Bivariate Classical Linear Regression Model Flashcards
What does the coefficient Beta represent in the Bivariate CLRM?
It represents the change in dependent variable y for a one-unit increase in the independent variable x, ceteris paribus.
What is the objective of the Ordinary Least Squares in regression analysis?
The objective is to find the coefficients that minimize the sum of squared residuals between the observed values and the predicted values.
What is the economic significance in regression analysis?
Economic significance refers to the magnitude of the effect of the independent variable on the dependent variable.
What is statistical significance in regression analysis?
Statistical significance indicates whether the relationship observed between variables is likely to be due to chance, assessed through hypothesis testing.
What is homoscedasticity in the context of OLS?
Homoscedasticity refers to the assumption that the variance of the error term is constant across all levels of the independent variables.
What are the consequences of violating the homoscedasticity assumption?
If homoscedasticity is violated (heteroscedasticity). OLS estimates remain unbiased but the standard errors will be incorrect, potentially leading to invalid hypothesis tests.
What does R-squared measure in regression analysis?
R-squared measures the proportion of the variance in the dependent variable that is explained by the independent variable(s).
What are the key assumptions of the CLRM?
A1. Linearity in population model
A2. Random sampling
A3. Variation in x
A4. Zero mean of errors
A5. Homoscedasticity
What are the properties of OLS estimators under CLRM assumptions?
Unbiasedness - Expected Value of the Estimated Coefficient = Actual Value of the Coefficient
Efficiency - OLS has the smallest variance among all linear unbiased estimators (BLUE).
How is the coefficient Beta interpreted in a bivariate model?
Beta represents the change in y for a one-unit increase in x, assuming no other variables affect y.
What is the role of the error term in OLS regression?
The error term u captures unobserved factors affecting the dependent variable y.
How is Beta interpreted in a quadratic regression model?
Beta 1 measures the initial rate of change in y for a one-unit increase in x, without considering the nonlinear effects.
Beta 2 captures how the rate of change in y varies as x increases (acceleration or deceleration)
How is the coefficient interpreted in a log-level model?
Beta represents the percentage change in y for a one-unit increase in x.
How is the coefficient interpreted in a level-log model?
Beta represents the change in y a for a 1% increase in x.
How is the coefficient interpreted in a log-log model?
Beta represents the elasticity, or the percentage change in y for a 1% change in x.
