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EDA Classical Assumptions
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- 1What are the first 3 classical assumptions?1. The regression model is linear, correctly specified, and has an additive error term
2. The error term has a zero population mean
3. All explanatory variables are uncorrelated with the error term - 2(Assumption 1) What is a linear, correctly specified model?Linear: All the coefficients are to the power of 1
Correctly specified: The model includes all the relevant explanatory variables - 3(Assumption 1) What is an additive error term?Yi = β0 + β1X1i + β2X2i + εi
(εi is the error term)
Error term: accounts for variation in the dependent variable that is not explained by the model. - 4(Assumption 1) Does this follow the first assumption? Yi= e^(β0)Xi^(β1)e^(εi)Yes, it can be transformed by using logs
ln(Yi)== β0 +β1 ln(Xi)+ ε
(This form follows the assumption) - 5(Prelude to Assumption 2) What are the components of a regression?A regression can be decomposed into a deterministic component and a random component
- 6(Prelude to Assumption 2) What is the deterministic component?The expected value of Y for a given value of X
(Y=β0 +β1X)
Also defined as E(Y|X), i.e. the mean (or average) value of the Ys associated with a particular value of X - 7(Prelude to Assumption 2) What is the random component?Y=β0 +β1X is not a complete explanation for the variations in Y
There are 4 ways (other than the included X variables) to explain Y's variations:
1) Omission of explanatory variables
2) Measurement errors
3) Incorrect functional forms
4) Random and unpredictable occurrences
The stochastic error term (ε) effectively ‘takes care’ of all these other sources of variation in Y that are NOT captured by X - 8(Assumption 2)*** What is a zero population mean?The average of the entire population's sample is zero ***(confirmation needed)
- 9(Assumption 2) Explain Assumption 2 : "the error term has a zero population mean"When we calculate the average of the error terms of the entire population, the answer should be 0.
- 10(Assumption 2) How does this work?Think of the bell curve. Error terms are assumed to be drawn from a "random variable distribution" with a mean of 0.
- 11(Assumption 2) What if the mean does not =0?It becomes a problem because the error term can influence the estimated coefficients.
This is why the constant term is necessary, as it will force the mean to become 0. - 12(Assumption 3) Explain it: "All explanatory variables are uncorrelated with the error termIt means there is no relationship between the independent variables and the error term
/
The covariance between any pair of random errors is 0. - 13(Assumption 3) What happens if there is correlation?The estimator will attribute to X some of the Y variations that actually came from the error terms. The regression will not provide a true estimation of X's effect on Y. E.g. the *actual* effect of X(income) on Y (spending) is low, but the correlation between X and e makes the estimated Y higher than it should be.
- 14When can this correlation happen?When there is an omission of an important explanatory variable from the equation
or
When there is a measurement error - 15What are the next 2 classical assumptions?4. Observations of the error term are uncorrelated with each other (No serial correlation)
5. Error term has a constant variance
(No heteroskedasticity) - 16(Assumption 4) Explain "no serial correlation"The error of one observation should not influence the error of another observation
If it does, there is serial correlation/auto-correlation - 17(Assumption 5) Explain "no heteroskedasticity"The error term must have a constant variance
The variance of the error term cannot change for each observation or a range of observations
If the variance is not constant, there will be inaccurate estimates of the coefficient's standard error - 18What are the final 2 assumptions (6 & 7)?6. No explanatory variable is a perfect linear function of any other explanatory variable(s) (no perfect multicollinearity)
7. The error term is normally distributed (this assumption is optional but usually is invoked) - 19(Assumption 6) Explain "no perfect multicollinearity"Perfect multicollinearity between two IVs is a problem because it implies that:
1. They are really the same variable, or
2. One is a multiple of the other, and/or
3. A constant has been added to one of the variables, and/or
4. Two IVs always sum to a third IV
5. An explanatory variable doesn't change within the sample - 20Implication of assumption 6Having perfect multicollinearity ruins our ability to estimate the coefficients because the perfectly collinear variables cannot be distinguished from each other:
You cannot ‘hold all the other independent variables in the equation constant’ if every time one variable changes, another changes in an identical manner!
Solution: one of the collinear variables must be dropped (they are essentially identical, anyway) - 21Explain Assumption 7Error term: sum of a number of minor influences on y by variables not captured by the regression. The more minor influences there are, the closer the distribution of error terms to a normal distribution (follows the central limit theorem: explain this too!)
Assumption 7 mainly used in hypothesis testing
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- Business/Economics Karteikarten am EDA Classical Assumptions, erstellt von Felix Culas am 04/04/2017.
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