- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 8. Is R
^{2}related to statistical significance?

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**CFA Practice Question**

Each time we add regression variables to the model, the amount of explained variation will decrease. Is this true?

Correct Answer: False

If you add a completely unrelated variable to the model, R

^{2}will not decrease at all. The amount if explained variation (and R^{2}) will decrease only if the new independent variable explains any of the unexplained variation in the model. Such a reduction occurs when the new independent variable is even slightly correlated with the dependent variable and is not a linear combination of other independent variables in the regression.###
**User Contributed Comments**
6

User |
Comment |
---|---|

GileOne |
pls can anybody explain this? |

katybo |
If you add a new independent variable, the unexplained variation decreases, and R2 increases. R2 = 1- SSE/Total SS |

epiziL2 |
Adding a new variable will reduce the quantity of error from the model as you creat an additional explanation to the overall model. Hence SSE reduces(ie only when the new variable is corelated to the independent variable and is not linearly related to the previous independent.(In that case the new effects the new variable comes in with has not yet been captured by the model).Hence SST=SSR+SSEreduces |

mishis |
epizL2: you meant to say SSE reduces only when new variables correlated to dependent variable.... |

daverco |
This is an unsatisfactory explanation. If adding an independent variable helps explain any of the unexplained variation (meaning, it is a "useful" variable to the model), wouldn't that increase R-squared? If it is even slightly correlated with the dependent variable, wouldn't that add explanatory power to the regression, and therefore increase R-squared? |

davidt876 |
yea daverco, i think the wording in the answer is mixed up and they're trying to say what u said |