Interpret Software Output for OLS (Part II)

okay so now let's talk about let's talk about part two so in part one we talked about the intuition of least square root of eight SEC intuition of Alpha the beta and how we find the regression line so but the most important part is probably intuition how would you use all of this is not done in the and the software packages a computer program can do this and I'll give you the output so you can find the data for our is the student sign for exam the score that they got on the exam and put it on the computer program it'll give you the results I mean there's so many programs on Stata you use math lab can do it now I don't want to try to list them all but they output they give you is very simple and you need to know how to you should be able to interpret that yet this is the output that they give you any any program will give you something like this so they will give you a constant or to intercept something like that it is going to be our our 20 it will also give you a coefficient coefficient this is our a slope we did in the previous part that was a it was the beta this was did another thing they'll give you is they'll give you your standard error standard errors in the way you calculate standard error is remember to take some of all those values visiting this they square it that this square and sum it all up later on though divided by number of observations minus two and take a square root of that just write it down on the board so this is standard error they keep for years it's really dependent on how how closely the line fits between between the our observations if observations are really far out here the standard error would be large because this number would be large monthly would give you this standard error another thing they will give you is an important thing is T statistic T statistic an old test statistic is is that's your coefficient or in a value for intercept divided by your standard error so they give you a T step divided by the standard error so what Yui we bring it up all this stuff because whenever we get we get this we get this regression line we get the data we get the the constant we want to know we want to know how certain they are that there is this relationship we want to do we're going to do a test on it I'm going to do a two-tailed test on it to see whether that is statistically significant so that that's why we're calculating the test statistic and remember that the T statistic the larger the two statistic is the less likely this the the more likely outcome is we can reject the null hypothesis and what is our null hypothesis in this case it is that the beta coefficient or the poorly understood but I'm just going to use I'm just going to talk about the coefficient so the coefficient is equal to zero so that's our null hypothesis to our NASA this is our null hypothesis it's the beta 0 beta 0 means this is this there's no relationship there's no relationship between our starting and the score in the exam that's when we made a 0 implies and we're going to use this test statistic to see whether we can reject this null hypothesis and we get the distant a stick by using size of the coefficient plus the what's the standard error and remember whatever the larger the test statistic is the more likely we are to reject the more likely we are to reject the null hypothesis so generally we get the usually around 2 the statistic is about 2 we can reject the null hypothesis at 5 percent significance level so let me let me remind you that is about screw SIGGRAPH in here well that would save if they this is mystical about to then we get then the likelihood that there is a more extreme T is only in this area only in this area so so well we can reject so now at this significance level that the larger that T gets the larger the smaller the probability that there is a more extreme teams that are even more extreme so if it is that this it goes maybe like Ted we'd be way out here this part would be really small this number would be a lot smaller it's not would be a lot smaller and that would mean that there that sees that this distribution the values that are more extreme would be even less likely so that would help us reject the null hypothesis so the larger the t statistic is generally generally should be larger than two we should be able to reject the null hypothesis then meetings to this there's no relationship that's what this the bistec does but it's not really that easy to to remember the size of the t-statistic it's not really that easy what what what is the gist of this take off of cilix say what is it of 10 well it depends on degrees of freedom so more convenient ways to to use the p-value so it is definitely given some time some statistical package of got probability but most of them call it p value and the value gives you gives you this number it gives you the the probability of having a T in this distribution that is more extreme more extreme that the number that we are getting we are getting is this distance is thick and the lower the number is but the lower the probability of having more extreme number that we're getting here the easier we can reject the null hypothesis so P values easier to interpret so if let's say we got this statistic of around two would have a p-value of around 1:05 meaning that 5% is around here if a p-value was 10.1 it means only really really few it would really really few more Tripta statistically are getting so we could really safely reject this null hypothesis but as long as that there's one more thing I want to mention is the r-squared right in here if they are squared is high r-squared tells you how closely the observations are through the line our squared is between 0 and the 1 between 0 and 1 if the every observation is perfectly aligned on on the on the line then our 0 I'm sorry the R squared is 1 it's perfect every observation is right the differences is non-existent that's 1 if I don't know with our su it up it probably is never 0 but if they're really all the observations here here here all over the roll over the place then R 0 sorry R squared would be very small or close to zero the interpretation of R squared is the large R squared is the more lab of the results so in sum if you if you know how you know how to interpret the intercept you know how to interpret the coefficient and you know how to test it for statistical significance then you can you can just take any computer package give any put in your data in a software don't give you this up will give you the other stuff but it will give you this for sure and then you can make inferences about the data that you messing around with and here I just yet one one variable you could actually put in more than one input something else and then you be harder to show it on my graph but for for statistical package they can handle more observations one that you have to have only one dependent variable but you can have many independent variables okay so this is it for far too and now just do part 3 for the drawbacks or

Channel: ktemlyak

Views: 22,724

Rating: 4.9544158 out of 5

Keywords: OLS, linear regression, least squares

Id: k_pROUwY-Fw

Length: 11min 18sec (678 seconds)

Published: Sat Jul 30 2011