Residual Analysis in Regression Models

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

• It is uniformly distributed.

• It has a constant mean.

• It is normally distributed.

• It is dependent on X.

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

• Because it is not a standard practice.

• Because they are unrelated.

• Because it would give a misleading picture.

• Because it is too complex to interpret.

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

• A need for model transformation.

• A problem with the model assumptions.

• A violation of the normality assumption.

• No indication that the model assumptions are false.

What does increasing variance in a residual plot suggest?

• A violation of the constant variance assumption.

• A perfect model fit.

• A need for more data.

• A violation of the normality assumption.

What might systematic curvature in a residual plot indicate?

• The model is perfectly linear.

• The variance is constant.

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

• The residuals are normally distributed.

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

• Ignoring the variance.

• Using weighted regression.

• Collecting more data.

• Transforming the residuals.

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

• The linearity of the model.

• The variance of residuals.

• The normality of residuals.

• The independence of residuals.

In the context of residual plots, what does a check mark typically indicate?

• A violation of model assumptions.

• A problem with the model.

• A need for model transformation.

• No obvious problems with the model.

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

• To fit a curve through the data points.

• To make the model linear.

• To reduce the number of variables.

• To increase the model's complexity unnecessarily.

What is the purpose of transforming variables in a model?

• To increase the variance.

• To make the model more complex.

• To achieve a straight-line relationship.

• To reduce the number of data points.