Introduction to Regression Models (Fundamentals of Quantitative Modeling)

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Из курса от партнера University of Pennsylvania

Wharton Business and Financial Modeling Capstone

307 оценки

University of Pennsylvania

Wharton Business and Financial Modeling Capstone

307 оценки

Курс 5 из 5 — Specialization Business and Financial Modeling

In this Capstone you will recommend a business strategy based on a data model you’ve constructed. Using a data set designed by Wharton Research Data Services (WRDS), you will implement quantitative models in spreadsheets to identify the best opportunities for success and minimizing risk. Using your newly acquired decision-making skills, you will structure a decision and present this course of action in a professional quality PowerPoint presentation which includes both data and data analysis from your quantitative models. Wharton Research Data Services (WRDS) is the leading data research platform and business intelligence tool for over 30,000 corporate, academic, government and nonprofit clients in 33 countries. WRDS provides the user with one location to access over 200 terabytes of data across multiple disciplines including Accounting, Banking, Economics, ESG, Finance, Insurance, Marketing, and Statistics.

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Step 4: Optional exercise using CAPM tables

The Capital Asset Pricing Model, or CAPM, is another tool used by investors to weigh the risks and rewards of potential investments. In this optional module covering Step 4 in the Project Prompt, you can use CAPM as a vehicle to further strengthen your financial modeling skills, including using regression concepts. You may revisit the Specialization lectures below touching on regression. To test whether you've grasped the concepts in the CAPM model, this module includes a short quiz. This assessment is formative, meaning your score will not count towards your final grade. The work you do this week may inform how you build the mixed asset portfolio of your final project, but it is not necessary to complete the final project.

Introduction to Regression Models (Fundamentals of Quantitative Modeling)7:16

Use of Regression Models (Fundamentals of Quantitative Modeling)15:33

Correlation and Regression (Introduction to Spreadsheets)7:28

Познакомьтесь с преподавателями

Richard Lambert
Professor of Accounting
Accounting- Wharton School
Robert W. Holthausen
Professor
Accounting
Don Huesman
Managing Director, Wharton Online
Innovation Group- Wharton School
Richard Waterman
Professor of Statistics
Statistics-Wharton School

Welcome to Fundamentals of Quantitative Modeling: Regression models.

In this module, we're going to talk about a regression model.

We'll define what that is.

We'll discuss questions that a regression model is able to answer for us.

We're going to talk about correlation.

And linear association because these regression models are examples of

linear models.

We're going to discuss the mechanics of fitting a line to data.

We are going to spend some time interpreting

the output from these regression models.

And we're going to talk about prediction and

in particular prediction intervals from a regression model.

We will briefly see the topic known as multiple regression it allows us to create

potentially more complicated and realistic models of a business process.

We'll end up by talking about logistic regression which is an appropriate form

of regression to use when the outcome variable is a categorical variable.

Typically, a zero one outcome a binary random variable.

So what is a regression model?

Well, a simple regression model uses a single predictor variable

with which often give the letter X to, to estimate the mean or

the average of an outcome variable Y as some function of X.

And so, the example that I have here plots

the price against the weight of a set of diamonds.

Each point in the plot represents a diamond.

The X coordinate is the weight of the diamond and

the Y coordinate is the price of the diamond.

So, there's a single predictor, that's why we say a simple regression and

what a regression model will do is say at any given value of X.

What do you expect Y, the price to be?

So that's the idea of a regression model.

It's a model for the mean of Y as a function of X, and

very frequently we will use a linear model to capture the relationship.

Continuing with the diamonds example, the predictive variable

is the diamonds weight and the outcome variable is the price of the diamond.

Now, we can see just by looking at the plot that heavier stones, bigger

diamonds tend to cost more money, we would often term that positive association.

But, we can go beyond that simple statement by using a regression model

that will formalize the idea of the association.

And more precisely define how we expect or

what value we expect the price to be at for any given weight of a diamond.

So we're going to formalize how the expected price varies with weight.

And as I just said, one of our most frequently used ways of capturing that

relationship is with a straight line, and we'll then call it a linear regression.

The formula that you can see at the bottom of this slide is how I

would write a regression model.

And it says that the expected value that's the average of y and

then, the straight line there means given, we articulate that as given.

The expected value of Y given X.

The expected price of a diamond given its weight

is then equal to some function of X and

the most straightforward function that we might choose to use is a linear function.

And we write the linear function in this instance as b knot plus b1 times X.

Sometimes you will have seen the equation of a straight line written as Y equals

MX plus b.

This is still a straight line but we have a slightly different notation

typically in the regression models and there's a reason for that.

And the reason is that there's a form of regression called multiple

regression which has many Xs in and

then we can use a notation that incorporates B1, B0, B1, B2, B3 etc.

So we subscript the coefficients,

B naught is still the intercept and B1 is still the slope.

So a regression model is relating the average of Y to a particular value of

x and it's not at all uncommon to assert that that association

is at least approximately linear and in that case we're doing a linear regression.

On this slide, I have overlaid

the straight line model that is calculated from the underlying data.

I haven't told you how this line is calculated yet, I will.

In a few minutes, but there is the regression line and the slope and

intercept in this particular instance, are presented in the formula below.

The expected value of the, price of a diamond, given it's weight,

is equal to -260, that is the intercept, plus 3721 times the weight,

whether weight is measured in carats.

So that's what a linear regression is going to do for you,

it's going to put a line through the data basically.

And once you've got a line going through the data there are a number of

useful things that you're going to be able to do with that.

So there's a quantitative model that has been derived from underlying data.

So we let the data talk to us in the sense that the data chose the best fitting line.

Now there's a very commonly used number

to describe the strength of what we term linear association.

So essentially, how close are the points to a line?

The way that we capture that is through a concept called correlation.

So correlation is a measure of the strength of a linear association and

correlation is typically given a lesser, we called r the sample correlation.

And it's a fact that the correlation will always lie between- 1 and + 1.

If you have a negative value to the correlation then you have negative

association that would be a lying from top left of the bottom right we

had positive correlation.

You got positive association,

that would be aligned from the bottom left of the top-right.

But if you have zero correlation,

what that means is that this no linear association.

It doesn't actually means there no association between the two variables just

as there's no linear association between the two variables.

Now how would you calculate the correlation in practice?

The answer is with a computer program or a spreadsheet.

So we won't worry about the details or the actual calculation, it will happen.

And I have calculated the correlation for

the diamond's data set and it turns out to be 0.989.

There's the correlation,

which is incredibly a strong correlation as far as correlations go and it's just

asserting the fact that the points really do lie very close to a straight line.

So a linear model is quite reasonable in this particular instance.

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