Linear regression - extracting info using matrix algebra

Hello!

I have a preloaded data which contains four columns and each column contains the following data in the following order:

1. Income (dollars)
2. Education
3. A dummy variable, 1 for male and 0 for female
4. Another dummy variable, 1 for STEM and 0 for not STEM

I've been given the linear model:

INCOME = α + β1EDUCATION + β2MALE + β3STEM

I should answer the following questions:

a) How large is α in the above equation

b) How many dollars greater is the salary of a male than the salary of a female

From what I understand, I should start with storing each column in the data in separate variables. How would I do this?

Any hints to get me started with this task are appreciated!

Answer 1

[Stephan]

add a column of ones to your matrix DATA in pos. 4. isolate income as a column vector and remove this column from DATA then use:

X = DATA\INCOME

you get the beta values (1-3) and the last one is alpha.

Also possible:

DATA = [DATA ones(size(DATA,1),1]
vals = DATA(:,2:end)\DATA(:,1)

The other stuff should be not a problem by using logical indexing.

[Daniel Miller]

Hello, thank you for the help! This sounds logical, however I'd need advice on doing this:

"add a column of ones to your matrix DATA in pos. 4. isolate income as a column vector and remove this column from DATA"

I'm still very new to MATLAB so it's all quite challenging.

Thanks in advance!

[Stephan]

DATA = [DATA ones(size(DATA,1),1]
vals = DATA(:,2:end)\DATA(:,1)

[Daniel Miller]

Thank you so much! I'll try to solve as much as I can on my own from here on.

[Stephan]

Did you notice that you can accept and or vote for useful answers? If you have more problems come back with a new question.

[Daniel Miller]

Cheers, I forgot to do that!