3. Multiple Regression

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Из курса от партнера University of Colorado Boulder

Predictive Modeling and Analytics

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University of Colorado Boulder

Predictive Modeling and Analytics

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Курс 2 из 5 — 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.

Из урока

Predicting a Continuous Variable

This module introduces regression techniques to predict the value of continuous variables. Some fundamental concepts of predictive modeling are covered, including cross-validation, model selection, and overfitting. You will also learn how to build predictive models using the software tool XLMiner.

1. Introduction to Linear Regression8:33

2. Assessing Predictive Accuracy Using Cross-Validation5:18

3. Multiple Regression4:10

4. Improving Model Fit3:45

5. Model Selection3:25

6. Challenges of Predictive Modeling5:06

7. How to Build a Model using XLMiner8:02

Познакомьтесь с преподавателями

Dan Zhang
Professor
Leeds School of Business

So far, we have

discussed linear regression with a single predictive variable.

Such regression models are also called, simple regression models.

As we showed before, a regression model with one predictive variable,

can be realized as a line, and is relatively easy to understand.

However, simple regression models are usually not practical, as we often

expect the target variable to be related to more than one predictive variable.

A regression model with more than one predictive variable,

is called a multiple regression model.

Realizing the multi-regression model is much harder,

as we have to deal with the rather abstract, high-dimensional space.

In a high-dimensional space, a linear function of the predictive variables,

defines a plane, or a flat surface.

Fortunately, most of the intuition we obtain from simple regression,

can be extended to multiple regression.

To give a concrete example, we consider one more predictive variable.

The side-by-side box plot, shows the list prices for homes, with and

without a garage.

Notice that homes with a parking garage are typically more expensive, and

the list prices exhibited much more variability.

This is a strong indication that the PARKING.TYPE variable,

our facts are target variable of interest, the list price.

In this scatter plot, I plotted homes with and without a garage in different colors.

Homes with garages are blue, and homes without garages are red.

There are many more homes with a packing garage.

Given the heavy snowfall from time to time in Boulder, this is not too surprising.

This graph also confirms that homes with parking garages tend to be more expensive,

as red circles are concentrated in the lower left corner of the graph.

To add PARKING.TYPE to the regression model, the regression equation will have

one more term on the right-hand side, which measures the impact of PARKING.TYPE.

As before, what had represented the predicted value of the list price?

b0 is the intercept, and b1 is the slope for square footage.

We also have b2, as the slope of PARKING.TYPE.

For the data set we have, we obtain that b0 is about -43,

b1 is 0.43, and b2 is -99.

Note that b2 essentially changes the value of the intercept.

When PARKING.TYPE equal to 1, or in other words, there is a garage,

we deduct 99 from the intercept.

When PARKING.TYPE is 0, the last term on the right-hand side vanishes,

and intercept stays at about 43.

Another way to interpret this result is that,

garage parking is worth about, elective $99,000.

This is quite surprising, intuitively, we expect that houses

with garage parking to be worth more, which we demonstrated visually before.

This cautions us in interpreting regression results, the underlying

intuitive result here can be contributed to what we call multicollinearity,

which is a very important concept in multiple regression.

Multicollinearity, also called collinearity, is a phenomenon in which two

or more predictor variables in a multiple regression model are highly correlated.

In this particular example, PARKING.TYPE and square feet are correlated

in a sense that, larger houses are more likely to have garage.

When you add PARKING.TYPE to the model, you can see the estimates for

different predictive variables vary considerably.

This creates two issues, in the extreme case,

when two variables are highly correlated, the numerical procedure that we use to

estimate the regression models becomes unstable, in the sense that,

a small change in the data can cause huge swing in the coefficient estimate.

That is certainly an undesirable feature of the linear regression model.

The second issue is that,

multicollinearity causes difficulty in interpreting modeling results.

We would like to attach an intuitive interpretation to the coefficient

estimates, however,

changing used estimates depends on predictors included in the model.

Therefore, certain interpretations may not be as reliable

as we are willing to believe.

This is not as serious an issue,

if we're only interested in the predictive accuracy of the models.

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