Selected Mathematical Technique Flashcards
What is Ordinary Least Squares (OLS) Regression?
A statistical method for estimating the relationship between one or more independent variables and a dependent variable.
What are common questions answered by OLS Regression?
Does relationship duration affect customer lifetime value? Does education influence fertility rates?
What is Simple Linear Regression?
An OLS regression with one independent variable.
What is Multiple Linear Regression?
An OLS regression with multiple independent variables.
What is the formula for OLS Regression?
E(y | X) = ŷi = α + βXi.
What do the components of the OLS formula represent?
ŷi: Predicted value, Xi: Independent variable, α: Intercept, β: Slope coefficient.
What does the slope coefficient (β) indicate?
The change in the predicted value of y when X increases by one unit.
What are residuals in OLS Regression?
The differences between actual and predicted values, represented as εi = yi - ŷi.
What are the five key assumptions of OLS Regression?
Linearity, Exogeneity, No Multicollinearity, Homoscedasticity, and No Perfect Collinearity.
What is the Linearity assumption in OLS?
The relationship between variables must be linear, meaning terms in the model must be constants or parameters multiplied by X.
What happens if the Linearity assumption is violated?
The model ceases to be linear, e.g., when β is squared.
What is the Exogeneity assumption?
Independent variables must not be correlated with the error term to avoid biased coefficient estimates.
What is Multicollinearity?
A high correlation between independent variables, which undermines their independence.
Why is Multicollinearity a problem?
It distorts the significance of independent variables, making coefficient estimates unreliable.
What is Homoscedasticity?
The error variance should remain constant across all observations.
What is Heteroscedasticity?
A condition where variance changes across different observations, violating OLS assumptions.
What is the No Perfect Collinearity assumption?
The observed data in the variable Xi should not be identical for all cases.
Why is No Perfect Collinearity important?
If all values of Xi are the same, the denominator in the slope estimate formula would be zero, making calculations impossible.
What is the normality condition in OLS Regression?
The error terms should be normally distributed for valid inference and hypothesis testing.
