Quantitative Methods

Question 1

Covariance definiton and equation

Answer 1

• Covariance – Statistical measure of the degree to which the two variables move together in linear relationship
  *

Question 2

Correlation Coefficient definition and equation and result interpretation

Answer 2

· Correlation coefficient – measure of the strength of linear relationship b/t 2 variables, no units

Question 3

Spurious correlation definition

Answer 3

i. Spurious correlation – appearance of causal linear relationship when there isn’t one

Question 4

Nonlinear relationship definition

Answer 4

i. Nonlinear relationship – correlation doesn’t capture nonlinear relationships

Question 5

t-test if population correlation coefficient equals zero, degrees of freedom equation, accept/reject rules

“statistically significant”

Answer 5

[equation]

[equation]

i. Df = n-2
ii. Reject H0 if +tcritical < t, or t < –tcritica

Question 6

Linear regression assumptions

Answer 6

i. Linear relationship exists bt dependent and independent variables
ii. Ind. Variable is uncorrelated with the residuals
iii. Expected value of the residual term is zero
iv. Variance of the residual term is constant for all observations
v. Residual term for one observation is not correlated with that of another
vi. Residual term is normally distributed

Question 7

Linear Regression slope coefficient equation and represents

Answer 7

[equation]

1. Represents a stocks systematic risk (beta), value of 1 would be average risk, >1 would be higher risk

Question 8

Linear regression intercept equation and interpretation

Answer 8

[equation]

1. Called “ex-post alpha”, measures excess risk adjusted returns, (-) value means it underperforms

Question 9

Standard Error Estimate (SEE)

Answer 9

· Degree of variability of actual Y values from regression Y’s

i. Smaller the SEE, better the fit
ii. Standard deviation of residual terms

Question 10

Coefficient of Determination (R²)

Answer 10

· Percent of the total variation in the dependent variable explained by the independent

i. For simple linear regression: R² = r² = (correlation coefficient)²

Question 11

Regression slope coefficient confidence interval

Answer 11

Is slope significantly different than zero?

[equation]

i. standard error of the regression coefficient is denoted as sˆb1
ii. Df= n -2
iii. If confidence interval does not include zero, then slope/coefficient is significantly different than 0

Question 12

T - test for regression slope coefficient

Answer 12

[equation]

i. Df = n – 2
ii. Reject H0 if t > + tcritical or t < –tcritical
iii. Rejection of the null means that the slope coefficient is different from the hypothesized value of b1

Question 13

Confidence interval for predicted values

Answer 13

[equation]

for predicted value of dependent variable

i. tc = two-tailed critical t-value at the desired level of significance with df = n – 2
ii. sf = standard error of the forecast

Question 14

Total sum of squares (SST)

definition and equation

Answer 14

i. measures total variation in dependent, difference b/t actual and mean Y values

[equation]

Question 15

Regression Sum of Squares (RSS)

definition and equation

Answer 15

Measures the variation in the dependent variable that is explained by the independent variable, difference b/t predicted Y’s and mean Y

[equation]

Question 16

Sum Squared Errors (SSE)