Linear Regression Flashcards
Strictly Exogenous
The error term is untreated to any instance of the variable X; past, present, and future
What does mean independence imply for explanatory variables in relation to the error term?
The explanatory variables are uncorrelated with the error terms.
Residuals
The different between the observed values and the predicted values
Residuals
The different between the observed values and the predicted values
Assumptions between the relationship between xt and εt
A.1. Linear in Parameters
A.2. No Perfect Collinearity
A.3. Zero Conditional Mean of Error Term
What is the finite sampling distribution of an estimator
The probability distribution of the estimator
Why is sampling distribution of prime interest
It allows us to draw statistical inference (conduct hypothesis tests about the unknown population parameter)
Sampling Distribution of an Estimator
The probability distribution of that estimator across all possible random samples of a fixed size drawn from a population.
Sampling Distribution according to the Central Limit Theorem
The sampling distribution of the sample mean often approaches a normal distribution as the sample size increases
Reasons why sampling distribution is importance in statistical inference
- Understanding the behaviour of an estimator
- Quantifying Uncertainty
- Basis of Inference
- Evaluating the properties of estimators
- Model validation
Weakly Exogenous
The error term is mean independent conditional only on the current explanatory variables.
Linearity of the Model
The relationship between the depended variable (y) and the independent variable (X) is linear : y = Xß + e
Full Rank of X
No Perfect Multicollinearity, no independent variable is an exact linear combination of the other.
Exogeneity of the Errors
The error terms have an expected value of 0: Ex[e|X] = 0
Homoskedasticity
The error terms have a constant variance
