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Oh, hey, technology is sort of working today.

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So 1st, what I was doing on.

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Thursday as I was on a review panel, um, for the National Science Foundation for 2 days, we were looking at a pile of proposals and there were.

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8 of us on the panel to NSF program directors, and we were reviewing the proposals.

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It's like 100 pages each over 201 point, and rating each proposal on many different categories and then making a recommendation.

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To NSF, and they may or might not follow our panels recommendation and then maybe 10% to 20% of them would get funded.

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Oh, that's what I was doing. Um, I do it whenever NSF asked me our likes me to do those things, because our likes good relations with the National Science Foundation.

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And it's also a chance to see what good proposals and bad proposals look like. Um.

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I'm being a little vague about which panel I was on because actually, um, my membership on the panel is, um.

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Is a confidential matter, um, the specific panels I'm on and in fact, if you ask NSF.

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You know, who the names of the reviewers were, if you submitted a proposal to ask us to NSF and propose say NSF declined it is they do maybe 80% of the proposals.

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If you ask the NSF who the reviewers were NSF would refuse to tell you.

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Because the names of the reviewers are confidential.

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And the legal way that that happens is that we reviewers are providing Pre decisional advice to NSF.

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Um, they don't have to follow our advice they generally do, but not always.

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For example, they for distributional requirements, they might fund a proposal. That's not at the top of the list.

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Um,

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if it's from a state or a group that doesn't submit many proposals that are proposal from there would be more likely to get funded and the program director would then overrule the panel that say but that's why,

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um,

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if you see in the news,

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for example,

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you'll see about some government advisory group,

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and the names the members of the advisory group are confidential and the government will say,

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refuse to say who they are.

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The reason is that the group.

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They're only providing opinions and advice. They're not.

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You know, they're not making decisions they don't actually do something so.

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And that's where weird legal things happen.

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But, um, I actually, at 1 point spent a couple of years at the National Science Foundation for 20 years ago. So I, I was a program director.

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And, um, so I just made recommendations too, to my boss, but each year I recommended the spending of about 10Million dollars on various proposals. So I also did some liaison with darva defense events. Um.

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Research Projects Agency and we funded some work together. Actually I put some money in the mass petitions and let's not put some money in and Barbara put some money in funded 2 rounds of a joint program. So.

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It's a fun chance to see how dark operated. Okay, so that's your revolving door that you read about people going from the government to private industry and also with NSF half the people at NSF and.

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Are what our so called rotators they're full time day jobs are at a university. Usually sometimes have some sort of other government agency, and they rotate to the National Science Foundation for a couple of years.

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In my case, it was 3, but almost 3 years and then they rotate back to their home.

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To their home institution is a lot in there's a lot of faculty members have spent time with the National Science Foundation.

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Um, and then the other half of vendors that program directors are.

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Are, um, full time and the highest level people at NSF are rotators also for 6 years. 4 years.

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Dark, everyone's a rotator a dark or they're there for 4 years or.

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Maybe Max, 6 years or so and then they go back somewhere else.

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In darkest case, it could be a university it could be a private company. It could be a military agency or something. So but.

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Everyone at Starbucks does so the, and the support staff, they don't work for darker. They work for some.

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Um, consulting company who has a actually has their building next across the street from dark. So the staff, the assistants are not darker employees. There'll be dark employees and professional people. So.

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But, um, so it spreads the expertise around the country. Um.

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So, I used to joke, in fact, because the darker headquarters at that time was what is going on here just 3rd, this.

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And keep stopping, um.

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The 2nd here, um.

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Okay, so with luck, maybe this is broadcasting. Um.

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As long as I'm not typing a 2nd, so dark I used to joke because the, um.

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The bill is the headquarters is on a public street.

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And just set in, you know, 100 feet or so. So if whoever was a car bomb or something, it wouldn't be that bad because have everyone, there's a rotator and half the people there on travel. So, in the real work done by the community. So.

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Okay, so what is happening here today?

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Okay, so, 1st, the homework 11, the date was wrong. We're setting it to Thursday, which is.

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3 days, um, and well, we'll have it will allow them to be submitted late, but.

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The thing is, I'm not allowed to have due dates that are in, um.

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In the reading period, it's already 1 day and but we'll ignore that.

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And when homework 11 gets great and I'll calculate your guaranteed grade if you don't write the final exam.

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So, from the syllabus, the 3 exams, their equal weights, the top 2 will be used the 3rd will be dropped and for the homeworks, the lowest homework will be dropped.

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And I'll calculate that I'll calculate the letter grade that you will get. If you do not write the final.

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If you do write the final, it cannot lower your grade it might raise your grades.

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Um, particularly some people, for example, who, um, skip the 2nd exam.

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They will very much be helped by writing the 3rd exam and getting a grade in it. So, um.

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The final exam is the date time mentioned, um, turn down here somewhere.

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There they mentioned in on the registrar's page, it'll be in, it'll be in that room.

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Using grade school, just like we did before.

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You know, bring some blank work paper. If you want, um.

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Do you want to bring a calculator? Go ahead. I guess we've tried to write questions and it won't help you. You can bring 3 crib sheets.

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For the 3rd exam, so presumably your 1st, 2 sheets and 1 more.

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Um, there will be no statistics on the exam, because we haven't had homework on that yet. So so it'll be up to the end of chapter 7.

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um, the ta's will have several, um, office hours before the exam. We'll try to have an office hour every day before the exam will announce them.

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Um, there was no final examine this course last year, cause was shut down because our computers got back.

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Um, our refused to offer any specifics, except it's supposed to have been some administrative person who screwed up.

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Um, I continued going okay mostly because I oh, I do my email outside, you know, my preferred emails outside our API.

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And I've had a private account with for 20 years now. So, I mean, and I, and the master copy of my websites is on my own machine. When I push.

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I push copies out to the RPI web servers and everything, so I just.

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1st, a new copy out to another, you know, web server off our I was doing okay, but we still canceled the exam last year.

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However, um, uh, sorry for that 1. um, I'll fix that.

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I didn't re, read it. Okay. I'll fix the link so you'll have a, um, link from, um.

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So so you'll have a link to see the 2 years ago understanding that.

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Topics changed slightly, perhaps, um, the 1 more point for after the course before I get to some material.

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Um, so we got a professional relationship.

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Um, and about last you leave.

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Then, um, you're welcome to discuss any legal and ethical topic with me. Um, just, you know.

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And I encourage you to get your own, um, non email. I.

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Put my on non email after, um, on all of my signature files.

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And I may retire at some point, but so you'll have an archive email to get hold of me.

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And some parting thing also, uh, Eco outside.

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The windows have these pictures of famous alumni is they were once measurable undergrads at some point. Okay, they did it. Okay. So you might be asking yourself after you leave.

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Could you do something that might end up result in your picture being up on a window there? So, I'll just think about it.

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Make some difference in the world when you graduate.

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Okay, back to direct material talking about statistics. Um.

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So, I, I, I'll review some videos to look at on your own on Thursday if you want it and just, um.

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My take on some of them just for a few minutes and.

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So T, test is I mentioned a little before, but.

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It's worth say, okay, I'm going to take the keyboard off.

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The disadvantage it means, of course, the camera is not pointing at me. It's pointing up at the ceiling, but the advantage is the iPad flat on the counter. I can actually write on it semi allegedly. So the T test is.

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You've got to in her mind, you've got 2 populations.

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And you're plotting thing, so you've got red and blue let's say so.

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Um, you got red dots here.

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Read observations and then you've got blue observations.

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Okay, something like that, if you can see the caller differences. So basically, so are, you know.

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Means different or whatever. I mentioned a little a weekoh.

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Some standard deviation variances or whatever so.

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And, um, and we construct, I keep mentioning this every time, but I construct and all hypothesis is, I'm saying this again and again, because it's important.

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Means the same.

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Okay, and then the alternative hypothesis.

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Is the different now you might get particular about how they're different. Um.

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Particular about how they're different.

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A blue is greater than red.

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Here it looks. Okay, so then the question, the big question is.

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If there's no difference how likely is what you saw.

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Okay, and here the blues look a little higher than the reds, the law bottom to our reds and so okay.

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And that's the T test. Okay. So the little video on that, um.

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And we saw different versions, and I mentioned quickly, uh, a week ago. Um.

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Then the next video is something called.

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And now called analysis analysis.

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I give an example, I take example, I made up here. You can take this example and map at the current events. If you want by changing the names. Um.

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We have the population of people, and some people they're infected with looking for.

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And the symptoms of looking for is that on full moons, they turn into a firewall so the hair gets longer.

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And let's say we test if they are.

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Suffering from the control by making the length of their hair. So if the hair gets longer in a full moon, then we say the suffering from the control let's say here are longer whatever.

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pete's get longer. I don't know. Um, okay.

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So so there's various possible here, is that we're, we're investigating curious. We're looking for LP. Um, well, 1st, we do nothing. That's a control group. 2nd. We may give the people aspirin.

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3rd we may have the people who are across 4th. We may, um, try lots of sunlight during the day time. Um, we might bring in Dracula. I'd have Dracula bite to people, um.

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Or whatever,

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and so we have maybe 5 different groups of people control groups people with crosses people with aspirin people treated with sunlight people being bit by Dracula and we measure the length of their hair and their teeth at the next full

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moon.

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And, and we, um, see, um, and each, each population of these 5, sub populations, you know, we've got a, we've got a distribution for airlines and 2 flights.

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Um, and we're looking at this and.

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We're trying to decide, do we see a difference? Um, so.

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And so I'm giving you the executive summary so the analytic things they look at all these different things and say, are we seeing something.

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Um, happening, I mean, the thing is, this you're going to get some variants anyway. Okay the people will have their hair grow at different lengths in a full moon. Anyway. Maybe.

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Uh, but you're looking to see if there's some, if these different populations look different so it's a, it's a, it's related to the T test, but, um, it looks at several populations and this is very popular with social scientists.

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They they don't know any mathematics. They just plug it into 1 of your take your favorite statistics package and does calculate it. I'm so, I'm giving you the executive summary of this now. Real World looking. Trophy is a fictional disease, but let me throw real world numbers.

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At you.

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I mentioned these little before, but there are enough money that it's worth looking at again. Um.

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Look at the worldwide pharmaceutical industry, the drug business they every year grows 1Trillion dollars.

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Half of which is in the United States. So 502Billion dollars of drugs are bought in the United States each year.

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Which is 1500 dollars per person on the average legal drug. Okay this is all legal stuff I'm not talking marijuana. Okay. Or cocaine, or anything the league might be bigger goal.

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I don't know the legal pharmaceutical industry United States is 1 half a 1Trillion dollars. 500Billion dollars 1500 bucks a person.

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Um,

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and so they want to develop new drugs because,

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you know,

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the drugs,

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um,

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they start off,

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they're on patent and they're very expensive,

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but then,

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as they go off Pat,

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and they become very cheap.

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And then the revenues of the company falls, so they're developing new drugs. Um.

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Developing 1, new successful drug cost a few 1Billion dollars when you work in the cost of the failures because most of the attempts are failures. Um, so so bringing a successful drug to market is.

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The number is very, but maybe 2Billion dollars or 25Billion dollars or something, which sounds like a lot of money, but remember the grossing a 1,000,000,000,000.

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Okay, so what new drug is, um, you know, whatever, a 3rd of 1% of the annual growth so you can afford you the number. Okay.

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So, now, what does it take to bring the new drug to market is DC United States you have to prove that it works to the satisfaction of the FDA.

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So, that involves clinical trials and statistical tests and so on. So, this is where the statistical test.

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Come in, and, you know, they're published and they'll say they tested a 100 patients.

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And again, um, so, you know, for again, you can work it into the news. Um, you need to read the DOS, um, you got diseases that people have and you got.

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Things that are claiming to be curious and things that are officially.

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You know, their official.

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You know, bless this official things that will help. And how, how do they do they did the statistical tests and they found out that some people were hurt by the.

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New drug, and some people were helped and and the drug company statisticians convinced the FDA that, um, the drug.

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On on the balance was good and therefore the FDA approves it.

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And then that's how the system works and well, 1st, that it's better and 2nd, that it.

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Doesn't have really bad side effects. Um, let me so.

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I mean, the poster child for the regulation that you mentioned before is.

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Several decades ago, there was a drug called that helped with morning sickness for pregnant women, I think, and.

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I basically every country in the world, but the United States.

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Approved it for use, cause it did help this morning sickness. Um.

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The problem is that it also met the poor baby when it was foreign, had no arms or legs cut off about they lost the last fit.

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Not not in the United States, cause United States had never legalized that, um, any case. So, back to statistics, this is the real world application where there's a lot where statistics is very important.

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So, okay, so, um.

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And these, you know, you read the medical, they published, they'll say they did this test and, um.

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The drug, if he doesn't talk about type 1 type 2 errors, it's slightly different way of doing the analysis but.

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You know, they do it. Um, 1, big thing for making these stats valid is they have to say what they're measuring before they measure it. Um, let me forward. So, what you must do for these for these, like, these.

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Drug trials, et cetera um, you know, fine.

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But they'll be measured and, um.

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And what success will be, um, before the test. Okay.

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Before the Trump before the trial, so let's say.

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What is very bad is what's called data?

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And data is, you you look at the results.

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To find, you know, to find whatever interesting.

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Interesting things. Um, but very what's very bad is you do your experiments, you do your trials, and you look at the results and see if there's any interesting stuff you can see in the results.

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And that's bad, because you see coincidences and stuff. What you have to do is to find the experiment for the trial. What, what you define in advance what the measure of success will be. And then you run the trial.

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And then, did the trial meet that measure of success that you defined in advance?

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And that's the key um, yeah, before the trials. So.

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Key to making things solid because the companies are going to push things and, um, you know yeah, yeah. Then you have to have rules here. You also want to have the rules defined in advance because so very much money is involved.

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If there's any ambiguity then, um.

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Everyone gets, you know, there's lawsuits flying everywhere. Okay so that's that's where things, analysis of variance T, tests and stuff like that. Come in.

189
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And so, you know, the underlying mass is available if you want to look at that, but I gave you the executive summary. So.

190
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Questions okay um, next thing I had a film on was linear regression.

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So, again, you see, the whole thing was the test X is, um, so the whole thing, but statistics let's talk about.

192
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Is you know, we want to find parameters.

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Brian parameters test hypotheses.

194
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And find relations, and so on find relations. Okay. Um, between stuff.

195
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You know, and the goal is to say to predict predict the future.

196
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Better so, um, stock market fell by 3% last Friday. I mean, I haven't even looked at my phone today. I've been working all day, but.

197
00:24:31.618 --> 00:24:35.308
You know, what's it doing today? Um.

198
00:24:46.888 --> 00:24:57.568
Trying to figure out, uh, I can't even read my chart.

199
00:25:00.538 --> 00:25:06.959
I think I may have gone up today or something. Um, it'll but still below a few days ago. So you want.

200
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To do predictions and 1 way.

201
00:25:10.288 --> 00:25:14.729
Is a linear regression that you look at? Um.

202
00:25:16.588 --> 00:25:20.608
Um, no, let, let me use the stock market say.

203
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Saturday, 4 or 500, it's an average of, um, a weighted average of the approximately the top 500 stocks and 5 hundred's only in approximation. It could be 499 or something.

204
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Um, and they're weighted by the value of the stock outstanding, which is another question. That's not well defined, so we might look at something like, um, here, our old values for.

205
00:25:49.288 --> 00:25:59.368
You know, maybe this doesn't mean maybe this hypothetically is this is Friday, Thursday, Wednesday, Tuesday, Monday and so we'd want to say.

206
00:26:02.009 --> 00:26:05.729
Um, whatever.

207
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What's going to happen here? See it.

208
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In the new regression means say you fit a line.

209
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If it aligned to the data and then maybe extrapolate it. Okay.

210
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And here, I'll do a year, I'll throw some math at you. Um, just for fun. I can't just be, you know, we got to have a little quantitative stuff.

211
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And so what we have is say these are points X and Y.

212
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And we want to fit a line Y, equals X. plus B, let's say.

213
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I'll do it on the next page here. I'll rewrite this so we got the data.

214
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That's why I.

215
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Be, and I gave you the example, say, for exam 2, where we had these were the ads I gave you the actual part of data from exam. 2 x access was.

216
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Time to finish the exam and Y axis was great.

217
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Okay, so, um, so the way what we do here is we want to, you know, we want to, um, find.

218
00:27:19.528 --> 00:27:24.568
A, and B, to minimize error.

219
00:27:26.308 --> 00:27:32.788
And, uh, okay now error. Okay, basically, you know how to define the error.

220
00:27:32.788 --> 00:27:41.128
And what they, what we do often is we'll have the vertical distance here, and we want to minimize it. Um.

221
00:27:41.128 --> 00:27:45.509
So, we defined equals, say.

222
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Plus B, I minus Y, I. or something and squared.

223
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So this is the actual value and this is the computer.

224
00:28:00.838 --> 00:28:04.828
You know, from the line from the line. Okay.

225
00:28:04.828 --> 00:28:09.358
So, we take the difference between the computed number from our.

226
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Progression line, and it would take the different set from the actual Y, and we square it. Now. Why do we square it? Um.

227
00:28:17.459 --> 00:28:22.199
The real reason I think is because the mass is easier to do.

228
00:28:22.523 --> 00:28:35.153
And, um, what it does is that, um, means that big errors that are treated more seriously than small errors. Cause his error is twice as big as 4 times the weight, because it's a squared here.

229
00:28:35.993 --> 00:28:44.453
So, in any case, this is what's conventional to minimize the sum of the square there so we want to do we want to minimize the sum of all the, um.

230
00:28:44.759 --> 00:28:51.959
Some of all the squared errors sets, minimize some of all the, um.

231
00:28:54.118 --> 00:28:58.378
8 times plus B minus Y. Y.

232
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Squared so we wanted we wanted to pick a and B to minimize this that.

233
00:29:05.159 --> 00:29:12.328
Minimize that. Okay. So how do we do that? Um.

234
00:29:12.328 --> 00:29:16.199
And be a variable and the X, and the whys are all fixed.

235
00:29:16.199 --> 00:29:20.249
Well, um, so they've called out our big error equals E. um.

236
00:29:22.409 --> 00:29:26.969
Well, equals, um.

237
00:29:29.729 --> 00:29:34.229
And, you know, the sum of all the, um, okay.

238
00:29:37.588 --> 00:29:40.648
Oh, I can expand the square. Okay. Um.

239
00:29:40.648 --> 00:29:44.189
So E, is the, um.

240
00:29:44.189 --> 00:29:47.398
Hey, squared to sum of all squared.

241
00:29:47.398 --> 00:29:51.778
Plus, um, and be squared.

242
00:29:51.778 --> 00:29:54.898
Plus the sum of all the Y, I squared.

243
00:29:55.949 --> 00:30:00.959
Plus, to a B, to some of.

244
00:30:02.578 --> 00:30:08.909
Minus to a sum of all the Y, I.

245
00:30:10.618 --> 00:30:16.288
Um, plus, um.

246
00:30:16.288 --> 00:30:19.558
Who, and some of all the.

247
00:30:19.558 --> 00:30:25.499
On 23456.

248
00:30:25.499 --> 00:30:35.009
Okay, um, okay, now here, um, some of those things are.

249
00:30:36.989 --> 00:30:45.209
Constant and so, okay, so now some of all the why I squared. Okay. So, now what we need to do is, um.

250
00:30:45.209 --> 00:30:51.538
Actually, if I got this, right?

251
00:30:59.878 --> 00:31:03.328
So, now we want to find a, and be the minimize that.

252
00:31:04.648 --> 00:31:10.078
Well, I can take the E over D. a derivative.

253
00:31:11.278 --> 00:31:14.308
To a, some of all the squared.

254
00:31:17.278 --> 00:31:23.219
Plus, to be some of all the .

255
00:31:23.219 --> 00:31:28.288
The X, Y, and that's it.

256
00:31:28.288 --> 00:31:33.778
Okay, and you want to set it equal to 0. okay. It goes 0 at the men.

257
00:31:36.749 --> 00:31:39.898
Okay, so basically what we have.

258
00:31:42.509 --> 00:31:48.538
Is a X squared plus B, some of all the.

259
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Minus some of was 0.

260
00:31:54.328 --> 00:31:59.038
Okay, and that is, um, 20 equation.

261
00:31:59.038 --> 00:32:06.239
And now we can also take the E. R. D. B.

262
00:32:06.239 --> 00:32:15.058
And that is, um, 2 and B.

263
00:32:17.429 --> 00:32:24.209
+2 a 2.

264
00:32:26.098 --> 00:32:32.818
But, um, go ahead and some of.

265
00:32:35.729 --> 00:32:41.489
0, um, and so what we get is, um.

266
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And B.

267
00:32:50.159 --> 00:33:01.348
Hey, sorry, this should be in capital in flux end. Some of the only was there or something, and then we can solve and then we can solve.

268
00:33:02.969 --> 00:33:08.038
For a, and B, and this is how we can do linear regression.

269
00:33:08.038 --> 00:33:16.798
Um, I might have gotten some something wrong. You get the idea, and you can solve for a B and then you can also compute.

270
00:33:19.169 --> 00:33:23.098
Okay, yeah. Okay.

271
00:33:23.098 --> 00:33:29.578
Basically, in your aggression, um, now.

272
00:33:31.378 --> 00:33:35.249
That's the basic thing now it can start getting interesting.

273
00:33:35.249 --> 00:33:39.028
Um, because next is, um.

274
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Up here next, you can get things such as.

275
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Multi linear regression and, um.

276
00:33:54.028 --> 00:34:06.719
So you've got several in dev, so what you want is some, your output why? I will say +, plus a 3 X3+some error term.

277
00:34:08.369 --> 00:34:15.659
All right, but lots of eyes in here. So you've got several independent variables. Um.

278
00:34:15.659 --> 00:34:21.179
And I use an example here, um, let's propose was trying to predict.

279
00:34:21.179 --> 00:34:26.728
Freshman CPAs that's the dependent variable GPA.

280
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And then what our might be using to try to predict this, um, they might look at your high school grade, your high school class rank, which are 2 different things.

281
00:34:39.143 --> 00:34:43.793
Um, the number of AP courses you had the, are you in a fraternity.

282
00:34:44.128 --> 00:34:56.039
That just be is there a 1 variable? Are you an athlete? Is there a 1 variable on, um, the home state? You're from how far maybe how far you travel to come to our, maybe your height, your weight.

283
00:34:56.039 --> 00:35:03.599
So, I got the example here, I've got 8 different, possible, independent variables. And then the dependent variable is, you GPA this year.

284
00:35:03.599 --> 00:35:08.068
And then, so we'd want to do the regression.

285
00:35:08.068 --> 00:35:14.009
And we'd get the 8 coefficient of how much each 1 of these affected your GPA.

286
00:35:14.009 --> 00:35:22.619
And then we'd get the error, which is how, you know, how well, those 8 of them do and that. So.

287
00:35:23.034 --> 00:35:36.503
And you could do the formula, just you find error, you know, the unknowns are the coefficients and then the error and then you just go and you do the derivative and optimize it.

288
00:35:36.893 --> 00:35:39.923
Well, that's how you get to derive the formula then to use.

289
00:35:40.918 --> 00:35:46.739
I'm sorry um, okay.

290
00:35:48.539 --> 00:35:53.849
Do share screen.

291
00:35:59.969 --> 00:36:01.164
It's being recorded,

292
00:36:01.164 --> 00:36:02.364
it's being shared,

293
00:36:06.474 --> 00:36:08.304
so here's the probability question,

294
00:36:08.304 --> 00:36:13.164
but just to be random variable the time until the screen sharing crashes again,

295
00:36:13.164 --> 00:36:15.414
it's crashed twice so far in 30 minutes.

296
00:36:17.034 --> 00:36:31.733
So this is a random variable. Do you think it's exponentially distributed or what you know so, what we could do is we could record the time until the, um, Webex screen sharing crashes again. And we get a number of data points for the class.

297
00:36:32.213 --> 00:36:39.114
And then we could say, do they look like they're exponential or what that's testing a fit for distribution?

298
00:36:40.108 --> 00:36:51.449
Okay, so, in any case, I'm giving you a high level description of multi, linear regression. We've got a number of independent variables and we want to find coefficients to predict.

299
00:36:51.449 --> 00:36:54.628
Say your GPA at Christmas or something.

300
00:36:54.628 --> 00:37:01.228
Um, the next thing is to go step wise.

301
00:37:03.389 --> 00:37:09.628
That's wise progression and we want to.

302
00:37:09.628 --> 00:37:16.619
Pick the most important independent variables.

303
00:37:22.648 --> 00:37:29.398
And add them to the mix 1 by 1 by 1 by 1.

304
00:37:31.018 --> 00:37:37.528
And so what you might do is you might say, you say correlation coefficient.

305
00:37:46.378 --> 00:37:51.449
So, what you do is, um, say that's called role typically. So we compute.

306
00:37:53.699 --> 00:37:58.318
Row for each independent variable separately.

307
00:38:02.969 --> 00:38:13.289
And the dependent variable, and we pick the variable.

308
00:38:15.750 --> 00:38:20.940
What's the biggest absolute value per row?

309
00:38:20.940 --> 00:38:25.619
Okay, and then we can do that and then what we can do.

310
00:38:25.619 --> 00:38:31.530
Is we can then, um, compute the residual.

311
00:38:37.079 --> 00:38:42.210
Um, so the residual errors, let's say.

312
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And add the new, most important variable.

313
00:38:55.619 --> 00:38:59.280
And this will be a step wise, multi, linear regression. Um.

314
00:39:01.079 --> 00:39:05.400
So, at each step, you, um, you have a new, um.

315
00:39:06.480 --> 00:39:17.610
Dependent variable, it's the errors and you'll find the most important independent variables you haven't yet used and you add it in your compute errors and re, computer new regression.

316
00:39:17.610 --> 00:39:24.179
And as you add more and more independent variables, if it gets better and better.

317
00:39:24.179 --> 00:39:28.260
You hope so um.

318
00:39:30.869 --> 00:39:37.440
So, that's, um, let's say, um, you know, that's used a lot social sciences and so on, um.

319
00:39:39.210 --> 00:39:46.380
Now, funny things can happen because independent variables might be strongly correlated with each other.

320
00:39:46.380 --> 00:39:58.289
See, you might have 2 independent variables, and they both have very strong correlations with a dependent, but they're also strongly correlated with each other. So you don't need both of them. You only need 1 let me give an example here.

321
00:39:58.289 --> 00:40:02.039
So, I'm trying to predict your say your 1st.

322
00:40:02.039 --> 00:40:08.219
Semesters GPA RPI and maybe a high school grades a strong predictor.

323
00:40:08.219 --> 00:40:15.809
And maybe your high school ranks a strong predictor, but you're great in your rank are correlated with each other strong is you don't need both of them.

324
00:40:15.809 --> 00:40:19.380
That sort of thing, so weird things can happen. So.

325
00:40:20.969 --> 00:40:27.179
And another thing is that if you bring in enough independent variables, you can explain anything and it doesn't mean anything. So.

326
00:40:28.650 --> 00:40:32.190
And you may have nonlinear relationships so, um.

327
00:40:33.719 --> 00:40:37.860
You see that with statistics about health and so on that, um.

328
00:40:40.704 --> 00:40:53.635
Well, an example, silly example would be if you, um, eat fewer calories, you will live longer. And that's actually the really the only really proven way to live longer is even fewer calories.

329
00:40:53.635 --> 00:40:59.094
But if you 2 few calories, you die starvation. So there's a nonlinear relationship there.

330
00:41:00.000 --> 00:41:09.960
Okay, so that's examples of linear regression to motivate where it fits in the universe.

331
00:41:11.550 --> 00:41:18.510
And if there's a non linear effect, then you add to square some variable is a new independent variable when you fit on that. 1.

332
00:41:18.510 --> 00:41:28.260
Okay, now there's other ways to have errors in just the square of the difference you're going to have some value of the difference and so on.

333
00:41:28.260 --> 00:41:33.960
And people might argue, 1 is better than the other, but all those other ones are very difficult mathematically.

334
00:41:33.960 --> 00:41:48.804
Where there's a number of tests that you see that statisticians people tend to use and if you ask why they use these tests and not some other

335
00:41:48.804 --> 00:41:49.434
tests,

336
00:41:50.034 --> 00:41:52.315
the honest answer is back when they were developed,

337
00:41:52.315 --> 00:41:55.375
they're actually easier to work with before computers.

338
00:41:55.585 --> 00:41:55.914
So.

339
00:41:56.280 --> 00:41:59.730
But the books don't necessarily say that the real reason.

340
00:42:00.809 --> 00:42:05.789
Okay um, so.

341
00:42:14.909 --> 00:42:19.860
A non parametric stats have a couple of different definitions, but maybe.

342
00:42:19.860 --> 00:42:29.699
1 is don't assume anything about the distribution let's say.

343
00:42:34.559 --> 00:42:47.159
Um, so maybe the distribution of the underlying things is not, um, or you don't know. So these tests, they're, they're much more robust.

344
00:42:50.519 --> 00:42:56.639
But they're weaker, um, which makes common sense.

345
00:42:57.719 --> 00:43:04.860
So, um, so maybe we're testing, um, we're looking at some numbers and.

346
00:43:07.260 --> 00:43:13.289
Let me, um, that's my.

347
00:43:18.449 --> 00:43:25.769
I got some blue things here and let's say, I don't know, and we got some red things. Um.

348
00:43:32.610 --> 00:43:43.920
Something like that perhaps um, okay 12345 blue 12345 red. Okay. So now the question is.

349
00:43:47.039 --> 00:43:54.869
Um, either read observation, smaller.

350
00:43:58.469 --> 00:44:05.699
Or well, does the red population have a smaller mean? So.

351
00:44:18.900 --> 00:44:24.389
This is a parametric method would be to a T test, so we're not gonna use that. We're going to use.

352
00:44:27.150 --> 00:44:32.579
Use only their order.

353
00:44:32.579 --> 00:44:38.880
Okay, and what we're going to do.

354
00:44:40.619 --> 00:44:47.969
They're going to count the number of times sort of a red number is less than a blue number.

355
00:44:50.760 --> 00:44:57.630
Okay, and here the 1st, red is, um, less than all 5 flu numbers.

356
00:44:57.630 --> 00:45:06.179
Probably you statistic the 2nd, red is less than all 5 blue numbers. The 3rd rate is less than 4 of them.

357
00:45:06.179 --> 00:45:11.969
The 4th thread is less than 3 and the 5th rate is less than 3.

358
00:45:11.969 --> 00:45:17.670
And we're going to get 1014 and 6, which is 20.

359
00:45:17.670 --> 00:45:22.440
And this is called a use that this is called a.

360
00:45:22.440 --> 00:45:31.050
This is a man Whitney. You statistic.

361
00:45:32.429 --> 00:45:44.670
And the thing is that if the red of the blue populations are the same and is reasonably big, then you is actually normally distributed. And, um.

362
00:45:49.199 --> 00:45:53.219
And actually it's an old hypothesis.

363
00:45:53.219 --> 00:46:03.030
Then, you mean as, like, event squared over 200 is 5 here will be 12.5 and use and then the, um.

364
00:46:03.030 --> 00:46:07.679
Then the variants for you.

365
00:46:09.030 --> 00:46:13.289
Okay, um, I don't actually mind if you make a.

366
00:46:13.289 --> 00:46:16.980
A betting pool among yourselves to, um.

367
00:46:16.980 --> 00:46:20.849
As to when this will happen again, so it's okay by me.

368
00:46:20.849 --> 00:46:29.610
I want 10%. Um, okay.

369
00:46:34.199 --> 00:46:37.230
So this used it, so I count the number of times.

370
00:46:37.230 --> 00:46:42.750
A red observation is less than a blue 1. I do for all the N squared tears.

371
00:46:43.105 --> 00:46:54.594
And, um, so there's, um, that's 25 pairs, and I count the number of times right assess the boy if it's all random, it'll be 12 and a half times. Actually, it was 20 times.

372
00:46:54.594 --> 00:47:01.644
And the variance on you, if it's random is 25 times 11 divided by 12.

373
00:47:04.110 --> 00:47:07.800
Which is about 23 or something.

374
00:47:07.800 --> 00:47:11.039
So, the Sigma is say.

375
00:47:12.750 --> 00:47:19.110
4.8 or whatever, and so, in other words, so I observed 20.

376
00:47:19.110 --> 00:47:25.170
Um, that the red is less from blue, 20 times so, which is way more than a Sigma.

377
00:47:25.170 --> 00:47:31.739
So, um, okay, so this suggests that this, this.

378
00:47:31.739 --> 00:47:45.030
So, the non hypothesis, the red and blue means are the same.

379
00:47:51.300 --> 00:47:59.610
You know, this is something like, um, you know, that's, you know, let's give or take, um.

380
00:48:00.840 --> 00:48:09.869
1.5, um, you know, as as a normal variable as a normal variable or something.

381
00:48:09.869 --> 00:48:16.320
So, it could happen, but it's very unlikely. So, and also my 5 here, quite small.

382
00:48:16.320 --> 00:48:22.289
That's it. So, yeah, I, I took the shortcuts here.

383
00:48:25.079 --> 00:48:39.744
This is unlikely. Okay. So what I showed you was what's called a non parametric way it was a quick way. I2 populations, red and blue that maybe had different means. Maybe not.

384
00:48:39.744 --> 00:48:41.605
My all hypothesis is the same mean.

385
00:48:42.570 --> 00:48:49.469
And, yeah, I did not use a T test because that would assume that the populations that are normal.

386
00:48:49.469 --> 00:48:56.730
Um, this is this code called a, or it's called a W, wilcoxen write some test or Amanda Whitney you test.

387
00:48:56.730 --> 00:49:03.809
And I sort the observations, red and blues together, and I count the number of times I read is less than a blue.

388
00:49:03.809 --> 00:49:15.210
All in squared pair so, if the underlying population is, in fact, normal, this is a weak test. It will.

389
00:49:15.210 --> 00:49:23.250
It will not rejected all hypothesis at times and all that process ought to be rejected perhaps. But if the distribution is really weird.

390
00:49:23.250 --> 00:49:30.000
Then, um, then this will be more robust, so.

391
00:49:31.139 --> 00:49:34.500
And there's a lot of different tests like that. So.

392
00:49:37.139 --> 00:49:40.590
And finally, oh, not finally.

393
00:49:40.590 --> 00:49:46.170
Well, okay, the current thought thing was statistics is, of course, machine learning.

394
00:49:46.170 --> 00:49:50.610
So, um, let me put this the.

395
00:49:59.010 --> 00:50:03.869
This is your current hot application? This is the current.

396
00:50:05.849 --> 00:50:10.349
Big application of statistics. Okay.

397
00:50:12.300 --> 00:50:20.489
So, um, you know, so I drive a Tesla and, um.

398
00:50:20.489 --> 00:50:27.539
So tests, you know, they want to have full self driving, which I think, basically is a fraud at the moment, but it's getting there.

399
00:50:27.539 --> 00:50:36.239
So, you know, it tries to recognize objects, recognize speed, limit, signs, and lines on the road and bicyclists and whatever.

400
00:50:36.239 --> 00:50:41.190
And so it's using statistics of the videos.

401
00:50:41.190 --> 00:50:50.369
So, it's computer and using massive amounts of compute power server farm. So that's the big application that's whole courses on its own. But that's the current thought.

402
00:50:50.369 --> 00:50:54.210
Topic for statistics machine learning, so.

403
00:50:54.210 --> 00:50:58.349
So, I won't go into that much more detail, but.

404
00:50:58.349 --> 00:51:05.309
Then the next fun thing is, of course, since we're learning statistics that we got to do is see how the lie with statistics.

405
00:51:06.690 --> 00:51:21.449
Um, and there's various books on it and so on. So, this one's for other old, but it's a famous 1, um, 1617 years old but, um.

406
00:51:21.449 --> 00:51:26.730
So, you can have fun looking at these, how to mangle things and, um.

407
00:51:29.940 --> 00:51:33.750
All your jokes about by standardized and statistics, so.

408
00:51:35.639 --> 00:51:38.005
Bring in Mark Twain, stuff like that.

409
00:51:50.815 --> 00:51:54.114
Don't for sale. This wasn't new addition. So you can have fun.

410
00:51:55.440 --> 00:52:09.329
Oh, okay. So that's a good point to stop. What I was doing today is re, giving us some new ideas and statistics talking about the videos that I recommended for Thursday. So.

411
00:52:09.329 --> 00:52:15.480
We saw things like, well, just a quick thing, but analysis of various, what it is very, in a few words.

412
00:52:15.480 --> 00:52:18.750
Progression, um, linear regression.

413
00:52:18.750 --> 00:52:26.699
We're trying to we have a dependent variable. It's a function of independent variable, trying to fit a straight line and then see how good the fit is.

414
00:52:27.264 --> 00:52:39.775
Um, because it's a fit that's expressed by the correlation coefficient the square of that is how much was a variance you explain lots of independent variables for multiple regression and we can do a step wise thing.

415
00:52:40.255 --> 00:52:44.454
We got lots of possible that are independent variables. You don't know which ones are important. We.

416
00:52:45.000 --> 00:52:51.480
We do the correlation coefficient to them with the dependent on we bring them in 1 by 1 and read compute after every step.

417
00:52:51.480 --> 00:53:05.309
By the way I had a hobby project, I think when I was in grad school with a friend of mine with my roommate, when we're at Harvard, we were doing animal performance statistics with reference to something down. So it was a thoroughbred race. Course. So.

418
00:53:05.309 --> 00:53:11.250
What we did was we bought we advertised and bought 6 foot high stack of racing forms.

419
00:53:11.250 --> 00:53:15.780
And we typed in by hand on computer punch cards.

420
00:53:15.780 --> 00:53:19.440
2000 cards worth the statistics for horses.

421
00:53:19.440 --> 00:53:23.460
Um, we're trying to predict what horses would win and the.

422
00:53:23.460 --> 00:53:27.780
The independent that was the dependent on the independent variable was how many times the horse and.

423
00:53:27.780 --> 00:53:35.429
1, in the past, how many dollars that had won it? Speed how fast it was raised in the past installer and we tried to do, um.

424
00:53:35.875 --> 00:53:48.804
So, we tried to do that and compute that then we wrote, like, 4 trend programs and computed that I was interested in the mathematics of it, but my roommate was interested in the horses themselves and so he went to the track a lot.

425
00:53:49.074 --> 00:53:55.344
He was getting a PhD I was getting a PhD in applied math, computer science. He was getting a PhD in psychology.

426
00:53:55.800 --> 00:53:59.039
And he spent like, 4 years on the program and then.

427
00:53:59.039 --> 00:54:02.639
I don't know, he decided he didn't like the topic any more.

428
00:54:02.639 --> 00:54:06.599
He likes statistics and stuff, so he dropped out of the, um.

429
00:54:06.599 --> 00:54:14.400
Infants like PhD after he's done all the experiments on infants and seeing how they interacted with each other.

430
00:54:14.400 --> 00:54:18.539
And then he went into.

431
00:54:18.539 --> 00:54:25.079
Law school got a law degree, then work to choose from Canada where, if you enter your securities commission.

432
00:54:25.079 --> 00:54:34.829
Doing regulating on companies and then doing stuff like that, making much more money than it was made. If he got his PhD and insights. Of course.

433
00:54:34.829 --> 00:54:39.480
But any case that's, um, doing multiple stepwise, linear regression. So.

434
00:54:40.559 --> 00:54:48.510
There used to be a couple of people at there was an associate dean of an engineering called Paul and the chairman of math. Um.

435
00:54:48.510 --> 00:54:54.179
Used to go up to, um, Saratoga in the summer. In fact, they did. Okay.

436
00:54:54.179 --> 00:55:03.210
We're mathematics, but actually make you some money. Okay, so that's a reasonable point to stop again to remind you, um.

437
00:55:03.210 --> 00:55:07.530
After your homework 11 is done and then.

438
00:55:07.530 --> 00:55:12.239
Made it to Thursday, because that's already 1 day later then we can officially make.

439
00:55:12.239 --> 00:55:18.210
And I'll compute and it gets great. It'll take the ta's 2 days to grade it because it's not just multiple choice. Um.

440
00:55:18.210 --> 00:55:24.420
Then I'll compute a guaranteed minimum grade for you that you'll get. If you don't write the final.

441
00:55:24.420 --> 00:55:32.880
You do write, it can only help and then we'll have a QA office hour every day before the final.

442
00:55:32.880 --> 00:55:40.079
And good luck and and then after the course, again, I'm open to questions and stuff.

443
00:55:41.369 --> 00:55:45.150
So have fun and hope your semester finishes off. Oh, okay.

444
00:55:55.769 --> 00:55:58.889
Doing 1 person. Okay.