Confidence Intervals for \(\displaystyle\beta{1}\) and \(\displaystyle\beta{2}\) 'm

Adolfo Hebert

Adolfo Hebert

Answered question

2022-03-28

Confidence Intervals for β1 and β2
'm having a bit of trouble with the question below.
Using this Data -> Data
Question: Establish 95% confidence intervals for β2 and β3.
I know I use the formula: β2± (t-value)(standard error)
How do I find the standard error using the data given in the pic?

Answer & Explanation

Gia Edwards

Gia Edwards

Beginner2022-03-29Added 12 answers

I assume that you want to construct two different CIs (for each parameter) and not simultaneously for the vector (β2,β3 ). As such, you can use the result
var(β^)=σ2(XX)1.
When instead of σ2 you can plug-in its estimator, namely
σ^2=1103i=110ei2. And you should invert the following matrix 
X'X=NX2tX3tX2tX2t2X2tX3tX3tX3tX3tX3t2,
then, var(β^i)=σ^2(XX){ii}1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?