Topic 1.2 Estimation.pptx

# Topic 1.2 Estimation.pptx - Topic 1.2 Simple linear...

• 24

This preview shows page 1 - 6 out of 24 pages.

Topic 1.2: Simple linear regression (Estimation) 1

Subscribe to view the full document.

1.2 Estimation Our goal is to estimate the PRF based on the SRF, as accurately as possible But how is the SRF determined? The method of estimation used to achieve that goal: Ordinary Least Squares (OLS) method To understand the OLS method, must first understand the least-squares principle 2
Estimation Figure 3.1: given n pairs of (X, Y) observations, we need to determine the SRF in such a manner that the SRF is as close as possible to the actual Y To do this, can use either of the two criterion to choose the SRF (1) the minimum residual sum criterion (2) the least-squares sum criterion 3

Subscribe to view the full document.

(1) the minimum residual sum criterion Choose the SRF in such a way that the sum of the residuals is as small as possible See Fig 3.1 But, this is not a very good criterion Cos the residuals receive the same weight in the sum 4
(1) the minimum residual sum criterion The residuals uhat_2 & uhat_3, as well as uhat_1 & uhat_4 receive the same weight in the sum: uhat_1 + uhat_2 + uhat_3 + uhat_4 But from Fig 3.1, we notice that uhat_2 & uhat_3 are much closer to the SRF than uhat_1 & uhat_4 5

Subscribe to view the full document.

(1) the minimum residual sum criterion That is, all the residuals receive equal importance no matter how close or how far apart the observations are from the SRF An unwanted consequence: it’s possible to get a sum of zero, i.e., residuals of the same magnitude but with opposite signs will cancel out each other This will give a wrong impression of no residuals 6
You've reached the end of this preview.
• Spring '14

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern