it is too complex to interpret.

• Because they are unrelated.

What does a random scattering of points in a residual plot indicate?

• No indication that the model assumptions are false.

• A violation of the normality assumption.

• A need for model transformation.

• A problem with the model assumptions.

What does increasing variance with X in a residual plot suggest?

• A need for more data.

• A perfect model fit.

• A violation of the normality assumption.

• A violation of the constant variance assumption.

What might systematic curvature in a residual plot indicate?

• The residuals are independent.

• The model assumptions are perfect.

• The linear relationship between Y and X is not reasonable.

• The linear relationship between Y and X is reasonable.

What is a possible solution for dealing with increasing variance in residuals?

• Ignoring the variance.

• Applying weighted regression.

• Increasing the sample size.

• Using a different dataset.

What does a normal quantile-quantile plot of residuals help determine?

• The mean of residuals.

• The variance of residuals.

• The normality of residuals.

• The independence of residuals.

What might be a reason to add an X^2 term to a model?

• To fit a linear relationship.

• To address systematic curvature in residuals.

• To increase the complexity unnecessarily.

• To reduce the sample size.

What does a residual plot with no major outliers and no systematic curvature suggest?

• The residuals are not normally distributed.

• The data is not suitable for analysis.

• The model needs significant improvement.

• The model assumptions are likely valid.

What is a potential benefit of transforming variables in a model?

• To make the model more complex.

• To achieve a straight-line relationship.

• To increase the number of variables.

• To decrease the model's accuracy.