Final Module (8, 9, 10)

Question 1

PDF

Answer 1

a function of random variable with a fixed distribution parameters, while Likelihood function is a function of model parameters for a fixed data set

Question 2

To find the Likelihood of a data set

Answer 2

find the likelihood of each data point under specific parameters (pdf), and then multiply all of them (joint pdf)

• Use LogLikelihood LL=ln(L) to simplify calculations

Question 3

The model with the highest LogLikelihood is

Answer 3

the most likely distribution for the data

Question 4

Derivative

Answer 4

is the function that shows instantaneous rate of
change of the given function for all values of 𝑥

Question 5

Velocity

Answer 5

the derivative of position with respect to time

Question 6

Acceleration

Answer 6

is the time derivative of velocity

Question 7

Steepness

Answer 7

derivative of height with respect to horizontal displacement

Question 8

Extremum (or extreme value)

Answer 8

a point at which a maximum or minimum value of the function is obtained in some interval

• When 𝑓(𝑥) reaches its extremum, 𝑓′ 𝑥 = 0

Question 9

Extrema at maximum and minimum

Answer 9

• At maximum: 𝑓′ 𝑥 = 0, 𝑓”(𝑥) < 0
• At minimum: 𝑓′ 𝑥 = 0, 𝑓”(𝑥) > 0

Question 10

What if 𝑓”(𝑥) = 0?

Answer 10

Then it’s a point of inflection – the point where the curvature changes sign

Question 11

Duration of a Bond

Answer 11

Cash-weighted average of time it takes to receive the bond’s cash flows, including both coupon payments and the bond’s face value

Question 12

Sensitivity of a Bond

Answer 12

derivative of a Bond divided by y

Question 13

Linear Regression

Answer 13

a process that determines the parameters of a linear model describing the relationship between the response variable and one or more explanatory variables

Question 14

One explanatory variable

Answer 14

simple linear regression

Question 15

Two or more explanatory variables

Answer 15

multiple linear regression

Question 16

Normal equations

Answer 16

a system of equations for 𝛽1 and 𝛽0 after we take the derivatives of 𝑆𝑆𝑅 with respect to 𝛽1and 𝛽0

Question 17

𝑆𝑆𝑇 =

Answer 17

𝑆𝑆𝑇 = 𝑆𝑆𝑅 + 𝑆𝑆𝐸

Question 18

𝑅^2 equation

Answer 18

= 𝑆𝑆𝐸 / 𝑆𝑆𝑇
= 1 − 𝑆𝑆𝑅 / 𝑆𝑆𝑇

Question 19

𝑅^2 definition

Answer 19

“coefficient of determination” – shows what percent of variation in 𝑦 is explained by the linear model

• The quality of fit / coefficient of determination

Question 20

Assumptions of Linear Regression

Answer 20

• Linear relationship between 𝑥1, …,𝑥𝑛 and 𝑦
• The residuals ∈ 𝑁(0, 𝜎2)
• 𝜎2 is constant across all values of ˆ𝑦𝑖 (homoscedasticity)
• Cov(𝜀𝑖 , 𝜀 𝑗 )– the residuals for different data points are uncorrelated
• What if the relationship is not linear?
• Sometimes 𝑦 depends linearly on 𝑓(𝑥1, …,𝑥𝑛)

Question 21

Adjusted 𝑅^2 definition

Answer 21

used to account for multiple independent
variables

Question 22

Adjusted 𝑅^2 equation

Answer 22

𝑅𝑎𝑑𝑗^2 = 1 − (1 − 𝑅^2) * 𝑛 − 1 / 𝑛 − 𝑘 − 1

𝑛– number of data points
𝑘– number of independent variables