2. Building Logistic Regression Model

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来自 University of Colorado Boulder 的课程

Predictive Modeling and Analytics

150 个评分

University of Colorado Boulder

Predictive Modeling and Analytics

150 个评分

课程 2（共 5 门，Specialization Advanced Business Analytics）

Welcome to the second course in the Data Analytics for Business specialization! This course will introduce you to some of the most widely used predictive modeling techniques and their core principles. By taking this course, you will form a solid foundation of predictive analytics, which refers to tools and techniques for building statistical or machine learning models to make predictions based on data. You will learn how to carry out exploratory data analysis to gain insights and prepare data for predictive modeling, an essential skill valued in the business. You’ll also learn how to summarize and visualize datasets using plots so that you can present your results in a compelling and meaningful way. We will use a practical predictive modeling software, XLMiner, which is a popular Excel plug-in. This course is designed for anyone who is interested in using data to gain insights and make better business decisions. The techniques discussed are applied in all functional areas within business organizations including accounting, finance, human resource management, marketing, operations, and strategic planning. The expected prerequisites for this course include a prior working knowledge of Excel, introductory level algebra, and basic statistics.

从本节课中

Predicting a Binary Outcome

This module introduces logistic regression models to predict the value of binary variables. Unlike continuous variables, a binary variable can only take two different values and predicting its value is commonly called classification. Several important concepts regarding classification are discussed, including cross validation and confusion matrix, cost sensitive classification, and ROC curves. You will also learn how to build classification models using the software tool XLMiner.

1. Introduction to Logistic Regression4:02

2. Building Logistic Regression Model6:08

3. Multiple Logistic Regression3:05

与讲师见面

Dan Zhang
Professor
Leeds School of Business

In this video, we use an example to illustrate how to pair a logistic

regression model and interpret the result.

Missed appointments cost the US healthcare system over $150 billion a year.

Missed appointments directly cause loss of revenue and

under-utilization of precious medical resources.

It also leads to long patient waiting times and in the long run,

leads to higher medical costs.

We obtained a data set with 7,463 medical appointments over a three year

period at a specialized care clinic.

In this data set, each row corresponds to an appointment and

indicates whether it was cancelled or not.

In total, 1662 out of 7463 appointments were cancelled.

Since we are interested in appointment cancellations,

the target variable is whether an appointment is cancelled or

not and success in this particular context means that an appointment is cancelled.

The data set has many columns.

The columns can be roughly divided into two groups.

One group captures appointment information.

One particularly important variable here is lag,

which is the time between appointment date and the time an appointment was made.

For example, if an appointment is made one week in advance, then the lag is seven,

representing a time difference of seven days between appointment date and

the time appointment was made.

The other group is patient information, including personal information such as

gender, age, martial status, employment status, and medical related information,

such as time since the patient registered with the clinic and

the insurance policies the patient carries.

We will only use a few columns of the data set.

We would like to explore the relationship between appointment lag and

appointment status.

We'll first explore the data using different graphs.

Note that here the appointment lag is a numerical variable, but

the appointment status is a categorical variable.

Therefore, a scatter plot cannot be used.

Here is a histogram of the appointment lag.

Observe that the lag ranges between 0 and 130 and its distribution is right skewed.

The majority of appointments are made within 60 days.

The distribution is bi-modal with one mode between 10 and 20, and

another mode between 90 and 100.

Another way to explore the relationship is to use a bar graph.

This bar graph shows the number of cancelled appointments

against appointment lag.

Not surprisingly, most cancelled appointments have lag less than 60.

This is simply because the majority of appointments have lag less than 60.

In fact, the pattern of the bars are similar to that in a histogram of

appointment lags.

Perhaps a more relevant statistic here is the cancellation rate,

which is the proportion of cancelled appointments.

This rate can be used as an estimate of cancellation probability.

This line graph shows the cancellation rate against lag.

The cancellation rate fluctuates widely as a function of lag.

However, line graph seems to have some positive trend,

where cancellation rate appears to be higher for larger lag values.

Our logistical regression model will try to capture this trend.

Here is our first logistic regression model, where we model the log odds of

appointment cancellation as a linear function of the lag variable.

Beta 0 and beta 1 here are the intercept and slope respectively.

After the model, we obtain beta 0 equal to minus 1.7431 and

beta y equals to 0.01658.

Let me emphasize here that the coefficient estimates, beta 0 and

beta 1 are related to the cancellation probabilities in a non-linear manner.

These coefficients are relative log odds in a linear manner.

For example, for one day increase in lag, the log odds increases by beta 1.

By exponentiating on both sides, we obtain the odds.

After some algebra,

we obtain the cancellation probability as a logistic function.

It can be verified that since beta 1 is a positive number,

the predicted probability is increasing in lag.

That is, appointments with longer lags are more likely to be cancelled.

The equation can be used to make predictions on cancellation probabilities.

What is the predicted cancellation probability for

an appointment with a 10 day lag?

Taking lag equal to 10 and plugging it into the equation, we obtain 0.1712.

Therefore, the predicted cancellation probability is 17.12%.

How do we assess model feed for logistic regression?

For linear regression, we discussed before, we can use r squared.

However, r squared is not applicable to logistic regression.

There are several commonly used measures including pseudo r squared, deviance,

and AIC.

These measures are used for comparing models.

In general, larger pseudo r squared, smaller deviance and

a smaller AIC are preferred.

Note that there are many different variances of pseudo r squared.

All of them try to mimic r squared for linear regression and

have similar properties as r squared.

Several tools typically report a subset of these measures.

For example, rx minor reports both pseudo r squared and deviance.

Another question is how reliable the coefficient estimates are?

Like linear regression, this question can be assessed using statistical

significance, indicated by p-values.

For our models, p-values for both coefficients are close to zero,

indicating that both coefficients are statistically significant.

P value can also be used as an imperfect way to determine whether to include

a variable.

Coefficients in logistic regression model represent the change in the log odds of

the outcome for one unit increase in the predictor variable.

In our model, the coefficient estimate beta 1 gives the increase in log odds for

one day increase in the value of the lag variable.

It is common to exponentiate the coefficients and interpret them as odds,

which might be more intuitive to understand.

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