in regression analysis, which of the following is not a required assumption about the error term ? This is a topic that many people are looking for. daweaselonline.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, daweaselonline.com would like to introduce to you Difference between the error term, and residual in regression models. Following along are instructions in the video below:
“Guys phil from statistics. Mentor comm one of the most common things i get asked asked by students about in regression is what s the difference between a residual and error term. The error term is also known as the disturbance term. So i m going to discuss that in this video for this example.
Let s look at some earnings data earnings is the dependent variable tenure is the explanatory variable when a builder model to help to explain earnings from tenure. Which is the time spent in a company. Let s forget about the units. We see what we have is five observations.
Five pairs of observations. We draw a scatterplot labeling. The x. Axis y.
For the vertical axis and x. For the horizontal axis next. We plot. The 5 points.
So for the first observation. We have earnings of 25 and tenure of 8. We take that over down to the respective axis and then we put a dot. There that coordinate is where x is equal to 8 and y is 25.
We do the same thing for the other observations..
So we get something looking like this all right now to fit the model. So the model has to explain why given x. This is where we need to draw a line through the data dude pick. Any two points and draw a line like this.
The answer is no we have to consider all the points. A good line will tend to be among the points. So not that something more like this perhaps okay now given this line. We can see that there s a formula for a straight line in textbooks.
They call. It alpha plus beta x. Alpha. And beta.
What are known as the coefficients or parameters. And x. Is the explanatory variable okay we re on the graph our coefficients. The y intercept that where the line cuts.
The y axis that is the value alpha. Remember alpha and b to their coefficients prime otherwise. Known as parameters. They actually numbers all right they re numbers.
So the alpha just stands for the intercept whatever that number happens to be in this example..
It will be a positive number because we re on the positive part of why the beta is the gradient of the slope in this example. The gradient is positive the gradient can either be positive negative or you can have it as zero. Okay then now this is about reading using the model use the model by reading off the graph. I think you ve learned in school.
How to read off a straight line. So given a value like x is 8. We want to find value cut on the line corresponds. It to x is 8.
That s y is 20. That s reading off the graph. But you can see here that come to the model this alpha plus beta. X.
Is the model given x is 8. We are slightly off the true value of y. Is 25 right we get y of 20 from the line. So we re off by a value of 5.
All right that s a kind of a mistake now you consider all the other points. You can see also there someone close to the line than others that each time is off the line. The dot is off the line. The model makes a slight mistake all right together we can write the model as this then dependent variable is equal to a value on the line plus a value off the line as shown by the arrows in the graph and x is 8.
So it s made up two parts then y value on your line..
Plus. That thing off the line. Which is called the error term otherwise known as the disturbance term. So the name suggests error disturbance.
I don t need to explain that okay so now. We know one error term is look. At this model. Alpha plus beta x.
We in practice. Never know what these coefficients are all right. But if we did know them we would know the true line so i m calling this thing. The true line since we don t know what the true line is we have to kind of estimate.
It is where the estimation problem comes in this is where you re going to start. Studying things like ols and and then higher courses maximum likelihood. And even high courses method of moments. So that i all those estimators are trying to kind of get a line close to true line.
Which we don t observe so say your estimated line looks something like this i m trying to show you it s it could equal to it. But generally it will be something close to it. But maybe not equal to it so this is the estimated line well. We now know that the dot to the true line.
That is called the error term..
But what about the distance of the dot to the estimated line that is also kind of like a mistake isn t it made using the estimated line in predicting the value of y. What is that called that is called wait for it the residual so in other words. The residual is like the error term. This is where student is a subtle kind of difference here i asked students this can we observe the error term students think a bit maybe.
The guess well observe the error term to know the value of the errors. You would need to see the true line. Yeah. Because you need two things you need the observations and you need the true line well observe obviously we ll have the observations that s the data.
But you have the true line. The answer is yes. If you know what the coefficients are but in general do not the coefficients are the answer is no because if you did know what the coefficients are there wouldn t be no such thing as econometrics because you would then know what the model is right that s a key thing so we don t know what coefficients are so we don t know what true line is hence you do not observe the errors ever apart from here in this hypothesis set supposing. I can see the true line here.
But can you see the residuals. The answer is yes you can because residuals you have the observations and you also have the estimated line the estimated line you get from some kind of econometrics package like stata eviews. Possibly spss and so on okay. So that is the difference between an error term and a residual fantastic thanks for watching i m phil.
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