Measures for In-Sample Evaluation

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来自 IBM 的课程

Data Analysis with Python

262 个评分

IBM

Data Analysis with Python

262 个评分

课程 7（共 9 门，Specialization IBM Data Science Professional Certificate）

Learn how to analyze data using Python. This course will take you from the basics of Python to exploring many different types of data. You will learn how to prepare data for analysis, perform simple statistical analyses, create meaningful data visualizations, predict future trends from data, and more! Topics covered: 1) Importing Data sets 2) Cleaning the Data 3) Data frame manipulation 4) Summarizing the Data 5) Building machine learning Regression models 6) Building data pipelines Data Analysis with Python will be delivered through lecture, lab, and assignments. It includes following parts: Data Analysis libraries: will learn to use Pandas, Numpy and Scipy libraries to work with a sample dataset. We will introduce you to pandas, an open-source library, and we will use it to load, manipulate, analyze, and visualize cool datasets. Then we will introduce you to another open-source library, scikit-learn, and we will use some of its machine learning algorithms to build smart models and make cool predictions. If you choose to take this course and earn the Coursera course certificate, you will also earn an IBM digital badge. LIMITED TIME OFFER: Subscription is only $39 USD per month for access to graded materials and a certificate.

从本节课中

Model Development

Model Development1:44

Linear Regression and Multiple Linear Regression6:34

Model Evaluation using Visualization4:44

Polynomial Regression and Pipelines4:25

Measures for In-Sample Evaluation3:37

Prediction and Decision Making5:03

与讲师见面

Joseph Santarcangelo
Ph.D., Data Scientist at IBM
IBM Developer Skills Network

Now that we've seen how we can evaluate a model by using visualization,

we want to numerically evaluate our models.

Let's look at some of the measures that we use for in-sample evaluation.

These measures are a way to numerically determine how good the model fits on our data.

Two important measures that we often use to determine the fit of a model

are mean squared error (MSE) and R-squared.

To measure the MSE,

we find the difference between the actual value Y

and the predicted value Y-hat, then square it.

In this case, the actual value is 150.

The predicted value is 50.

Subtracting these points, we get 50.

We then square the number.

We then take the mean or average of all the errors by

adding them all together and dividing by the number of samples.

To find the MSE in Python,

we can import the mean_squared_error from sklearn metrics.

The mean_squared_error function gets two inputs.

The actual value of target variable and the predicted value of target variable.

R-squared is also called the coefficient of determination.

It's a measure to determine how close the data is to the fitted regression line.

So how close is our actual data to our estimated model?

Think about it as comparing a regression model to a simple model, i.e.

the mean of the data points.

If the variable x is a good predictor,

our model should perform much better than just the mean.

In this example, the average of the data points Y Bar is six,

coefficient of determination R-squared is one minus the ratio of

the MSE of the regression lined divided by the MSE of the average of the data points.

For the most part it takes values between zero and one.

Let's look at a case where the line provides a relatively good fit.

The blue line represents the regression line.

The blue squares represent the MSE of the regression line.

The red line represents the average value of the data points.

The red squares represent the MSE of the red line.

We see the area the blue squares is much smaller than the area the red squares.

In this case, because the line is

a good fit the mean squared error is small therefore the numerator is small.

The mean squared error of the line is relatively large,

as such, the numerator is large.

A small number divided by a larger number is an even smaller number.

Taken to an extreme,

this value tends to zero.

If we plug in this value from the previous slide for R-squared,

we get a value near one.

This means the line is a good fit for the data.

Here is an example of a line that does not fit the data well.

If we just examine the area of the red squares compared to the blue squares,

we see the area is almost identical.

The ratio of the areas is close to one.

In this case the R-squared is near zero.

This line performs about the same as just using the average of the data points.

Therefore this line did not perform well.

We find the R-squared value in Python by using

the score method in the linear regression object,

from the value that we get from this example.

We can say that approximately 49.695

percent of the variation of price is explained by the simple linear model.

Your R-squared value is usually between zero and one.

If your R-squared is negative,

it could be due to overfitting that we will discuss in the next module.

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