02. Quantitative Methods Flashcards
Correlation Equation:
What are the three limitations of correlation analysis?
- Outliers
- Spurious correlation
- Only measures linear relationships.
What does a t-test determine?
- A t-test is used to determine if a correlation coefficient, r, is statistically significant.
- Significance is supported if the test statistic is less than −tcritical or greater than tcritical with n − 2 degrees of freedom.
General linear regression equation:
Yi = b0 + b1Xi + εi.
- Yi and Xi are the ith observations of the dependent and independent variable, respectively.
- b0 = intercept.
- b1 = slope coefficient.
- εi = residual error for the ith observation.
Linear regression assumptions:
- A linear relationship exists between the dependent and independent variables.
- The independent variables are not random, and there is no exact linear relation between any two or more independent variables.
- The expected value of the error term is zero.
- The variance of the error terms is constant.
- The error for one observation is not correlated with that of another observation.
- The error term is normally distributed.
The confidence interval for the regression coefficient, b1, is calculated as:
Standard Error of the Estimate Calculation:
What does the coefficient of determination, R2, measure?
The proportion of the total variation of the dependent variable explained by the regression.
R2 equation:
F-Stat calculation:
Used to test the significance of all (or any subset of) the independent variables (i.e., the overall fit of the model) using a one-tailed test
MSR calculation:
MSE Calculation:
Describe the p-value:
The p-value is the smallest level of significance for which the null hypothesis can be rejected.
- If p-value is less than the significance level, the null hypothesis can be rejected.
- If p-value is greater than the significance level, the null hypothesis cannot be rejected.
What is the equation for a t-test used for hypothesis testing of regression parameter estimates:
with n − k − 1 degrees of freedom
Confidence interval for regression coefficient calculation:
estimated regression coefficient ± (critical t-value)(coefficient standard error)
R2 Adjusted Calculation? Why is it relevant?
- R2 increases as the number of independent variables increases—this can be a problem.
- The adjusted R2 adjusts the R2 for the number of independent variables.
What is Conditional Heteroskedasticity?
When residual variance is related to level of independent variables.
What is the effect of Conditional Heteroskedasticity?
- Coefficients are consistent.
- Standard errors are underestimated.
- Too many Type I errors.
How is Conditional Heteroskedasticity detected?
Breusch-Pagan chi-square test = n × R2
How is Conditional Heteroskedasticity fixed?
By using White-corrected standard errors
What is serial correlation?
When Residuals are correlated
What are the effects of serial correlation?
- Coefficients are consistent.
- Standard errors are underestimated.
- Too many Type I errors (positive correlation).
How is serial correlation detected?
Durbin-Watson test
≈ 2(1 − r)
How is serial correlation corrected?
By using the Hansen method to adjust standard errors
What is multicollinearity?
When two or more independent variables are correlated
What are the effects of multicollinearity?
- Coefficients are consistent (but unreliable).
- Standard errors are overestimated.
- Too many Type II errors.
How is multicollinearity detected?
Conflicting t and F statistics; correlations among independent variables if k = 2
What is the correction for multicollinearity?
Drop one of the correlated variables
