Introduction to OLS (Part I)

okay hello today I want to talk about OLS ordinary least-squares also known as linear regression this helps us this helps us to show the relationship between the dependent variable and independent variable so let's do an example suppose we were looking and we want to see the relationship between the hours students study and how well they do on the exam let's let for at that so in this case our dependent variable is the scores that the students gets on the test because with that that value that depends on on how much they study so our dependent variable is is on the y-axis and it is the uploaded score that's the score they get on the exam our independent variable is how much the student studies but let's say s in hours it's on the XX advances this is ours this is an independent variable so we want to see the relationship between those two variables so let's say let's suppose we get some guitar some data we get some observations we get a survey maybe from from the students of how much they studied and how that corresponds with their with a score that they got on the exam so let's just because I'm suppose some one student got this or another student got this and nothing students studied this much and got this score and so on and kind of randomly going to put bunch of dots here so how's all this going to show us going to help us see the relationship between those variables well all that steps to wants to summarize some where is all this information and it summarizes that by drawing a line a line that represents this this relationship so we begin you can characterize it by say this line so hahaha so how do we get this line so then let me go first let me say what is this line say this line has an intercept and this line has a slope so we so we can write it what write this line as as y equals the intercept was the slope beta of the X button air so this is the equation of this line in this case that is the score equals a constant usually known as alpha sometimes people call it beta zero but it doesn't really matter what its goal was beta hours so this is this is what the line sets so how do we get this line how do we get ordinary least-squares what it's doing it takes this distance squares it adds this distance this is the distance between the actual value and the predicted value so it adds all it takes all those values it dates finds all those differences squares it and that sums all of this up sums all this up in mathematical notation it would look like it would look like this so thanks there's the difference between the actual value y:i and the predictive value it squares this difference and then it sums it up and zoom all up and is the number of observations so the two reasons why this is pretty modest what why why is it squared if the reason is that you want to have a positive value all the time because if you just add up all the difference some some of those will be positive and some of those would be negative so this way you want to square everything the second probably most important reason this is squared is that it's just easier to do it mathematically it's easier to find the line that minimizes this then suppose if we had an absolute value here I'm not going to go into the method of how we exactly we find this line but I just want to give you the intuition so how they all let's go how they're all s works how we find this line it minimizes those difference so that that's how we get them but get the line so we get the regression so so how does it use the intuition of those open something Alpha and the beta or the alpha alpha tells you what what the value of dependent variable would be if the value of independent variable was zero suppose suppose the students studied zero hours for the exam so this value will be zero and the score will be equal to alpha so let's just plug it in at number make it 20 what is the beta see the beta tells you by how much the the value of independent variable changes if the value of dependent variable changes by one unit so let's suppose our beta the beta is the slope of the line then suppose this would be 10 so that would be as student studies an extra hour for the exam we expect their score to increase by 10 points something like this so the score a student who studied for for six hours would be the indeedy the score of someone who studied for for seven hours would be 90 an extra hour of study will translate into plus 10 points on the exam so this is it when and then the put this is that read this part so now I mean next part I'm going for two

Channel: ktemlyak

Views: 78,863

Rating: 4.9088607 out of 5

Keywords: OLS, linear regression, least squares

Id: 9JboAs6AcEA

Length: 6min 46sec (406 seconds)

Published: Sat Jul 30 2011