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In this session on bigoted analysis, we are particularly interested in finding the relationship between

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two independent variables in the previous sessions I talked about.

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Dependent variable being dependent on many independent variables.

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Please note what I just said, I'm interested in finding the relationship between two independent variables

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itself.

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If there is a relationship between two independent variables, I can predict one independent variable

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from another independent.

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Very.

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Ideally, I don't want this kind of relationship among my variables.

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As far as developing machine learning model systems.

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This is what is known as multipolarity, that is one independent variable can be predicted from another

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independent variable itself's.

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OK, so let's see all the techniques that are available in my video analysis.

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So by immediate analysis, helps find the relationship between two variables, right?

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I know I said we are more interested in finding the relation between two independent variables, but

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why we need analysis.

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Broadly speaking, can be used to find out the relationship between any two variables.

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Right.

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So we are looking at both association and this association, meaning there is a relationship, there

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is no relationship that can be a positive relationship, that can be a negative relationship.

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All the possibilities are endless.

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OK, and by various analysis, can be performed for any kind of combination of variables.

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That is, one variable could be continuous, another variable could be categorical, like both the variables

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could be categorical.

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Both variables could be continuous.

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There are different types of techniques for different types of combinations.

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We are going to see all of them in this issue.

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OK, we will first start with the relationship between two continuous variables.

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That is two members, so to speak.

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Remember, I gave the example, right?

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Number of marks of the number of hours I study.

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That is an example right here.

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The primary technique that we'll be looking at is what is known as a scatterplot, OK?

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It graphically shows whether there is a relationship between two variables like you can you can be sure,

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Lucy, as I mentioned, it can be a positive.

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It can be a negative relationship.

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That can be a relationship, that may not be a relationship and the relationship can be a linear which

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a straight line can be fitted.

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OK, what is called is the line of best fit, OK?

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Or it can be a non-linear relationship, like a polynomial kind of relationship, OK, or a logistic

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relationship.

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So Scatterplot shows the relationship between two variables, but it doesn't tell you the strength of

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the relationship.

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OK, so for this, we use what is known as quotient of correlation.

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It derives from the scatterplot because it's got to be food, what is known as the line of best, OK,

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using the line of best food, you can find out what is the extent of correlation between two continuous

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experience for this?

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As I said, the use coefficient of correlation.

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So correlation there is between minus one and plus one.

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OK, one indicates.

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Minus one indicates perfect negative correlation, plus one indicates positive linear correlation,

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Zettl indicates no correlation.

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This is minus one.

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OK.

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The point is many times, you know, you won't get this minus one, plus one, or you will get values

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that are closer to one.

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So which means in order for this point nine six, if it is closer to minus one.

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So it means it's a nearly a perfect linear correlation.

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You can even get a value of eight point six.

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That means positive correlation to some extent.

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So those are the judgments, you know, you need to make based on the quotient of correlation.

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Right.

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So this is the scatterplot, right?

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In this example, I have drawn this kind of prop for a relationship between applicant's income and loan

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amount.

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Remember, these are two different variables.

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We can find that there is more relation between the two, right in the other scenario, the applicant

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income KOPLIK and then that is also being compared.

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But see, the scatterplot divide is scattered all along and quite literally, it is scattered all around.

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That means there is no relationship like you can plodders, whenever you have two variables and you

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want to find the relationship immediately.

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Plot scatterplot right.

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A very, very simple tool to ascertain the relationship between any two variables.

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And you can be sure you see if there is any relationship or not.

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You can also see, is it a case of linear relation or is it a case of a polynomial or other types of

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relationship?

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All those things can be seen here, you know, using this scatterplot.

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Right.

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And as I discussed the earlier, I use quotient of correlation.

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That is the extent of correlation.

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That is the numerical measure of correlation is the correlation coefficient.

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But in this case, you are taking applicant's income and loan amount by we are getting a correlation

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coalition of point Feiss, which means that is a moderate relationship, a more positive relationship

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between applicant income and corporate income.

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It is a negative correlation, but it is a weak correlation.

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Please understand this is closer to zero, right, than to minus one hour plus one.

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If you look at the relationship between applicant income and long term, it is in fact closer to zero

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point minus point zero.

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For that is a little weak relationship between two variables.

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Are you getting what I'm what I'm trying to say?

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Right.

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Scatterplot helps him to visually see the relationship.

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Right.

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Whether that is a relationship or not, who have Schindall correlation, gives us a numerical measure

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to find out the extent of correlation.

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That is that between two variables, I can use this concept to determine whether that is in any relationship

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and decide my course of action.

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OK, what is the course of action?

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Ideally, I don't want correlation between two independent variables.

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I will remove such variables.

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Right, so that is the primary action.

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Now, the other typists, categorical and categorical, if the two variables are most of them are categorical

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in nature, we use what is known as a chi square test, right.

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It is used to derive the statistical significance of the relationship between two categorical variables,

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right.

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It is based on the difference between expected and observed frequencies in one or more categories.

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Right.

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So categorically, it can have multiple levels of categories.

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Right.

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We create what is known as up to a table expected and observed frequencies.

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Right.

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It basically returns the probability for the chi squared distribution.

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Basically returns the probability if the probability is zero.

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It means that both the categorical variables are dependent probability of one to choose.

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Both are independent, right.

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So that's closer to zero.

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Closer to one.

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But we are looking at a 95 percent confidence level, which means that you will take a P value of point

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zero probability value of one zero four if it is less than one zero five.

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It means that there is a relationship between variables.

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My.

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Please note, this is what we will be using for.

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Finding out the relationship between two categorical variables, it chi square test is what you're going

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to use to get to understand this, OK, because we'll be using the concept of hypothesis testing.

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I frequently talked about dependent variable and an independent variable rate, the high school mathematics

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concept.

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This is also something that we learned in our high school and probably colleges.

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Right.

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So hypothesis testing is the concept that I'm trying to derive an inference about a population based

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on the information I have about sample.

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Remember, the population was a sample concept that we discussed in the earlier session.

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Like I am doing an opinion poll by taking feedback from some of the groups.

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Right.

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From some of the people who are eligible to vote.

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Right.

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I'm not going and taking feedback from all of the people who are eligible to vote.

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I'm only taking feedback from some of the people and hence I'm interested in that particular particular

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party is expected to win the elections.

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Right.

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So how can I conclude that the responses of a few people are.

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Good enough to determine the outcome of an election that more people are employed.

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So that is where the concept of hypothesis testing, cos I am trying to draw inferences about a sample

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based on the performance I'm trying to draw on in terms of the population, based on the results of

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a sample, based on the sample.

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I thought about the entire population for this.

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I'm making use of the concept of hypothesis testing.

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Right.

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So if you see the photo that is there, I apply fertiliser on the plant goes.

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Right.

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So what is the hypothesis?

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The hypothesis is application of fertiliser increases plant.

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Right.

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So that is stated as an alternate hypothesis.

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Alternate hypothesis is what we want to prove.

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Right.

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What we don't want to prove is data.

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Neither my life, what the application of fertiliser does not increase plant growth.

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Right.

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There is no impact.

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Right.

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So an alternate hypothesis is what we are trying to prove.

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I'm not like what?

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This is the opposite of that, right?

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We actually don't try to prove hypothesis.

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Rather, we try to either accept or reject the argument hypothesis.

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So that is the way the concept of hypothesis testing works.

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Right.

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So in our case, the alternate hypothesis would be that is the relationship between two variables.

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It's not there is no relationship between two.

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It is like if the P value is less than one zero five.

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We accept that.

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We conclude rather than is the relationship between two variables.

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Is this clear?

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Is this clear to everyone?

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Let's see some examples here.

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I'm taking two variables, right, the education level and the whether the individual is self-employed

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and there's no kind of scenario.

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Right.

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So please note that in all, if there are more than two levels, also, you can still use Bisquick,

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not just when I have to live.

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It's like education, graduate or not graduate, self-employed person.

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But if I have a variable in which more than two options are it, then also quietist can be used.

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Although the example that I showed you that only two possible outcomes for each of these variables might.

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Two possible levels here.

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The alternate hypothesis is education and self-employed are not independent.

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Look at the way I am structuring this.

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I'm saying they are dependent.

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So I'm essentially saying they are more dependent.

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Like the null hypothesis is they are independent of one another.

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There is no relationship.

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And the chi square value that I'm getting here, OK, is point zero to three six.

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But I am more interested in the P value.

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Right, that is what I'm interested in.

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So the p value is point eight, seven, seven, eight, right?

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That means.

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The value is greater than one zero five.

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That means we are accepting the null hypothesis.

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That means there is no relationship.

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In the case of let's see, one more example, education and property.

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Right, so here also the P values turning out to be greater than one zero five, that means there is

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no relationship between these two buildings.

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So whenever we have categorical variables, we use the concept of high school year.

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The primary metric that we are looking at is the value it is.

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If it is greater than one zero five, we can conclude that there is no relationship between the two

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buildings.

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So for this, we are using the concept of hypothesis testing to explain a little earlier in the session.

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Yes, now we are going to look at the relationship between categorical and countries, right?

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So for this, we are going to use the test detector on.

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Again, these are coming from statistical concepts, right on all counts whenever we are looking at

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more than two groups that are more than two groups.

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Right.

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Whereas if we are only looking at comparing two groups, we use the test already.

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This both are in fact, similar.

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OK, but it is used whenever the number of observations is less than 30.

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Right.

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Obviously, in most of the cases, the number of observations, the number of data, the number of historical

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data that we are taking up for building the machine learning model will be more than the people invariably

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will be going for a test.

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Right.

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So what what do I mean by two groups, which is what the categorical it is?

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Right.

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I have two variables if I want to compare more than two.

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We are looking at Kanawa.

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Like the example that you're going to see are only to fight, but if you have more than do, you can

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definitely use an all.

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Right.

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So here also we are going to primarily look at deep value.

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It is a P-value that is something that is of importance to us in this case, we are looking at if there

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is any relationship between applicant income and loans to.

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Right.

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This is a look at this.

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We are computing V Z, right.

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And they are using the Z test.

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Right.

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And we are computing the probability that is in one year.

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Also, we are stating we now like lotuses and alternate hypotheses, alternate hypothesis.

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That is the relationship model, that is more relationship.

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The P value comes to be greater than point zero five.

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In fact, it is closer to one.

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Right.

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We can very well not reject the null hypothesis.

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Remember the way I am stating this is the way the world of hypothesis testing works.

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I either accept or reject the null hypothesis.

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Right, which is there is no relationship here.

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I do not reject.

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OK, which means I accept whatever my hypothesis tastes like, but if you want to understand it, simply

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don't bother about the Amala argument by Waters's right.

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If this is confusing to you, just look at the people.

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Just see for the P value is less than or greater than point zero if it is greater than one zero five.

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That is that there is no relation.

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OK, nothing to worry if there's less than one zero five that is.

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And you need to worry.

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And the course of action is you remove the variable.

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Right.

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That is involved in the.

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Relationship like I do when there is a relationship between two independent variables, you want ideally

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remove one of them like so that's a you take, right.

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So a concept that is related to this is what is known as multipolarity.

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Right.

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And I predict an independent variable from another independent body.

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So it is like, for example, can I predict the outcome based on the applicant's in?

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Like, if such a relationship existed, it is definitely a big cause for concern.

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And the previous we saw there is a relationship, but here I'm going one step further, right?

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I'm checking if an independent variable can be predicted from another independent body.

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This is known as multicasting inheritance for those fathers would be using the concept of various variants,

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inflation, factor of value.

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And if you use this.

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Preloaded library that comes with Python, right, you can find out valiance, inflation factor in a

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jiffy.

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Right.

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So see the readings inflation factor for each of these independent variables.

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There are some there are some variables where it is higher, like six, 10.

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Right.

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Many variables.

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Many of the variables in it is not so high.

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So obviously, our interest level is higher than the average office.

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Higher.

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Right.

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Anything beyond fine is a cause for concern.

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But if it is greater than 10, you must do the more the MultiKulti and D right.

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Remove some of the highly correlated independent variables, which is the loan amount to multi-client

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feeling that right.

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You can also combine independent variables such as you can add them together.

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You can add, let's say, for example, applicant's income and corporate and income.

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Right.

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That is one way of looking at it.

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Or you can perform an analysis that is meant for highly correlated variables such as principal component

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analysis and partially square regression.

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Those are techniques you can adopt.

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But the one that I have found the best uses in already more than.

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Take a call and remove it all, you can add them together, right?

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These two have worked very well.

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So what is the primary action that you will be taking, if that is multipolarity, that is ViiV is greater

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than 10 remolded.

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So these are key, and I also don't want to highly correlated variables.

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I mean, we saw two guys square regression, right, which is the scatterplot and Zetterstrom.

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That also indicates that is the relationship between the two.

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I don't want to I don't want any relationship, especially a positive relationship between a positive

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relationship, between two independent variables.

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Right.

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So I don't want such variables in my data set because they will definitely pull down my forecast accuracy.

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So that's what I wanted to cover in this session, will be seen how to handle missing values, what

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what actions you need to be taking in the next session.

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OK.