Statistics 101: Linear Regression, Test and Interval for the Slope

[@MarcoVuerich]

I do not ever comment a KZbin video, but in this case I've felt the necessity to do that. Thank you Brandon for these great tutorials. You're greatly helping a PhD student here in Italy!

[@ramikhrais2189]

Thank you so much dear Brandon for these amazing tutorials. Do you have any plans to introduce tutorials about time series?

[@SiyaMedia]

Rami Khrais I have also asked the same question on LinkedIn

[@celvanna2692]

Thank you so much for these videos! and thank you for continually repeating what the values are in conceptual definition. I am good at numbers but I am terrible with combining meaning to the numbers. So having you continues repeat what every value represents throughout these videos has really help solidify their meaning. Thank you so much for that, the visuals, and going over things multiple times. I hope you find making these videos as rewarding as we are grateful to have them!

[@mmmommm237]

I watched all your vids as a recap for my phd. I am a little rusty :) thank you for everything!

[@nomcognom2332]

Accurate as always. Thumbs up.

[@elizabeth84323]

you helped me understand a grad level class in statistics! Thank you!

[@N0rmad]

Is this really grad level stuff? I would've thought this was undergrad statistics.

[@ginginong-cornel2136]

This is so helpful (all the videos!)

[@snigdhasinghvi7603]

Love your lessons! Very helpful. SUGGESTION: You could give a few questions for practice before you start the next video to ensure we get a stronger hold of the topic discussed! Thanks.

[@RememberThisBrand]

I love this!! Thank you Mr. Foltz

[@maskalon9505]

Your videos are absolutely great. I have one small notion to this one. I guess it's for simplification, but from a scientific view we cannot say that we are 95% confident, we can only say that, in the long run, 95% of confidence intervals that we model for samples from that population will not contain 0. Because a confidence is not a quantifiable concept in the sense of accuracy in statistics. I think it is not arbitrary to understand this slight difference when it comes to critical evaluation of one's data analysis. However only a tiny though I had about this. I love your videos and you help a lot of people here. Keep it up. ❤️

[@manojsubedi1643]

He elaborated on this in his old lecture. It means that we can confidently say that out of 100 times of sampling in the same population, the value of b1 in each sampling will fall between the given interval at 95 times.

[@amirrahimi212]

thank you

[@ganeshrkamath8781]

Hii Brandon..All i can say is great thank you to you.Just because of you im understanding statistics!! thanks a lot!!!

[@empaulstube6947]

12:45, should it be called Standard Error rather than Standard Devlation of the Slope?

[@hussameldinrabah5018]

Standard error for the full model, but sd for slope is just the standard error for the slope term.

[@adilsalim105]

@ 18:00 t vs. t critical, how does it tell us that it is significant. If the T ratio (3.46) is bigger than the t value (2.776), will it be significant? Can someone please explain?

[@amirrahimi212]

excellent

[@yichengliu4257]

Thanks so much !

[@suinkim7836]

Can you tell me how you ended up getting t.05/2? Everything will be appreciated :)

[@Humiliator115]

thats because its Two-tailed t-test (its just 2,5% at the left and right side (tail) of the distribution that gives you together 5% when you go for 95% confidence)

[@ronaldpereira4436]

Thank you so much for your videos, I just have a question on how to calculate the Intercept std Error and T ratio as show in the table Also the Prob> t 0.0259 - how is that calculated - Iknow you said it is taken from the back of the book of the table - which table is that ? as we would need the z stat to be caclulated if we were to look up the normal dist table -how do you calculated the z stat here? Hope to hear back, thanks

[@rossjohnson2220]

thanks very much Mr. As a liberal arts graduate, through your wonderful course, I start to apprecate the power and greatness of statistics.

[@N0rmad]

What does it mean for the slope to have a standard deviation? I don't quite understand that. We have one regression line with one intercept so where is the intercept "deviating" for us to even get a standard deviation?

[@Abha-com]

I also had same doubt. My guess is intercept is calculated from the data we have at hand which is only a sample of a large population. If we take another sample, intercept might change. So slope has a chance of getting many values, that’s why there is standard deviation. Remember central limit theorem analogy. Just my thoughts…

[@MashiroRedo]

Great vid, anyone know where the t .5/2 came from? Looks like the t value in the ANOVA table but wasn’t sure

[@nabajyotidey2832]

Two tail t test

[@Pefico]

Hi. It seemed like this video was not dealt by you. It was less descriptive. The voice was bit strange. Am I wrong?

[@RiteshKumar-lh1xn]

Can you suggest how to find the standard deviation of intercept, intercept being another point estimator. That will be of great help. Thank you.

[@russellkemmit73]

why do we do n-2 ?

[@victorcannestro3878]

n observations of sample data - 2 parameters we're estimating (slope and intercept) = the # of degrees of freedom. It would be just n if we had access to the population data.

[@russellkemmit73]

@@victorcannestro3878 Thanks

[@youcefyahiaoui1465]

Hi Brandon, I am not sure if you're still supporting this material. On the table at minute 8, why is the Sum of Squares the same as the mean Square? Isn't the Mean square at least the sum of the squares divided by n-df? Can someone comment on this if Brandon does not have the time to answer? I will appreciate that. Thank you in advance.

[@xuchuan6401]

divided by df not n-df, and here df = 1

[@chandanrajanna705]

how is the value .0259 obtained

[@christianc8265]

But how do we get the standard error of the intercept?

[@martynasvenckus423]

So the standart error of the estimate is sigma or just s? I am confused with the notation....

[@xuchuan6401]

sigma is the population parameter (the ground-truth), and s is its estimator.

[@MrRollieOllie]

Small error you have t-value of 2.776 which is t-value for 4 degrees of freedom but 97.5% confidence interval not 95% should be 2.132

[@mrraam2151]

No, you are wrong. 2.132 is 90% confidence level but I guess he was talking about 95% CL for which the value 2.776 is correct

[@christianc8265]

And how can I get the Prob > |t| column. Is it correct in R doing "pt(-3.4584,4) * 2" which gives 0.02585547? The "* 2" because it is a two tailed problem and for the negative I am not very sure but I think because _pt_ is growing from the left?

[@xuchuan6401]

you are correct

[@andrev142]

Are you assuming that your population has a normal distribution? Since you're using parametric tests... What happens if it isn't normal?

[@andrev142]

Great lessons by the way!!

[@--ShivaS]

He assumed it based on central limit theorm ig...