Lecture 1 - Intro

Question 1

What is a simple linear regression?

Answer 1

Regresses the dependent variable on 1 indepdent variable and assumes their relationship bewteen the dependent and independent are linear

Question 2

Example of a linear regression:

Answer 2

• y = return variable
• x = defalted earnings change
• we estimate a and b by finding the line of best fit / a(hat) and b(hat) is determined by OLS in a way that minimises the trend lines and sample observations

Question 3

What is the Ordinary Least Square?

Answer 3

Used to estimate intercept and slope coefficient - drawing a random sample of observations from an underlying population
In a simple regression, observations are y and x value

Question 4

What is a multiple linear regression?

Answer 4

Regresses dependent variable on several independent variables and assumes the relationship between the dependent variable and independent variable is linear

Question 5

Example of multiple linear regression:

Answer 5

Question 6

What does R^2 measure?

Answer 6

The degree to which variations in the independent variables explains variation in the dependent variable
Values lie between 0 (no explanatory power) and 1 (perfectly explanatory)
The larger the estimated error terms (residuals - e(hat)) the smaller the R^2

Question 7

What is a t-test?

Answer 7

A statistic used to determine if there is a significant difference between the means of two groups and how they’re related

Question 8

What is the usual question answered by a t-test?

Answer 8

How likely is it to obtain the value a(hat) or b(hat) if the true value of the slope coefficient/interecept is 0?
If the probability is less than a certain value (5%) then one concludes the true population vaue is different from 0

Question 9

What is the measurement error in dependent variables?

Answer 9

Measurement error in the dependent variable results in lower explanatory power for R^2

Question 10

What is the measurement erorr in independent variables?

Answer 10

Measurement error in independent variables reduces the explanatory power and leads to an estimate of the slope coefficient that is downward biased (too low relative to value)

Question 11

What is a dummy variable?

Answer 11

0 or 1 - indicates the absence or presence of some categorical effect that may be expected to shift the outcome