July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short Course
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
12.4 Decomposition of the Sample Variation in Y
Let us express the variance of the random variable Y as
We noted above that there were two components to Yi—a systematic component reflecting the linear influence of Xi and a random component εi due to chance factors. A moment's reflection reveals that if most of the variation in Y is due to random factors, then the estimated least squares line is probably worthless as far as predictions are concerned. However, if most of the variation in Y is due to the linear influence of X, then we can obtain a meaningful regression equation. So the question arises—“How much of the variation in Y is due to the linear influence of X and how much can be attributed to random factors? We can answer this question with the aid of Fig. 12.7.
Figure 12.7 Decomposition of 
into 
and ei.
Since our goal is to explain the variation in Y, let's start with the numerator of Equation (12.10). That is, from Fig. 12.7,
where is attributed to the linear ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.