Multivariate Classical Linear Regression Model Flashcards
Why is the multivariate regression model often better than a bivariate one?
A multivariate model is better because most variables are influenced by multiple factors.
It also improves the model’s goodness of fit.
It reduces bias through omitted variables by including those variables.
How do you interpret Beta in a multivariate regression?
Beta represents the effect of an independent variable on the dependent variable, ceteris paribus.
What is the consequence of omitting a relevant variable in multivariate regression?
Omitting a relevant variable introduces bias in the estimates of the included variables, leading to omitted variable bias. The direction of this bias depends on the relationship between the omitted variable and the included variable. Positive relationship leads to positive bias.
What is multicollinearity, and how does it affect OLS estimates?
Multicollinearity occurs when two or more explanatory variables are highly correlated. It inflates the standard errors, making it harder to detect statistical significance in relationships.
What is the F-test used for in multivariate regression?
The F-test is used to test whether a group of variables jointly has no effect on the dependent variable.
What is a dummy variable and how is it used in regression?
A dummy variable is a binary variable used to include categorical data in a regression model. It indicates the presence or absence of a characteristic, such as gender.
What does a robust standard error correct for?
Robust standard errors correct for heteroscedasticity, ensuring valid inference even when the assumption of constant error variance is violated.
What is perfect collinearity, and why is it a problem in multivariate regression?
Perfect collinearity occurs when one independent variable is a perfect linear combination of other variables. This makes it impossible to estimate the model using OLS, as the matrix X’X cannot be inverted.
How do omitted variables lead to biased estimates in multivariate regression?
If a relevant variable is omitted and correlated with the included independent variable, the OLS estimates will be biased due to the omitted variable’s influence.
What is the difference between R-squared and adjusted R-squared in multivariate models?
Adjusted R-squared adjusts for the number of explanatory variables and corrects for the fact that adding more variables can artificially inflate R2-squared.
How does the inclusion of irrelevant variables affect the OLS estimates?
Including irrelevant variables does not bias the estimates but increases the variance (standard errors) of other coefficients, making them less precise.
What are the assumptions for multivariate OLS?
- Linearity in population model
- Random sampling
- No perfect collinearity among independent variables
- Zero mean of errors
- Homoscedasticity
