Logit model explained: regression with binary variables (Excel)

Summary

This video from Nettle, a platform for distance learning in business and finance, is hosted by Sava who delves into the logistic regression model, a vital tool for estimating regression models with binary dependent variables. The tutorial covers the model's application in credit scoring, predicting loan defaults, and emphasizes the importance of variables like homeownership and full-time employment. It guides viewers through the process of estimating the model, optimizing coefficients, and interpreting results to assess credit risk, concluding with a practical example of scoring a loan application.

Takeaways

• 📚 The script introduces the logit model, also known as logistic regression, as a statistical technique for estimating regression models with a categorical or binary dependent variable.
• 🏦 The logit model is commonly used in finance and economics for applications such as credit scoring, predicting recessions, and analyzing exam success rates.
• 🔢 The model requires a balanced dataset with a significant portion of both zeros (non-defaults) and ones (defaults) to function effectively.
• 🏠 Two important categorical variables considered in credit scoring are homeownership and full-time employment status, which are used as predictors for loan default.
• 💰 Continuous variables like income, expenses, assets, and loan amounts are transformed into interpretable indicators, such as the natural logarithm of the ratio of expenses to income, to assess the likelihood of loan repayment.
• 📈 The logit model uses the logistic distribution function to estimate the probability of the dependent variable, ensuring the output is bounded between 0 and 1, suitable for probability estimation.
• 🔍 The model's coefficients are optimized by maximizing the log likelihood function rather than minimizing the squared sum of residuals, as in ordinary least squares regression.
• 📊 The variance of the estimator is calculated using the inverse of a matrix product that includes the weight matrix, which accounts for the heteroskedasticity inherent in binary outcomes.
• 📉 The significance of the model's predictors is determined by calculating z-statistics and p-values, which help identify variables that are statistically reliable.
• 🏢 The script provides a practical example of how the logit model can be applied in a bank's credit scoring process to assess an individual's creditworthiness.
• 👍 The video concludes by emphasizing the importance of understanding the logit model for various applications in business, finance, and economics.

Q & A

What is the primary purpose of the logit model discussed in the video?

The primary purpose of the logit model, also known as logistic regression, is to estimate regression models when the response variable is categorical or binary, which is common in fields like finance and economics.

Why is the logit model preferred over multiple linear regression for binary outcomes?

The logit model is preferred because it restricts the estimated values of the dependent variable to be between zero and one, making it suitable for estimating probabilities, unlike multiple linear regression which can yield values outside this range.

What are some applications of the logit model mentioned in the video?

Some applications include credit scoring, predicting recessions, and determining success or failure in exams. These applications often involve predicting a binary outcome based on various explanatory variables.

What is the significance of having a balanced sample in the logit model?

A balanced sample, where there is a roughly equal number of zeros and ones for the binary outcome, is important for the logit model to function properly. An overwhelming majority of one outcome would make the model less effective.

What are the two main categorical variables considered in the video for predicting loan default?

The two main categorical variables are homeownership and full-time employment status, as these are considered important factors when deciding whether to grant a loan.

How are income, expenses, assets, and loan amount transformed into explanatory variables for the logit model?

They are transformed into interpretable indicators such as the natural logarithm of the ratio of expenses to income, leverage after the loan is granted, and the natural logarithm of the loan amount over typical income to measure repayment time.

What is the logit transformation used for in the logit model?

The logit transformation is used to convert the logit value, which is the exponent of the weighted sum of explanatory variables and coefficients, into an estimated probability that ranges from zero to one.

How is the optimal value of coefficients in the logit model determined?

The optimal values of coefficients are determined by maximizing the log likelihood function, which is done using a solver to find the values that best fit the model to the data.

What is the purpose of calculating the covariance matrix in the context of the logit model?

The covariance matrix is used to estimate the variance of the estimator for the coefficients, which in turn allows for the calculation of standard errors and z-statistics to test the significance of the coefficients.

How can the logit model be used to predict an individual's likelihood of defaulting on a loan?

By inputting an individual's specific data into the model, such as homeownership status, employment status, income, expenses, assets, and loan amount, the model can calculate the probability of default, which can then be used to assess creditworthiness.

Outlines

00:00

📚 Introduction to Logit Model in Business Analytics

The video script introduces the logit model, also known as logistic regression, as a fundamental statistical technique for estimating regression models with a categorical or binary dependent variable. Common applications include credit scoring, predicting recessions, and analyzing educational outcomes. The script emphasizes the importance of having a balanced dataset with a significant number of both outcomes (0s and 1s) for the model to be effective. It also outlines the variables considered in the model, such as homeownership, employment status, income, expenses, assets, and loan amounts, and how they are transformed into interpretable indicators for the analysis.

05:01

🔍 Exploring Variables and the Logit Model's Application

The script delves into the creation of explanatory variables from raw data, such as the natural logarithm of the ratio of expenses to income, leverage, and the time needed to repay a loan based on income. These variables are then used in the logit model to estimate the probability of default. The logistic distribution function is highlighted for its role in scaling the variables to estimate probabilities between zero and one, making it suitable for categorical variable modeling. The process of calculating the logit and transforming it into an estimated probability is explained, setting the stage for the optimization of coefficients.

10:01

📈 Maximizing Log Likelihood in Logit Model Estimation

The script explains the process of optimizing the coefficients in the logit model by maximizing the log likelihood function, which is different from the least squares approach used in multiple regression. The log likelihood is calculated based on the actual and estimated values of the dependent variable, and the total log likelihood is maximized by adjusting the coefficients using a solver tool. The resulting optimal values of coefficients are interpreted to understand their impact on the probability of default, with the script noting the intuitive nature of the relationships found between the variables and the likelihood of default.

15:03

📊 Understanding Heteroskedasticity and Variance Estimation

The script discusses the heteroskedastic nature of the data in categorical variable estimation and the need to calculate a weight matrix based on the variance of individual probabilities. This is crucial because the logit model accounts for the different variances across observations, unlike linear probability models. The weight matrix is constructed using the diagonal of the probability estimators, and the covariance matrix of the estimator is derived to obtain standard errors for the coefficients, which are essential for statistical significance testing.

20:03

🔑 Statistical Significance and Predictive Power of the Logit Model

The script concludes with an analysis of the statistical significance of the coefficients, using z-statistics and p-values to determine which variables significantly predict the likelihood of default. It highlights full-time employment and leverage as significant predictors, while other variables like homeownership and the expense-to-income ratio are less significant. The script also demonstrates how to use the model to predict the default probability for a new applicant, showcasing the practical application of the logit model in credit scoring.

Keywords

💡Logit Model

The Logit Model, also known as logistic regression, is a statistical method used for estimating the relationships between one dependent binary variable and one or more independent variables. In the context of the video, it is used to predict the likelihood of a categorical outcome, such as whether a borrower will default on a loan. The model is essential for applications like credit scoring, where it helps in estimating the probability of default.

💡Categorical Variable

A categorical variable is a type of data that can take on a limited, and usually fixed, number of possible values, assigning each individual or case into different groups. In the video, the categorical variable of interest is the default status of a loan, which can be either 0 (non-default) or 1 (default), and the model predicts the probability of these outcomes.

💡Binary Outcome

A binary outcome refers to a situation where an event can result in one of two possible outcomes, often represented as 0 or 1. In the script, the binary outcome is the default status of a loan, with the logit model being a suitable technique for analyzing such binary data.

💡Credit Scoring

Credit scoring is the process of evaluating the credit risk of a borrower or debtor. It is used by banks and other lending institutions to decide whether to grant loans. In the video, the logit model is applied to credit scoring to predict whether a borrower would default on their debt, which helps in making lending decisions more efficiently.

💡Dependent Variable

The dependent variable, often denoted as 'y', is the variable being analyzed to understand its behavior in relation to other variables. In the context of the video, the dependent variable is the default status of a loan, which the model is trying to predict based on various independent variables.

💡Independent Variables

Independent variables are the factors that are believed to influence the dependent variable. In the video, independent variables include whether the borrower owns a home, whether they are full-time employed, income, expenses, assets, and loan amount, which are used to predict the likelihood of loan default.

💡Logistic Distribution

The logistic distribution is a continuous probability distribution that is used in logistic regression to model the probability of a certain event occurring. The video explains that the logit model utilizes the logistic distribution function to estimate probabilities, ensuring that the predicted values of the dependent variable fall between 0 and 1.

💡Odds Ratio

The odds ratio is a measure of association between two events, often used in logistic regression to describe the relationship between the independent variables and the likelihood of the dependent variable being 1. In the script, the odds ratio is used to estimate the probability of default conditional on the values of the explanatory variables.

💡Log Likelihood

Log likelihood is a measure used in statistical models to quantify the goodness of fit of a particular statistical model. The video describes how, in logistic regression, the model coefficients are optimized by maximizing the log likelihood function, which is based on the observed and estimated probabilities of the dependent variable.

💡Coefficients

In the context of regression analysis, coefficients are the numerical values that represent the relationship between the independent and dependent variables. The video explains how the coefficients in the logit model are estimated to determine their effect on the probability of the dependent variable, such as the likelihood of loan default.

💡Heteroskedasticity

Heteroskedasticity refers to a situation in a dataset where the variability of the unexplained part of the model is different across observations. The video points out that the logit model accounts for heteroskedasticity by using a weight matrix based on the variance of individual probabilities, which is not assumed in standard linear regression models.

💡Standard Errors

Standard errors are a measure of the average distance that the observed values fall from the estimated values. In the video, standard errors are calculated for the coefficients of the logit model to determine the precision of the estimates and to perform hypothesis testing for statistical significance.

💡Z-Stats

Z-statistics are a statistical measure used to express the number of standard deviations a data point is from the mean. In the context of the video, z-statistics are calculated by dividing the coefficients by their standard errors to test the significance of the model's coefficients in predicting the likelihood of default.

Highlights

Introduction to the Logit Model, also known as Logistic Regression, a technique for estimating regression models with a categorical or binary dependent variable.

The importance of subscribing and supporting the channel for consistent delivery of educational content.

The Logit Model's application in finance and economics for predicting outcomes like credit scoring and recessions.

The significance of the dependent variable being categorical in the Logit Model, allowing for binary outcomes such as 0 or 1.

The necessity of a balanced sample for the Logit Model to function properly, avoiding a majority of one outcome over the other.

Exploration of categorical variables like homeownership and full-time employment as predictors in the Logit Model.

Transformation of continuous variables such as income, expenses, assets, and loan amount into interpretable indicators for the Logit Model.

The use of the natural logarithm to scale variables and mitigate the impact of outliers in the model.

The process of estimating the Logit Model parameters using the odds ratio and logistic distribution function.

The distinction between the Logit Model and multiple linear regression in terms of the dependent variable's bounds.

The optimization of coefficients in the Logit Model by maximizing log likelihood rather than minimizing squared residuals.

The calculation of the covariance matrix and standard errors for the coefficients to test statistical significance.

The use of z-statistics and p-values to determine the significance of the model's predictors.

Practical application of the Logit Model in credit scoring to assess an individual's probability of defaulting on a loan.

The intuitive understanding of the model's findings, such as the positive impact of full-time employment on reducing the probability of default.

The conclusion summarizing the Logit Model's utility in credit scoring and its potential applications in various fields.

Transcripts

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details

my name is sava and we are going to

investigate the logit model

or as it's also called the logistic

regression

it's a go-to technique for estimating

regression models

when your response variable so your

dependent variable your y

is categorical or binary often in

finance

and economics you have got your

dependent variable

be not a real number but a categorical

number

so it can only be 0 1 or can only take

some limited number of outcomes most

importantly

and some of the most important

applications of the logit model

are credit scoring predicting whether

your borrower would default on their

debt

well zero bean and non-default

everything goes according to plan

and one being default and you are pretty

interested

in figuring out which characteristics of

your borrower

predict defaults so you could allocate

lending as a bank more efficiently and

minimize your credit risk

alternatively in economics you can be

interested in predicting recessions

zero being no recession and one being

recession and figuring out which

macroeconomic or some other indicators

perhaps

can forecast recessions

quite a legitimate research task or in

education we might be interested in

what predicts or determines uh success

or failure in an exam

how does the number of hours studied in

preparation to an exam

contribute to success rate and all of

these questions are also legitimate and

can be answered

using the logit model so without further

ado

let's try and estimate the logit model

on

a very textbook case for its application

that is credit scoring and predicting

retail

loan default so here we have got a

sample that's a real world

testing data sample of 500 applicants

that either

defaulted or haven't defaulted on their

consumer credit

so we have got zeros denoting

non-defaults so

the individuals repaid that that and

once being

default so here you can see that among

the 500

individuals that have applied for the

loan and being granted alone

127 have defaulted and that's quite

important

for our binary choice models login

included

to be functioning properly you need a

sizeable chunk

of your sample to have either

zeros or ones if the overwhelming

majority like 95 percent

of your sample being either zero one so

if almost everyone have repaid or

almost everyone have defaulted then the

logit model would have been not the best

choice however here as of what roughly a

quarter of our sample

defaulting logit model is appropriate so

that out of the way

we can study other variables that we've

got here so

the two most important perhaps

categorical variables that you could ask

for

when deciding whether to grant someone

alone or not

is to ask if they have got any retail

property on their hands

whether they are homeowner or not

whether they can pledge

their property as a collateral perhaps

for their loan

or whether they have such uh property as

an asset that could back them up if they

encounter some

difficulties in repaying and also

whether they have a full-time job so

whether they are full-time employed

and those two variables are again binary

variables that

are treated here as independent as

predictors as explanatory variables

for our why which is default or not

and we have got also some real numbers

as our explanatory variables

and we'll try and transform them into

some project that we could later use in

our logit model

so we've got income and expenses of our

borrower's household in thousands of

dollars per year

so we can see that this particular

household earns roughly

129 000 a year and spends

73 000 out of that we can also

record uh the assets and debt right now

before the loan is granted

of this particular household and the

amount of the loan they're asking for

so this data can be then coded into

other explanatory variables that we can

later use in our logic model

so first of all let's consider three

variables that transform

our income expenses asset that and loan

amount data

into some more interpretable indicators

for example we can figure out the

natural logarithm of the ratio of

expenses to income

and figure out how thrifty

how likely to save their income this

household is

and we expect that the more they save

and the less they spend

the more likely they would be to

repay their loan as they would be more

disciplined they would have more spare

cash

to meet their monthly payment schedule

and so on and so forth

so this is a legitimate variable to

consider

then we can consider leverage as in

that to assets like we do

for uh corporate analysis but here we've

got individuals

and their outstanding assets and that

and the debt that they're planning to

take

and they plan to fund some asset

purchases with such a debt perhaps they

want to buy

a new house or a new car or the like so

here we can figure out natural logarithm

this is just for

scaling purposes so that we have got no

outliers

at the top so we can figure out the

natural logarithm of the

leverage of our applicant after they

would have been granted

the low so in the numerator would have

total debt

which is outstanding debt that before

they were granted a loan

plus the loan amount divided by their

assets after they were granted

a low so assets plus the loan amount

here we assume that they'll spend the

loan amount to purchase

some assets for themselves

and here we can also figure out one

further variable that would basically

mean

how long would this individual need to

keep

earning to repay their loan and that

can be calculated as natural logarithm

of the loan amount

over their typical income

and here we have got five explanatory

variables which is

more than enough for a typical logic

model especially with

500 observations so here we can bottom

like it all the way down

and now start figuring out how to

calculate

the optimal values of these parameters

which denote

just the constant the constant term as

in all regression models

and our coefficients for our explanatory

candidate variables

in the logit model what you utilize is

the

odds ratio and you try and

estimate the probability of default

conditional

on these values of explanatory variables

and as it is also called the logistic

regression

it should not be a surprise that the

equation that relates the predicted

values

of y the variable of choice the

probability of default

utilizes the distribution function of

the

logistic distribution and we have got a

video on the logistic distribution our

channel already

so please check this out later on if

you're interested so here we use the

logistic distribution logic

to relate these variables they can be

anything they can be bounded or

unbounded they can be categorical or

real numbers

and so on and so forth so we basically

scale them

to meet the criteria that the

probability can be estimated from

zero to one and this is what

makes logistic regression and logit more

applicable

to categorical variable modeling than

for example

just multiple linear regression because

in multiple linear regression you can

theoretically get

estimated values of your dependent

variable outside of

zero to one bounds and that could be

tricky to interpret it in context of

probability of default for example or

probability of recession a probability

of failing

or passing an exam and the like

this transformation the logic

transformation allows to avoid that

so here we can calculate the logit which

is just the

exponent of the weighted sum of our

explanatory variables and the

coefficients so we can use sumproduct

and refer to our coefficients over here

and lock in the row as coefficients stay

the same for all observations

and referring to explanatory variable

plus a constant

for simplicity over here corresponding

to a particular observation

and here we calculate the value of log

it and unsurprisingly

as all the coefficients are zeros as for

now the value of log it is

one as the exponent of zero is one and

here we can use this logistic

transformation

to convert this logit value into our

estimated probability

so we just divide our log it by one plus

log it

and get a default estimated probability

of 0.5

which is unsurprising if you know

nothing about it

you can just assume it's a coin toss

it's 50 50

either you default or not quite

intuitive isn't it

and then we can bottom right click it

all the way down and estimate it for

all of our observations all of our 500

lone applicants and here it's

actually important to understand how one

might

optimize these coefficients to arrive at

the best fit

possible and here is where the logit

model

differs from multiple regression in

terms of

the function that you try and optimize

for multiple regression

you try and minimize the squared sum of

residuals

while for the logit model the most

robust approach

possible is to maximize log likelihood

and the log likelihood is defined

in terms of actual variables actual

dependent variables

that are zeros and ones y i over here

and the estimated values the expected

values of y

i denoted here as y bar and we can

estimate our log likelihood for every

single observation

by just multiplying our default

categorical variable

onto the natural logarithm of our

estimated probability

plus one minus the default categorical

variable

times the natural logarithm of one minus

the calculated probability

and we can bottom likelihood all the way

down and then we can calculate the total

log likelihood which would be the sum of

log likelihoods across

the whole sample and now we can

maximize our log likelihood by varying

the coefficient parameters

this can be done using solver so we can

go data solver

and specify our optimization task so we

want to maximize

the value of log likelihood currently at

cell

l1 we want to maximize it so here should

be max

and we need to change variable cells

that correspond to

b0 b1 all the way to b5 that are the

constant term

and the coefficients for all five

explanatory variables so we select

the array c2 to h2 and we don't want to

impose any constraints on our parameters

as theoretically any of these parameters

could impact

probability of default either positively

or negatively we just have some

reasonable suspicions whether for

example

leverage would affect the default

probability positive or negatively

but the whole purpose of logic

estimation is to test

these suspicions these hypotheses so we

need to untick

this box to make uh all parameters

either positive or negative depending on

what maximizes log likelihood

and click solve and wait until the

algorithm converges

to an optimal solution and we can see

that we have converged

to an optimal value of log likelihood we

can see it increased from roughly minus

350

to minus 233 here the negative value of

log likelihood should

not um be of concern it

doesn't really matter whether it's

positive or negative it only

matters in comparative terms whether it

have increased or decreased and we

can see that it increased quite a lot

and here we can already see

what the optimal values of coefficients

are the

closest values to some true parameters

that could be possibly estimated using

maximum likelihood and here we see quite

unsurprisingly that

being a homeowner and being full-time

employed

reduces your probability of default

makes it more likely for you to repay

the loan on time

and in full which is again quite

intuitive

while being more

careless in your spending habits

spending more

in proportion to your income makes you

less likely to repay

being more leveraged makes you less

likely to repay

and also taking on higher loan with

respect to your income

also makes you less likely to repay and

more likely to default

all of those relationships are quite

intuitive

in terms of the logic either

psychological or

economic of the theory that is behind it

but now we need to figure out which of

these relationships

are statistically significant and

reliable and which are perhaps

not significant and uh can be neglected

in further modelling so here we need to

use some procedure perhaps

to estimate the variance of our

estimator

to come up with standard errors for our

coefficients

just as we do with multiple regression

however here

just as with log likelihood instead of

minimizing

uh squared sum of residuals we have got

a slight tweak on the conventional

procedure of estimating the variance of

our grasses

and we have got it covered over here to

estimate the covariance matrix

uh the variance of estimator of b

we need to calculate the inverse matrix

of such matrix product

that has the transposed x the transposed

matrix of our explanatory variables

including the constant

multiplied by the weight matrix and

weight matrix will be explained a little

bit later so stay tuned

and again finally the matrix

of x as in explanatory variables

again and uh what is the weight matrix

well the weight matrix corresponds to

the variance of

individual probabilities and here

is actually one of the another reasons

why

logit model is preferable to linear

probability models

when you just regress your zeros and

ones

in a multiple linear regression as if

you recall in a binomial distribution

when you have

some probability that an event happens

and some probability that doesn't happen

the variance of the probability can be

defined as probability times one minus

probability

so basically in such a categorical

variable estimation

your data is heteroskedastic

by definition you have got different

variances for

different observations for example here

if you were to

regress it using the usual method the

simple multiple linear regression

you would have assumed as per the

gauss-markov assumptions

that variances for all these

observations are the same

while in fact they can be massively

different

and depending on the value of the

estimated probability

and the highest variance of probability

would be observable

for the estimated y being equal to 0.5

as is usually the case as is always the

case with the

bernoulli distribution so here we need

to calculate the

weight matrix that would be the

weighting matrix of our variance

estimator

based on the diagonal of our

probability estimators so here we have

got the template

to calculate the 500 by 500

weight matrix and here we need to first

figure out

whether we are on the diagonal and if we

are on the diagonal we need to input

this particular variance estimation and

if not we need to input zero

so first we check if the

column indicator and row indicates are

the same

we can input the product

of probability and we need to lock the

column here

times one minus probability

log in the column here as well and if

not if we are not on the diagonal

we just return zero and here we can

use ctrl right and bottom lightly knit

all the way down

we can calculate the whole weighting

matrix and we can see that on the

diagonal we have got

variance estimators them being quite

different

and being the highest the closest they

are

to 0.5 as expected

and now i can finally calculate our

covariance matrix

that we can then be used to derive

standard errors

of our coefficients so here we first

need to input min inverse

which is inverse matrix then we first

need to input

our mod function so matrix

multiplication

the first component would be the

transposed

array of explanatory variables x

starting from the constant

all the way to here so it would be a 6

by 500 array

and as a second component we input

another matrix multiplication

and here first we input our weight

matrix so from here all the way

to here so a 500 by 500 matrix

and as the second component

in this particular product will input

our

x and we don't need to transpose it at

that

particular point so we close all the

parentheses and make sure that we close

them

uh all and then enforce this formula

using shift ctrl enter as it multiplies

a bunch of matrices together basically

and we get our covariance matrix and now

on the diagonal of our covariance matrix

we would have

our standard errors squared so now to

derive our standard errors

we just can calculate the square roots

of the diagonal elements and that's what

we will do

first of all for our constant the

estimator

would be the square root of the very

first element of the matrix

and if we drag it across we'll get

the square roots of the first row

but we need to calculate the square

roots of the first diagonal so what we

can do here is we can

change the references here to refer to

the diagonal

just increasing the row reference by one

each time

and here that's how you get the standard

errors for the coefficients

now we can use the assumption that in

large samples

the distribution of coefficients is

approximately normal

so dividing the coefficients by the

standard errors we get

z stats our usual and uh

well-behaved z-stats that can be tested

for significance

using a two-tailed t-test so two times

one minus standard normal distribution

as

as arguments we input the absolute value

of our z stat

and one for cumulative and here we can

get our p values for

every single coefficient and here we can

see that

the most significant of the predictors

of default

are being full-time employed so if you

are

employed full-time you're much less

likely to default on your

consumer credit and also the significant

positive predictors of

default leverage and repayment

time given income the more leveraged you

are the less likely you are to repay

and the more it would take you to repay

your loan out of your income

the less likely you are to repay while

three other parameters the constant and

most notably

homeownership and expense to income

ratio

are of expected science but not as

significant as one could imagine given

these p-values

are greater than ten percent and now

we can use our logic model to actually

predict

uh whether a particular individual would

default

imagine we have got this model uh up and

running in our bank

and someone approaches us and asks out

for a loan so we in our credit scoring

procedure

ask them to provide some data about them

so obviously the constant

would be one um as it's always one

that's why it's a constant

uh and we ask the applicant whether they

own a home

and uh imagine they say yes

and we put one for yes then

we ask if they have a full-time job and

they say

yes and provide some evidence for that

then to calculate these three variables

we need to ask them

about their income expenses asset that

and what is the loan amount they want to

apply for

so imagine that this particular person's

household

makes 150 000 per year

and they spend roughly 120 000 of it

they own their home and it's currently

valued at

one uh one thousand thousand dollars so

one million dollars

and they haven't got any debt taken on

previously

and they want to take out one million

dollars

in loan potentially guaranteed as

collateral

by their property by their house so now

we can actually just copy these formulas

across

to calculate these ratios and we can

also copy this across to calculate our

log it

and our probability can be calculated

just like that

and we can see that our probability

which is

logged divided by one plus logit is less

than 20

so actually we can be reasonably sure

that such a person would not default on

their loan

their default probability being less

than 20 percent

19.19 which is quite good which is also

less than average over here we can see

that

roughly a quarter of our applicant's

default

and the probability of this applicant

defaulting is less than 20

so we can determine that our applicant

is actually credit worthy

and feel quite good about providing them

with a low and that's all there is for

the logit model

and its application for consumer credit

risk credit scoring

and much more please leave a like on

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