What is meant by the unexplained variation? How is it computed?

Name: Problem 2, Chapter 10: Elementary Statistics a Step by Step Approach
Uploaded: 2020-07-10T04:08:34-08:00
Duration: 6 min 22 s
Channel: Jai Chadha
Description: What is meant by the unexplained variation? How is it computed?

What is meant by the unexplained variation? How is it...

Key Concepts

Unexplained Variation

Unexplained variation refers to the portion of the total variation in a dataset that a statistical model does not account for with its predictors. It represents the variability in the observed data that remains when the model’s fitted values are subtracted from the actual data. This concept is pivotal in regression analysis, where the model is evaluated based on how well it can explain the variation in the response variable, with any residual variation being attributed to randomness or factors not captured by the model.

Residual Sum of Squares (RSS)

The Residual Sum of Squares (RSS) is the method used to compute the unexplained variation in a model. It is obtained by summing up the squares of the differences between the observed outcomes and the model’s predicted values. By squaring these differences, positive and negative deviations are both accounted for equally, and larger errors have a disproportionate impact on the RSS. It serves as a metric to assess and potentially improve the model by reducing this unexplained variation.

Transcript

0:00 Welcome.

00:02 Given that we now know what explained variation is, we're now going to delve deeper into the concept of unexplained variation.

00:11 Giving our official definition, our official definition for unexplained, unexplained variation is the variation for all points, all data points, for all data points, in a given sample that is due to chance.

00:40 So as you remember, explained variation is the variation that is due to the relationship between the independent and dependent variables.

00:50 The concept for explained variation is quite simple.

00:53 It's just the variation that is due to chance.

00:57 So explaining this graphically, we are going to, bring out our very familiar xy plot so on our x -axis we have our independent variable x and on our y axis we have our dependent variable y additionally we're going to go ahead and graph our y bar which is the average of all of our observed y values and we're going to put on our regression line once again let's make that a little bit steeper our regression line once again as you remember, the equation for our regression line is going to be y prime equals a plus b x.

01:44 We know that for any given point, let's put our point up there, make it a little big so we know what we're focusing on.

01:52 We know that our total variation is given by this red bracket.

01:58 We're going to go all the way down to our y bar line.

02:02 So this is our total variation.

02:05 Once again, we'll cover this more in more detail in upcoming videos.

02:11 But that is what our total variation is.

02:15 And if you watch the previous video, you know that this is what our explained variation is.

02:24 So now covering this last segment over here, the green bracket.

02:28 This is going to be our unexplained variation.

02:36 We're going to do unexplained like that.

02:40 We'll do unexplained like that...