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Hello.

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So in all of a previous version, we have learned some basics of nutrition.

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Yeah.

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What exactly is the allegation and what is it?

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You know, what is up mathematically utian of this linear regression we have learned?

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Yeah.

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This Y equals to see it is nothing, but it is just a mathematical representation of a regression.

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But we have this use case as well in which I have to predict what can with a bit of apples and if if

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the person has that much higher.

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So basically we are going to learn the basics of probability behind some slope concept behind this regression

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as well.

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So we have learned this is exactly the thing.

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But this my slope.

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And we have also learned, yeah, that's a basically a slope how you can complete within two points

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and what the slope at a particular point then we have also learned.

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Yeah.

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What if what if basically according to you is accurate one data points we can have multiple regression.

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So which line is exactly my best line that we have learned.

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Yeah.

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Whosoever has at least masc whosever line has at least MSE then that line gets selected as best foodline

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not a caution or what he had arises.

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What if what if we have let's say, let's say we have a thousand of lines for it makes no sense at all

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to calculate MFC to what each and every line.

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It makes no sense at all because it will take a huge amount of processing as well.

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So so far, what we can do so in such case, what we are going to do, we are going to use some once

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approaches, basically, which is exactly which is exactly looks like something this which is exactly

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my gradient descent approach.

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That's that's what we have learned some basics behind this in a previous session.

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So this is exactly my gradient descent approach so that if some of you of now are not comfortable with

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this three dimensional plot.

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So let me explain all of these things in two dimensions so that all you can digest is all these fancy

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terminologies in very easiest to let me explain all these things in a good format.

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Supples, let me consider some consider some data points and some advice as well for here.

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I'm going to select it.

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I have some data point with respect to some usages.

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I have some data points thought say this is my data point.

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Alexa, this is my X-axis and this is my wife there, too.

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These are my data point that I decided or here if I were to accept the number two.

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One, two, three, four.

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Similarly, the one something to something to something useful.

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So if I have to draw a best fit line that can do predictions in future.

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So if I have to our best foot line over here, it is nothing.

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But it is just like something like something like almost something like that.

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So basically, if the question will be if the question will be nothing but White goes to MS in the format

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of likely to emit, because you will also in this white goes to policy in this vital to MEAC.

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What we have learned, if this intersect, is viewable only if it is going to pass through this orison

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and we will see this line as possible.

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Or isn't it with the sea value, the sea value is basically zero.

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So this line is nothing but a format of this viscose to access.

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So anyhow, you have to compute this every once you will compute your best and your feasible and your

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statement is almost done.

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That's what we are.

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That's what we all are trying to achieve.

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It looks like these are all my apartment.

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These are all my data points.

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And let's say I have come up with let's let's say let's say I have come up with some solution of let's

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say I'm equal to one that's in very first kiss.

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The very first case I have with my Amazon is assuming I do it.

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So if if I have to do prediction in such a case, in such cases, what I can do is say if X equals to

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one.

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So what did your prediction, what to do, prediction?

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It is nothing, but you have to just put X equal to one over here.

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So it is nothing but a Y, one of equal to one.

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Similarly, four X equals do it is two.

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Similarly for three it is three.

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Similarly for four it is four.

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So in such case, in such case, your best fit line will be exactly like this and this equation would

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be nothing but Y equal to X.

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Because here is one here to stop Islam.

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So if I have the computer, if I have to compute my, my, my, my, my, my meniscal as such case,

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it is nothing but a zero.

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How, how?

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Because it formulates something.

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This one, in my estimation of one, because it'll be different if you have Y minus actually the by

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minus what exactly.

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The prediction you will see your prediction and actually the point I almost equate it with it means

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disvalue zero and it's multiplication will get that fight in some scenarios.

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My mzee, my masc will be zero.

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So let me let me open a new let me see.

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Just some diagrams.

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So it's a the very first line that we selected.

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Yeah.

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So let's say this is my land.

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This is my husband and this is my second.

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That's it here.

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Here on this on this X-axis, I have basically my slope.

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And on this Y-axis, basically I have something known as my masc and green is quite atah.

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So you will see when your arm is born, say, when you're elected.

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This is my one exoduses.

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My arm is four.

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So then your Amazon, your your meniscal add a zero.

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So it means, it means, it means this is that one.

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It means this is, this is this is that one.

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This is that point could change the color of the pen so that you all are very much comfortable with

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this.

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So this is this with respect to my Amoco's tour.

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Similarly, if I have to compute some other recognizability here, I have completed for equals to X.

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So what what if what if what if what if my and valued X.

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What if my values half it's.

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What if my values have so such.

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Is this why it goes to the thing.

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Where does half of X..

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So if I have to compute over here, if I have to compute in such case.

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So when my X is one, X is one my wife goes to house when my X is two.

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My wife is one where my ex's.

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My wife is three by two.

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This is my wife and if my ex is for my wife, I will be to see if I have to draw a line with respect

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to all these wire, with respect to all these vile and all these ex.

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Did I have to draw obsessed with life?

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I guess if I draw a line with respect to all these data points, all this data.

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So if I have to draw so let me let me draw one here.

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If I have to draw, it will it will go something like it will go something like this, something like

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this.

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Something something like this across something like this to here you will observe this, this, this,

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this cross, this cross.

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Not exactly.

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My actual data points.

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This cross are exactly my actual data points.

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And this is your prediction.

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This is your best line.

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This is exactly the best line, so in such case, if you have to compute, if you have to compute,

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if you have to compute your MSE, you're me, Escada, so it will nothing but my one by end.

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So here I have four data points and summation of all you add up with respect to each and every day for

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your prediction.

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You are ready for that because you are here.

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What is the actual data like one and what are your predictions have?

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Similarly here, what is your actually point, what you will see two to?

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It is, whereas your your what is your what is the prediction, you see one, what is it?

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What is it actually the actually the three.

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What is your prediction.

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My prediction he.

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Why do.

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What is what is actually actually tasteful, because here my bias for it, but what am I to say it isn't

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this is not Arab.

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So if I have to complete all this thing, it is nothing but one by four and it is nothing but just one

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by four.

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It will be just one.

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It will be just it will just undertows 294.

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And similarly with him, I have something for and I have to do some basic calculation.

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So it is nothing, but it is just in to become divided, which is which is almost equal to three point

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seventy five.

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And if I have to let's see if I have to block it, if I have to plot over here.

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So I have to plot this.

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I have the plot when my M when my M is zero point five, when my aim is zero point five four in such

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case, in such case likes it.

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Let's say this is my this is my little.

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This is my this is my MASC, which is exactly three point seven five, I said this is mine, that similarly,

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if you will compete for each and every M, if you will compete for each and every time, you will get

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some kind of some kind of go like this from the overhead, you will get some kind of code like this,

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some kind of go anywhere.

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If you have to match this dot, if you have to match this dot, it will look it will look something

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like this.

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It will look something.

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You have to just match it to just match all these datapoints.

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Let me let me match it and it will goes to yeah, so this is this this this this diagram is exactly

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it is exactly what gradient descent it is exactly your gradient descent that what we have learned of

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the recession in terms of three dimensional, it will look something like this because here you have

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Intersect as well.

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But here I had just just just to mention just so that you can digest all these concepts.

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So now what we have to do anyhow, anyhow, we have to reach at this particular point because because

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at this particular point, this is exactly my global M.O. I can say this is my global M.O. It means

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I have to reach if you if you have to remember some basics of calculus that you have learned in your

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Templestowe, if you have remember the basics of calculus.

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So this is exactly my global M.O. They're my sloper zero.

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Where my slope is zero, all you can see, where my MFC, where my MLSE is zero.

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So anyhow, you have to reach you have to is at this particular point and at this particular point,

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you have some value of em and whatever, and you will get you have to simply put, you have to simply

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put in this in this.

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Dictate that you promised that that's what you have to do.

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Now the question arises how you can reach at this point how, how, how you can teach at this particular

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point.

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Suppose initially, suppose initially I considered that, let's say some based on my slope.

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Let's say let's say I am this let's say initially I am over here.

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Let's say initially I am over here.

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I am over here initially at this point at one assuming it is by far, it means at this particular point

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what I can say, whatever M.S. you have at this particular point, you have to move in such a way.

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You have to move downwards in such a way.

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You have to move downward.

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You have to move down or you have to move downwards in such a way, in such a way that you will go at

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this point.

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Because at this at the Struble minimum, you have you zero at almost zero atah that that's what your

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goal is for.

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In order to in order to move down or in order to move downwards, you have a quorum.

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You have to ram what you can see.

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You have a concept known as convergence to the.

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You have a tour known as Clean Water Them, and using this term, you can easily move downward.

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So anyhow, you have to you have to understand what was all about this Ptolemy's select group in our

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very first new development.

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Yeah.

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So basically, basically this totem, Torrance's this term is basically this valuable arm will be nothing

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like my previous.

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And you can do it as an old and it is nothing but my arm new or I can say new slope.

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The new slogan, the thing will by all the slope minus this, this bell em by this with respect to M

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or you can see this is my daddy.

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This is my daddy.

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This is my daddy or my slope into into some learning rate.

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We will talk about later.

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What is this learning rate and how, how to select a value of learning which is exactly what alpha for

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how to select a value and what what is all about learning.

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So this is exactly my slope.

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I guess this is my slope.

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It is this totem, which is exactly my God, what a totem says that I have to subtract.

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Basically, I have to subtract slope at that particular point.

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You will see here and we are trying to compute it means here we have to subtract this the slope at this

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particular point at that one.

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What exactly is a slope at this particular point?

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What is the slope over here?

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What are the slope over?

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You will think what?

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The slope area.

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Well, first, let me let me it is all this thing so that it will not look that much messy like me.

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It is all these things.

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So what exactly is a slope over here slope we all have done what is a slope at that particular point.

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So for this, what do we have to do better?

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Just draw a straight line.

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We have to just just straight line this, this, this line, this straight and that we have draw that

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that could help us to find out that every tip of the slope.

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Then then what we have to do, we have to find whether it's slope, it's it's a positive slope or it's

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a negative slope.

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So you will see basically over here, it is my exactly.

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Negative slope.

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How.

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Because you will see your right hand is pointing towards downward.

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Is this the right hand?

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Is this this this thing this thing is pointing towards downward?

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It means if you're not if not, if it is pointing towards upward, if it is a positive flow, suppose

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suppose at this at this particular point.

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At this particular point, first, let's say you have some let's say you have some slope if you if you

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are going to map.

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So if you will, you will definitely get some slope over here.

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Let's say you have some slope, lets you have some slope.

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What here let's say.

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And it goes to zero point one.

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Amoco's two zero point one, but much, much more feasible value is one, but your feasible is is one.

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So how to read, how to read, find one to one, how to reach.

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So basically using our convergent formula and this learning rate whose value is basically low, somewhere

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close to zero point zero five to zero point zero zero one, it will definitely die between this range.

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Using our SEEMY using cross-validation approaches, we can find out what can be the best value of our

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learning.

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The question, the question that will come across your mind like we have a value in this.

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Why not?

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Why don't we have a higher value?

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Why don't we have a higher like five than 50?

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So we will talk about later.

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Why, why, why we can't we can't assume this high value as my learning read.

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So if I have, I have to put some values for here.

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Let's say here you sat here you have some value and it will nothing.

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But here you will see it.

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We have some negative stuff.

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So it will it will become positive something because it is it is already negative fact.

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It will be composter.

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So it will it is nothing but is positive.

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It is just positive because you will see this, the slope is negative.

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Basically this is negative.

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But what we have computed being discussed because that the slope is going towards downward slope.

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So it will you will see that's a very, very minimum, very minimum number.

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That's a very minimum that are against it.

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That's a very small value.

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It's very minimal value because we all know that this learning result is very low, approx approach,

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zero point zero zero one zero zero two.

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It's a very low number.

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So it means it means it means it's a very low number.

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And let's say what we have initial let's say initial values by one.

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That that what what that what we have computed this.

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Yeah.

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Using this, if you have to put all these things, it will become somewhere close to does this something

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something zero point something.

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So it means using this, using this, using this, doing, doing, doing some iterations you can definitely

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beat approx two one approx two one.

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Basically it means, it means if you have to do this operation multiple times flexin let's say how this

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this is what the Grandison and you have to do this attrition multiple multiplied multiple times until,

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unless you reach at this particular point, because this is the one that you have to reach.

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So you have to do lots of attrition and you have to keep going on and it will reach.

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It will reach at this particular point.

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And but but yeah, what if what if we win?

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We will we will assume higher value, higher value of the alpha.

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So if we if we pursue higher value of Alpha, if we assume higher value of Alpha, so is then moving

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downward, is then moving downwards, it will lose zigzag motion like this, like this, like this,

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like this.

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And it will never reach this global minimum.

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So what are you what are the advantages of using higher alpha value?

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That's why I always ignore higher alpha.

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Never, never, never use a higher value of alpha either.

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It will never it will never reach that particular point.

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It's what I am trying to that's what I'm trying to confess to.

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So basically, once you will achieve this point, basically we all lose this global in math here.

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My store will be zero here, my store will be zero and here my store by zero.

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It means here my Struble zero and whatever and whatever m whatever and I will achieve over here.

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This is an exact value is an exact value of over USD.

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But I can say this is the exact value of our best foot line.

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This is my best food, like let's say this is my best friend and I go to Amex.

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And whatever value you will achieve, this will become this will become this will become this, this

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and value.

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And so, yeah, this is a point basically this is a point where I have to stop my training because because

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we have achieved our best and value.

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So I hope you all can digest all these things.

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You have some doubts.

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You can definitely ask all these things in a personal conversation as part of the Q&A session as well.

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So that's all about this linear regression in that.

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I hope you I hope you love the session very much so.

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Thank you.

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How nice to keep learning.

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Keep growing, keep practicing.