FRM: Regression #3: Standard Error in Linear Regression

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A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a (slightly?) different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is the measure of this dispersion: it is the standard deviation of the coefficient. For more great Financial Risk Management videos, visit the Bionic Turtle website! www.bionicturtle.com

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Опубликовано:

24 апр 2008

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Комментарии : 39

@pollibob 15 лет назад

I'm about 95% confident for the exam next week after watching this demonstration Fantastic lecture!!

@WobbleKun 12 лет назад

How is the standard error for each of the intercept and slope calculated?

@wildpokermannh 12 лет назад

Thank you so much! You have saved my econometrics grade. Who could teach me SLS regression? Not my professor, not the textbook, not Sal Khan and not various other powerpoints out on the web. You showed me how to calculate this and I really appreciate it!

@bionicturtle 12 лет назад

hi Lawrence, n-1 is tempting, but for the slope coefficient (as a test of sample mean), d.f. = n - k, where k is number of coefficients, including intercept. In this case, slope & intercept are "consumed" ... so df = n - 2 in a univariate regression, df = n - 3 in a regression with 2 independent vars, etc

@firassami7399 5 лет назад

can you please tell me how to find standar error for intersept

@bionicturtle 12 лет назад

@rmdaspit oh right, i'm not sure from the information given. Definitely the flipped equation that solves for X as F[Y] is NOT a valid regression; it's slope will be incorrect. So, short of re-regressing, I cannot recall if the new intervals can be inferred from the current.

@scottmuck 10 лет назад

This is about the standard error of the coefficients, looking for a video on the standard error of the regression

@menacedemort2878 8 лет назад

same here

@rheinxromer 7 лет назад

Me 2!!!

@bionicturtle 12 лет назад

Why? the standard error of the intercept is shown in the ANOVA table, it = 7.618/3.052 = 2.496. As shown, so i don't understand your correction?

@fabianweiss7667 12 лет назад

hello thx for your very good explanations but I don't understand the thing with standart error... what was the calculation? which data did u use?

@rmdaspit 12 лет назад

Thank you for these videos. I do have one question. If you were to find out that one person spent $31 on the lottery, how would you find out what their disposable income was with error estimates?

@chigra11 12 лет назад

Hi David. Thanks for the great explanation. I read papers and people usually wrote linear regression by y=ax+b +- q . They said q is from standard deviation. I still don't understand about how to get the q value. can you tell me how to get it? If I use excel's formula, can I just easily use the standard deviation formula for the Y values... =STDEV(Y1:Yn)? Thanks for your explanation

@sasamuraki 13 лет назад

Sir, so we have two ways of testing the validity of t-stat? if it is < 1, and < critical t value to disprove the null hypothesis, ir the coefficients are zero?

@dizzinicol 16 лет назад

the multiple linear regression model follows a F distribution where.... F= (RSSo-RSS/q)/(RSS/n-p-1) any idea what the q and p stand for?? cheers

@yoyomamagawd 15 лет назад

theres a different standard error for every fitted value. we have less faith in the fitted values the further they are from the center of the distribution of the independent variable.

@31896eneri 9 лет назад

To get the Standard error of each coefficient: ms.cc.sunysb.edu/~hbenitezsilv/metrics5.pdf For the Slope Coefficient: You'll need to understand the standard error of estimate aka Standard error of regression σ ( there are lots of videos here explaining it) which is the numerator. The denomitor is pretty easy to understand which is simply the sum of all the squares of each deviation of a single X observation from the Mean of all X's.

@itt6057 7 лет назад

Thank you so so much!

@JakaRachmadetin 12 лет назад

The standard error value obtained in here is correct. Maybe you made a mistake like me. I get 2.547 because I take the square root from the sum of e^2 divided by n-2. to get the correct standard error value, the sum of e^2 must be subtracted by the slope times cross product of x and y. By this way you will get 3.052 which is the correct value. You can check the result from simple regression in excel by clicking the Data -> Data Analysis -> scroll down and choose Regression. Hope this help

@danielmeng1007 12 лет назад

How do you calculate the standard error??

@geiko187 15 лет назад

I believe p is your first probability and q is your second probability or (1-p)... could be wrong though.

@rmdaspit 12 лет назад

@bionicturtledotcom Right, I was just wondering if there was a way to put bounds or estimate how good $289 is.

@azophi 5 лет назад

How did you get the table down below on row 22!!!

@10babiscar 12 лет назад

when i combined this regression video series with my lectures it suddenly all made sense.

@tingtingxu7754 12 лет назад

hi，could you please help me calculate the steps of standard error? i could not work it out.

@bionicturtle 16 лет назад

hi christy, currently it's on my paid member page but i am happy to send to you a copy. i don't know how to do that via youtube, do you have an email?

@christy00008 16 лет назад

do have a website with that worksheet?

@bionicturtle 12 лет назад

@10babiscar Super, glad to hear it!

@miracle842004 14 лет назад

thank you! very helpful to watch right before the test!

@milanfilipovic746 9 лет назад

Can you find the error using calculus?

@bionicturtle 12 лет назад

@rmdaspit thanks, you'd solve the equation for X: x = y/0.081 - 7.618/0.081. If y = 31, then x ~ $289

@ruzee2001 6 лет назад

Thanks a lot dear it is really very helpful.

@soccereight1992 11 лет назад

thank you so much. i really appreciate these videos.

@31896eneri 9 лет назад

THANK YOU VERY MUCH! :D

@minasianas 14 лет назад

By any chance we are going to the same uni, cheerfullgiver? LoL :D great vid, helped me a lot!

@kenkoujin 14 лет назад

perfect! thank you!

@tmansencal 10 лет назад

I calculated the the coefficients standard errors using Wikipedia reference, here is a spreadsheet with them (Bottom block of manual regression): drive.google.com/file/d/0B_IQZQdc4Vy8Q2VSVEVpdVE1alU/edit?usp=sharing