Quiz #12
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Which one of the following statements is not true concerning residuals?
- [ A ] The residuals from a simple regression fit can be used to check for nonlinearity.
- [ B ] The residuals from a simple regression fit can be used to check on an assumption of homoscedasticity.
- [ C ] The residuals from a simple regression fit can be used to check on an assumption of approximate normality
for the error term distribution provided that a simple linear regression model is not inappropriate for the data.
- [ D ] Plotting the residuals from a multiple regression fit against the predicted/fitted values isn't so
important because scatter plots can be easily used to determine if there is nonlinearity.
- [ E ] Plotting the residuals from a multiple regression fit against each of the predictor variables is a way to
determine if any of the predictor variables should be transformed or if additional higher-order terms should be added to
the model.
The correct answer is [ D ]. While nonlinearity and/or the presence of outliers can easily be seen from a scatter plot
of the dependent variable plotted against the single predictor variable of a simple regression model, scatter plots,
which can only show the relationship between two variables at a time, aren't quite as useful for checking on
linearity in a multiple regression model since, due to predictor variables being possibly correlated with one another,
some scatter plots may suggest nonlinearity even though when all variables are considered simulataneously there is
not strong evidence against nonlinearity.