02. Quantitative Methods

Question 1

Correlation Equation:

Answer 1

Question 2

What are the three limitations of correlation analysis?

Answer 2

1. Outliers
2. Spurious correlation
3. Only measures linear relationships.

Question 3

What does a t-test determine?

Answer 3

• 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 −t_critical or greater than t_critical with n − 2 degrees of freedom.

Question 4

General linear regression equation:

Answer 4

Y_i = b₀ + b₁X_i + ε_i.

• Y_i and X_i are the ith observations of the dependent and independent variable, respectively.
• b₀ = intercept.
• b₁ = slope coefficient.
• ε_i = residual error for the ith observation.

Question 5

Linear regression assumptions:

Answer 5

• 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.

Question 6

The confidence interval for the regression coefficient, b₁, is calculated as:

Answer 6

Question 7

Standard Error of the Estimate Calculation:

Answer 7

Question 8

What does the coefficient of determination, R², measure?

Answer 8

The proportion of the total variation of the dependent variable explained by the regression.

Question 9

R² equation:

Answer 9

Question 10

F-Stat calculation:

Answer 10

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

Question 11

MSR calculation:

Answer 11

Question 12

MSE Calculation:

Answer 12

Question 13

Describe the p-value:

Answer 13

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.

Question 14

What is the equation for a t-test used for hypothesis testing of regression parameter estimates:

Answer 14

with n − k − 1 degrees of freedom

Question 15

Confidence interval for regression coefficient calculation:

Answer 15

estimated regression coefficient ± (critical t-value)(coefficient standard error)

Question 16

R² Adjusted Calculation? Why is it relevant?

Answer 16

• 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.

Question 17

What is Conditional Heteroskedasticity?

Answer 17

When residual variance is related to level of independent variables.

Question 18

What is the effect of Conditional Heteroskedasticity?

Answer 18

• Coefficients are consistent.
• Standard errors are underestimated.
• Too many Type I errors.

Question 19

How is Conditional Heteroskedasticity detected?

Answer 19

Breusch-Pagan chi-square test = n × R²

Question 20

How is Conditional Heteroskedasticity fixed?

Answer 20

By using White-corrected standard errors

Question 21

What is serial correlation?

Answer 21

When Residuals are correlated

Question 22

What are the effects of serial correlation?

Answer 22

• Coefficients are consistent.
• Standard errors are underestimated.
• Too many Type I errors (positive correlation).

Question 23

How is serial correlation detected?

Answer 23

Durbin-Watson test
≈ 2(1 − r)

Question 24

How is serial correlation corrected?

Answer 24

By using the Hansen method to adjust standard errors

Question 25

What is multicollinearity?

Answer 25

When two or more independent variables are correlated

Question 26

What are the effects of multicollinearity?

Answer 26

• Coefficients are consistent (but unreliable).
• Standard errors are overestimated.
• Too many Type II errors.

Question 27

How is multicollinearity detected?

Answer 27

Conflicting t and F statistics; correlations among independent variables if k = 2

Question 28

What is the correction for multicollinearity?

Answer 28

Drop one of the correlated variables