4.8 Summary of Regression Models

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University of Pennsylvania 提供のコース

Fundamentals of Quantitative Modeling

3711件の評価

University of Pennsylvania

Fundamentals of Quantitative Modeling

3711件の評価

Specialization Business and Financial Modeling における 5 の 1 コース

How can you put data to work for you? Specifically, how can numbers in a spreadsheet tell us about present and past business activities, and how can we use them to forecast the future? The answer is in building quantitative models, and this course is designed to help you understand the fundamentals of this critical, foundational, business skill. Through a series of short lectures, demonstrations, and assignments, you’ll learn the key ideas and process of quantitative modeling so that you can begin to create your own models for your own business or enterprise. By the end of this course, you will have seen a variety of practical commonly used quantitative models as well as the building blocks that will allow you to start structuring your own models. These building blocks will be put to use in the other courses in this Specialization.

レッスンから

Module 4: Regression Models

This module explores regression models, which allow you to start with data and discover an underlying process. Regression models are the key tools in predictive analytics, and are also used when you have to incorporate uncertainty explicitly in the underlying data. You’ll learn more about what regression models are, what they can and cannot do, and the questions regression models can answer. You’ll examine correlation and linear association, methodology to fit the best line to the data, interpretation of regression coefficients, multiple regression, and logistic regression. You’ll also see how logistic regression will allow you to estimate probabilities of success. By the end of this module, you’ll be able to identify regression models and their key components, understand when they are used, and be able to interpret them so that you can discuss your model and convince others that your model makes sense, with the ultimate goal of implementation.

4.1 Introduction to Regression Model7:16

4.2 Use of Regression Models15:33

4.3 Interpretation of Regression Coefficients4:32

4.4 R-squared and Root Mean Squared Error (RMSE)12:58

4.5 Fitting Curves to Data8:44

4.6 Multiple Regression7:27

4.7 Logistic Regression8:54

4.8 Summary of Regression Models4:32

コースの提供者

Richard Waterman
Professor of Statistics
Statistics-Wharton School

So just summarizing what we've seen in this model.

At the top level, we've been introduced to this idea of regression models.

Regression models are how you start off with data and

you reverse engineer an approximation to the underlying process.

In particular, you're modeling the mean of y as a function of x.

Sometimes, we'll use a straightforward linear regression model, but

we certainly are going to be willing to transform if we see curvature.

And sometimes, if our outcome variable is not a continuous variable,

we might consider using a logistic regression.

So we discussed regression models.

We talked about the questions regression models can answer.

In particular, regression modeling is your go to tool for predictive analytics.

But the important thing about a regression model

is because it incorporates uncertainty explicitly in the underlying data,

it's going to provide you with ranges for those forecasts.

Not just best guesses, which we sometimes call point estimates.

We'll give you a range of feasible values.

We've discussed correlation and linear association.

Correlation is a one number summary that is useful for basically saying,

how close are my points to a line?

How well does a line fit the data?

We've discussed the methodology that we used to fit the best line,

that's known as the method of least squares.

Find the line that minimizes the sum of the squares of the vertical distance of

the point to the light.

We've discussed interpreting regression coefficients.

Remember that interpreting your quantitative models is a very,

very important step.

If you can interpret your model,

you have a chance of discussing your model with other people.

And if you can discuss and convince people that your model makes sense,

is useful, then you have a chance of implementation,

which is typically our ultimate goal with the modeling process.

So we talked about interpretation regression coefficients.

We saw prediction from these regression models, and in particular the idea

of using the root mean squared error, the standard deviation of the residuals from

the regression, to create approximate 95% prediction intervals.

Now the sort of interval that I presented to you in these slides relied

upon a normality assumption for the spread of the points around the regression line.

Now that's an example of an assumption and if we're a good modeler,

we're going to check our assumptions.

And the way that I thought about doing that was saving the residuals from

the regression model, and then plotting them.

Plotting a histogram of the residuals and asking myself the question,

does it look like these residuals are approximately normally distributed?

In the example that I showed you, the answer to that question was yes, and so

we had some support for our underlying assumption.

So there's a bigger story here if you're making assumptions,

you need to check them.

We call those model diagnostics.

We also talked about multiple regression,

which is how we start to make more realistic models of the world.

If you don't think a simple regression is doing enough for you, for

example the prediction intervals are too wide for your use, you might look for

some additional predictor variables.

So we talked about putting horsepower into the fuel economy model.

And of course, there are many, many other variables that one could incorporate.

This is why these regression models are always implemented in software.

Nobody does these calculations by hand anymore.

With your spreadsheet program you're going to be able to fit these regression models.

We went beyond multiple regression with a discussion of logistic regression.

And the thing to remember about logistic regression is that it is an appropriate

methodology when the outcome variable is not continuous but rather dichotomous.

And many business processes that you come across are going to

generate dichotomous outcomes that you're interested in modeling.

For example, conversions on a website.

Does someone on my website buying my product, yes or no?

That's a dichotomous outcome formerly called a Bernoulli random variable.

And a suitable approach, a suitable type of regression model for

that sort of outcome is called a logistic regression.

And the logistic regression will allow you to estimate probabilities of success,

probabilities of purchase as a function of a set of predictive variables.

So that's what we covered in this module.

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