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Answer: The elastic net approach minimizes a loss function that contains both squared and absolute value functions of the parameters.
**C is correct.** The elastic net is a hybrid of the two regularization techniques: ridge regression and least absolute shrinkage and selection operator (LASSO), where the loss function contains both squared and absolute-value penalty terms in the objective (loss) function being minimized. It is then possible to obtain the benefits of both ridge regression and LASSO: reducing the magnitudes of some parameters and removing some unimportant ones entirely. **A is incorrect.** In ridge regression, the loss function has a shrinkage term that introduces a penalty in the form of the sum of squared coefficients. **B is incorrect.** In the LASSO approach, the penalty takes an absolute value form. **D is incorrect.** This is what ridge regression avoids, and this does not occur in an elastic net.
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An economic researcher at a financial institution is designing a model that forecasts macroeconomic variables. The researcher considers applying regularization techniques such as the ridge regression approach, least absolute shrinkage and selection operator (LASSO) approach, or the elastic net approach to address the difficulty of estimating parameters in models that include multiple variables. After considering these three approaches, the researcher decides on using the elastic net. Which of the following statements about the use of an elastic net is correct?
A
Unlike the ridge regression approach, the elastic net approach introduces a penalty term in the loss function comprised of the sum of squares of the regression coefficients.
B
Unlike the LASSO approach, the elastic net approach introduces a penalty term in the loss function comprised of the sum of the absolute values of the regression coefficients.
C
The elastic net approach minimizes a loss function that contains both squared and absolute value functions of the parameters.
D
The elastic net approach manages correlated variables by assigning large positive coefficients to some variables and large negative coefficients to others.