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Let's understand the mathematics behind regression in this session, we will use an example to get started.

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The example I'm considering.

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He is.

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A student studies for a certain number of hours and he gets different kinds of marks.

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Are trying to establish a correlation between the number of hours to read and the mark something.

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OK, I'm going to use Excel to create the scatterplot.

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OK, this can be created using Python or are as well, OK, or any programming language for that matter.

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If you see this view, Scatterplot Scatterplot is using regression and it shows the extent of relationship

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between X and Y.

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What is the dependent variable, an independent variable in this case.

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My obtained is the dependent variable, a member of our study is the independent variable because Mathabane

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is dependent on the member of our study.

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Right.

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A number of our study is not dependent on anything.

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OK, maybe it's dependent on something about which we are not concerned for now.

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OK, we are interested in establishing the relationship between number of us to the max.

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OK, so how will you go about creating this in Excel?

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So you facilitate the data points and you come to insert and then click the option here.

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OK, and then you will click this scatterplot, OK, and you will have a graph like this.

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Right.

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So that is the starting point for you on here.

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The relationship between the two is linear.

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OK, it is not logarithmic or anything else.

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So what is logarithmic?

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We are going to see that shortly.

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That means when I say that the relationship is linear, it means I can show this relationship in the

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form of a straight line.

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Right.

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So that is known as a linear relationship.

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OK, I can show the relationship between my dependent variable and independent variable in the form

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of a straight line.

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And what what is the straight line that I'm talking about?

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I am going to fit a line that will cover all these data points.

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In fact, that line is known as goodness of fit.

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Right, so let's create the goodness of it, how will I do it?

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I first to select these data points, just click one of the data points and right.

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Click you can see these options will be there.

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Click at Trend Line.

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Unusual how this straight line came up and you also choose display equation on chart.

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OK, you can also choose display R-squared, the number we covered the square in the previous session.

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So I display the equation.

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So this equation shows the relationship between dependent variable and independent variable.

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If you recollect your mathematics, there's this equation looks like a explicit Y equals M explicit.

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That means number of marks of pain equals ten point eight six to into number of our studied plus forty

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one point nine zero one.

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Right, if, let's say a student comes in on, that particular student comes and tells that he has studied

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for one point to us all, I can all I need to do is I need to put one point to fight here.

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That is ten point eight, six two and one point two five plus forty one point nine zero one will give

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marks the student will get when he or she studies for one point to fires nine.

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So I have not only established the fact I can also predict the future.

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Right.

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Are you getting it?

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So what is this Y equals M explosive.

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M is known as gradient and C is known as the intercept.

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This intercept corresponds to the value where the line means the y axis and slope is nothing but this

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distance divided by this distance.

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It is also known as Delta White, divided by Delta X..

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In this case, this distance is four and this distance is to four.

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Divided by two is to.

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I can also draw a smaller triangle and the same height divided by base that will give the same value

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of M.

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OK, I can draw a smaller triangle or a slightly bigger triangle also.

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OK, whatever.

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You draw a triangle on this line and when you compute the height divided by base, the value of him

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that you get will be the same, right.

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Are you understanding linear regression?

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OK, members of our study done massively OK in this case.

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The line meets the y axis at minus four, so interceptors minus four and gradients, see, I've drawn

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a smaller triangle.

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I didn't draw a bigger triangle like this.

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And the same height divided by base two, divided by one will you might slope or gradient.

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And they can have more than one variable also, like in the example that I just share, a member of

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Australia's one independent variable.

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And in the case of multiple linear regression, you will have more than one independent variable.

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Please note that dependent variable will always be onely one, right?

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So here I am looking at two variables, right in the case of multiple linear regression.

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I'm trying to predict what will be the quantum of carbon dioxide emission in a vehicle.

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And I am predicting that using two independent variables, volume of the vehicle and weight of the vehicle.

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Right.

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So there is a case of multiple linear regression.

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Right.

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I don't have just one factor, but I am more than one factor, and yet also the relationship is linear.

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That means I can express this in the form of a straight line.

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Right now, let's see logistic regression.

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OK, let's understand that with an example.

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Here we are trying to predict the malignancy of a tumor, what is malignancy that means whether the

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tumor is really cancerous or not, malignancy means cancer.

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I am trying to predict malignancy based on tumor size.

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I have plotted instances of Dumarsais on the malignancy here and I have represented in the form of a

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graph.

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If I tried to fit a linear relationship in this, which is a straight line, I cannot fit all the points

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right.

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As you can see here, if I tried to fit a straight line like this, even if I move that line a bit to

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the left, these points will be left on.

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Right.

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So my foot is not good at all, a straight line cannot cover all the data points.

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If you reconnect the linear regression, the straight line word, almost all the data points, that

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means the food is good here.

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The food is so bad that you cannot have a linear regression.

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You need what is known as logistic regression, because when it is in the form of a column like this,

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it covers all the data points.

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Right now, do you understand who you are?

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Because I have a cover, it covers all the data points, almost all the data points, OK?

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And in the case of a linear model, I have what is known as Y equals M explicit or B not plus B on X,

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B one is the slope and B not is the intercept.

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In the case of logistic regression, we use what is known as sigmoid function, OK, which is nothing

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but one plus E to the power of minus B, not plus B 1x.

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This E to the power of minus is basically a way of writing logarithmic value.

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Right.

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And the output is in the case of linear regression, the output is the numeric value.

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In the case of a logistic regression or a logic model, the output is a probability.

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Right.

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That is whether the tumor is cancerous or not, it will have a value between zero and one.

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Are you understanding the difference between a linear relationship and a.

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Logistic relationship.

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OK, let's see an example where we compare linear and logistic using similar or same independent variables.

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OK, let's take the carbon dioxide emission.

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I'm using these to X1 next to vehicle volume and vehicle weight.

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That's my independent variables.

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I'm trying to predict the quantum of carbon dioxide emission.

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I use multiple linear regression if I predict what is the likelihood of carbon dioxide emission coming

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from that vehicle, I use logistic regression.

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Please note here, I'm using the word likelihood.

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That means it is a probability, which means it can have a value between zero and one.

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Are you getting it?

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In logistic regression, one more aspect is because the dependent variable had as a value between zero

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and one, your X1 x2 should also have a value between zero and one.

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But you see here, the values here are not between zero and one.

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Right.

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They are numeric values.

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So I need to convert the numeric into.

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Logarithmic value, and then I will apply logistic regression.

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How you understanding is this clearly?