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Answer: The independent variables are random, and there is exact linear relation between any two or more independent variables
The correct answer is A because: 1. **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. 2. **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. 3. **Assumption C is correct**: There should be a linear relationship between the dependent variable and the independent variables. 4. **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
Author: Nikitesh Somanthe
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The following are assumptions of the multiple linear regression model EXCEPT:
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