medium · FRM Part 1

An analyst performs a regression with n=100 and k=5, obtaining an R^2 of 0.40.

If the analyst adds 5 more variables that are essentially random noise, which of the following is most likely to occur?

  1. Both the raw R^2 and the adjusted R^2 will increase due to the increased complexity of the model.
  2. The raw R^2 will increase or stay the same, while the adjusted R^2 will likely decrease.
  3. The F-statistic for joint significance will increase because the model now has more explanatory variables.
  4. The residual sum of squares (SSR) will increase, causing the adjusted R^2 to drop.

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