Regression Analysis Flashcards
What is the goal of inference in regression?
Use sample data to make conclusions about the larger, unobserved population.
What is the null hypothesis (H0) in regression?
The default assumption stating no relationship or no effect, typically H0: β = 0.
What does the alternative hypothesis (HA) state?
The claim that there is a relationship, often stated as β ≠ 0 for a two-tailed test.
What is the purpose of the t-statistic in regression?
To determine if the sample slope (b) is statistically significantly different from the hypothesized population slope.
What is the formula for the t-statistic?
t = (Sample Slope - Hypothesized Population Slope) / Standard Error of Sample Slope.
What does a smaller standard error of the slope (Sb) indicate?
It indicates that the estimate ‘b’ is more precise.
What is the decision rule for hypothesis testing in regression?
Compare the calculated t-statistic to a critical t-value; if |calculated t| > critical t, reject H0.
What is a p-value?
The probability of observing a sample slope as extreme as the one calculated, assuming H0 is true.
What does a small p-value indicate?
It suggests that the observed result is unlikely if H0 were true, providing evidence against H0.
What is the purpose of a confidence interval (CI)?
To provide a range of plausible values for the true population slope (β).
What assumptions must be met for OLS regression to be BLUE?
Linearity, random sampling, no perfect multicollinearity, zero conditional mean of errors, homoscedasticity, no autocorrelation.
What is the difference between causation and correlation in regression?
Regression shows association, not necessarily causation.
What is a confounding variable?
A variable correlated with both X and Y that biases the estimated effect of X on Y.
What is the purpose of multiple regression?
To estimate the effect of multiple independent variables on a dependent variable simultaneously.
What does R-squared (R²) represent?
The proportion of variance in Y explained by all independent variables in the model.
What are standardized coefficients (Beta weights)?
Coefficients that allow comparison of the relative impact of independent variables measured on different scales.
