Financial Risk Manager Part 1
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The following are assumptions of the multiple linear regression model EXCEPT:
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NNikitesh
A
The independent variables are random, and there is exact linear relation between any two or more independent variables
B
The error term has an expected value equal to zero, and is normally distributed
C
A linear relationship exists between the dependent and independent variables
D
The error for one observation is uncorrelated with that of a different observation
Explanation:
The correct answer is A because:
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Assumption A is incorrect: In multiple linear regression, independent variables should NOT be random (they should be fixed or non-stochastic), and there should be NO exact linear relationship (perfect multicollinearity) between any two or more independent variables.
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Assumption B is correct: The error term should have an expected value of zero (E(ε) = 0) and is typically assumed to be normally distributed.
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Assumption C is correct: There should be a linear relationship between the dependent variable and the independent variables.
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Assumption D is correct: Errors should be uncorrelated across observations (no autocorrelation).
Key assumptions of multiple linear regression:
- Linearity between dependent and independent variables
- No perfect multicollinearity among independent variables
- Homoscedasticity (constant variance of errors)
- No autocorrelation (errors are independent)
- Normality of error terms
- Expected value of errors is zero
- Independent variables are non-random/fixed
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