Question

CW 2

List 5 assumptions of the simple linear regression model.

You have estimated the following equation using OLS:

ŷ = 33.75 + 1.45 MALE

where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females.

a) According to this model, what is the average income for females?

b) According to this model, what is the average income for females?

c) What does OLS stand for? How are the OLS estimates calculated?

What does Gauss Markov theorem say about OLS estimates?

Suppose, you want to investigate what will happen to the demand of t-shirts if you increase price of the t-shirts that you are selling. Write down the regression model which will be able to investigate this relationship. From the theories that you have learnt in Principles of Micro, can you guess what curve are you estimating. What do you expect the relationship to be?

For each of the accompanying scatterplots for several pairs of variables, indicate whether you expect a positive or negative correlation coefficient between the two variables, and the likely magnitude of it (you can use a small range).

(a)  

(b)

6. a) Suppose you are estimating the following regression:
Y=B1+ B2X +e.
Using the below data, calculate estimates of B1 and B2 and the variance of B2.

b) Using your estimates, predict the value of y and the residual when x=3.

Answer 1

Answer for a)

ŷ = 33.75 + 1.45 MALE in this equation "MALE" is used as dummy which takes value 1 when Male is considered otherwise 0

Hence Average income of female is y_hat=33.75+1.45(0)=33.75

Answer for b)

And in case of male it should be y_hat(Male)=33.75+1.45(1)=35.2

Answer for c)

OLS stands for Ordinary least squares in which the error term that is the portion that moves away fromm population parameter we try to find minimum of sum of square of these error terms

For an example If Y=a+bX+error...(Y is dependant variable and X is independant variable i.e. value known to us and error term ) we can estimate only Y_hat=a+bx therefore (Y-Y_)^2=(error)^2 sum of these terms over the sample of observations.

Answer for d)

Gauss Markov theorem states that OLS estimats are consistent, efficient and unbiased.