Lecture 2

Question 1

What two things can regression analysis do

Answer 1

• Test the theory to establish whether there is a relationship and is it positive or negative
• Estimate the magnitude of the relationship

Question 2

What is y in the simple linear regression model and why

Answer 2

The dependent variable as it depends on the value of x

Question 3

What is x in the linear regression model

Answer 3

x is the independent variable

Question 4

What are 𝛽0 and 𝛽1

Answer 4

Underlying population parameters

Question 5

What does 𝑢 represent

Answer 5

• The factors other than X that affect Y
• Some of these factors may be unobservable

Question 6

What does the term 𝑢 also account for

Answer 6

Measurement error in variable

Question 7

What does 𝛽0 represent graphically

Answer 7

• The intercept, where X=0

Question 8

What does 𝛽1 represent graphically

Answer 8

The slope parameter of a linear relationship between x and y

Question 9

If all the other factors (contained in 𝑢) are held constant what is the equation for change in Y

Answer 9

∆𝑦=𝛽1 ∆𝑥

Question 10

What is the 1st assumption about the disturbance(u)

Answer 10

On average, the disturbance term is zero, 𝐸(𝑢)=0

Question 11

What is the 2nd assumption of u/disturbance

Answer 11

-The average of u does not depend on the value of x (X and U are unrelated)
-Knowing something about x does not tell us anything about u

Question 12

What is the zero conditional mean assumption combining these 1st 2 assumptions

Answer 12

𝐸(𝑢|𝑥)= 0

Question 13

What is the population regression function

Answer 13

𝐸(𝑦|𝑥)

Question 14

If the zero conditional mean assumption is valid then what does the population regression function=?

Answer 14

𝐸(𝑦|𝑥)=𝛽0+𝛽1𝑥

Question 15

What is the population regression function

Answer 15

A linear function of x

Question 16

What does a one unit increase in x change the expected value of Y by

Answer 16

𝛽1

Question 17

For any given value of x, the distribution of Y is centred about…

Answer 17

𝐸(𝑦|𝑥), the population regression function (PRF)

Question 18

What does the PRF tell us

Answer 18

how the average or expected value of 𝑦 changes with 𝑥

Question 19

What will the observations of Y look like

Answer 19

• Some higher than 𝐸(𝑦|𝑥) and some not, depending on u in each specific case

Question 20

What method is used to estimate B0 and B1

Answer 20

Ordinary Least Squares (OLS)

Question 21

What does the OLS estimator find

Answer 21

The values of B0 and B1 that minimses the sum of the squared vertical distances between each observation pointand the line

Question 22

What is this line called and what is the equation

Answer 22

• The OLS regression line
• 𝑦̂=𝛽̂0+𝛽̂1 𝑥
• Also referred. to. as the sample regression function (SRF)

Question 23

What is the sample regression function (SRF) used for

Answer 23

• An estimate of the PRF 𝐸(𝑦|𝑥)=𝛽0+𝛽1 𝑥

Question 24

Using the SRF , what can be written

Answer 24

𝑦𝑖=𝛽̂0+𝛽̂1𝑥𝑖+𝑢̂i

Question 25

What does 𝑢 ̂𝑖 stand for

Answer 25

The residual

Question 26

What are the two equations for 𝛽 ̂0, 𝛽 ̂1

Answer 26

Question 27

Diagram showing that the residuals are not the same as the disturbances, 𝑢𝑖, in the population relationship

Answer 27

Question 28

What does the OLS estimator rely on

Answer 28

- A population model and a corresponding PRF