In this final lesson on Regression, one of the basic _classic_ ML techniques, we will take a look at Logistic Regression. You would use this technique to discover patterns to predict binary categories. Is this candy chocolate or not? Is this disease contagious or not? Will this customer choose this product or not?
✅ Deepen your understanding of working with this type of regression in this [Learn module](https://docs.microsoft.com/learn/modules/train-evaluate-classification-models?WT.mc_id=academic-77952-leestott)
> Why are we talking about binary classification in a lesson grouping about regression? Only for linguistic convenience, as logistic regression is [really a classification method](https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression), albeit a linear-based one. Learn about other ways to classify data in the next lesson group.
For our purposes, we will express this as a binary: 'White' or 'Not White'. There is also a 'striped' category in our dataset but there are few instances of it, so we will not use it. It disappears once we remove null values from the dataset, anyway.
> 🎃 Fun fact, we sometimes call white pumpkins 'ghost' pumpkins. They aren't very easy to carve, so they aren't as popular as the orange ones but they are cool looking! So we could also reformulate our question as: 'Ghost' or 'Not Ghost'. 👻
Logistic regression does not offer the same features as linear regression. The former offers a prediction about a binary category ("white or not white") whereas the latter is capable of predicting continual values, for example given the origin of a pumpkin and the time of harvest, _how much its price will rise_.
- **Multinomial**, which involves having more than one category - "Orange, White, and Striped".
- **Ordinal**, which involves ordered categories, useful if we wanted to order our outcomes logically, like our pumpkins that are ordered by a finite number of sizes (mini,sm,med,lg,xl,xxl).
Remember how linear regression worked better with more correlated variables? Logistic regression is the opposite - the variables don't have to align. That works for this data which has somewhat weak correlations.
[](https://youtu.be/B2X4H9vcXTs "ML for beginners - Data Analysis and Preparation for Logistic Regression")
> 🎥 Click the image above for a short video overview of preparing data for linear regression
By now you have loaded up the [starter notebook](./notebook.ipynb) with pumpkin data once again and cleaned it so as to preserve a dataset containing a few variables, including `Color`. Let's visualize the dataframe in the notebook using a different library: [Seaborn](https://seaborn.pydata.org/index.html), which is built on Matplotlib which we used earlier.
Seaborn offers some neat ways to visualize your data. For example, you can compare distributions of the data for each `Variety` and `Color` in a categorical plot.
1. Create such a plot by using the `catplot` function, using our pumpkin data `pumpkins`, and specifying a color mapping for each pumpkin category (orange or white):
Our pumpkins dataset contains string values for all its columns. Working with categorical data is intuitive for humans but not for machines. Machine learning algorithms work well with numbers. That's why encoding is a very important step in the data pre-processing phase, since it enables us to turn categorical data into numerical data, without losing any information. Good encoding leads to building a good model.
1. Ordinal encoder: it suits well for ordinal variables, which are categorical variables where their data follows a logical ordering, like the `Item Size` column in our dataset. It creates a mapping such that each category is represented by a number, which is the order of the category in the column.
2. Categorical encoder: it suits well for nominal variables, which are categorical variables where their data does not follow a logical ordering, like all the features different from `Item Size` in our dataset. It is a one-hot encoding, which means that each category is represented by a binary column: the encoded variable is equal to 1 if the pumpkin belongs to that Variety and 0 otherwise.
On the other hand, to encode the label, we use the scikit-learn `LabelEncoder` class, which is a utility class to help normalize labels such that they contain only values between 0 and n_classes-1 (here, 0 and 1).
Now that we have pre-processed our data, we can analyse the relationships between the features and the label to grasp an idea of how well the model will be able to predict the label given the features.
The best way to perform this kind of analysis is plotting the data. We'll be using again the Seaborn `catplot` function, to visualize the relationships between `Item Size`, `Variety` and `Color` in a categorical plot. To better plot the data we'll be using the encoded `Item Size` column and the unencoded `Variety` column.
Since Color is a binary category (White or Not), it needs 'a [specialized approach](https://seaborn.pydata.org/tutorial/categorical.html?highlight=bar) to visualization'. There are other ways to visualize the relationship of this category with other variables.
**Watch Out**: the code above might generate a warning, since seaborn fails to represent such amount of datapoints into a swam plot. A possible solution is decreasing the size of the marker, by using the 'size' parameter. However, be aware that this affects the readability of the plot.
> Logistic regression relies on the concept of 'maximum likelihood' using [sigmoid functions](https://wikipedia.org/wiki/Sigmoid_function). A 'Sigmoid Function' on a plot looks like an 'S' shape. It takes a value and maps it to somewhere between 0 and 1. Its curve is also called a 'logistic curve'. Its formula looks like this:
> where the sigmoid's midpoint finds itself at x's 0 point, L is the curve's maximum value, and k is the curve's steepness. If the outcome of the function is more than 0.5, the label in question will be given the class '1' of the binary choice. If not, it will be classified as '0'.
[](https://youtu.be/MmZS2otPrQ8 "ML for beginners - Logistic Regression for classification of data")
> 🎥 Click the image above for a short video overview of building a linear regression model
While you can get a scoreboard report [terms](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html?highlight=classification_report#sklearn.metrics.classification_report) by printing out the items above, you might be able to understand your model more easily by using a [confusion matrix](https://scikit-learn.org/stable/modules/model_evaluation.html#confusion-matrix) to help us understand how the model is performing.
> 🎓 A '[confusion matrix](https://wikipedia.org/wiki/Confusion_matrix)' (or 'error matrix') is a table that expresses your model's true vs. false positives and negatives, thus gauging the accuracy of predictions.
- If your model predicts a pumpkin as not white and it belongs to category 'not-white' in reality we call it a true negative, shown by the top left number.
- If your model predicts a pumpkin as white and it belongs to category 'not-white' in reality we call it a false negative, shown by the bottom left number.
- If your model predicts a pumpkin as not white and it belongs to category 'white' in reality we call it a false positive, shown by the top right number.
- If your model predicts a pumpkin as white and it belongs to category 'white' in reality we call it a true positive, shown by the bottom right number.
As you might have guessed it's preferable to have a larger number of true positives and true negatives and a lower number of false positives and false negatives, which implies that the model performs better.
How does the confusion matrix relate to precision and recall? Remember, the classification report printed above showed precision (0.85) and recall (0.67).
🎓 Macro Avg: The calculation of the unweighted mean metrics for each label, not taking label imbalance into account.
🎓 Weighted Avg: The calculation of the mean metrics for each label, taking label imbalance into account by weighting them by their support (the number of true instances for each label).
Using Matplotlib, plot the model's [Receiving Operating Characteristic](https://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html?highlight=roc) or ROC. ROC curves are often used to get a view of the output of a classifier in terms of its true vs. false positives. "ROC curves typically feature true positive rate on the Y axis, and false positive rate on the X axis." Thus, the steepness of the curve and the space between the midpoint line and the curve matter: you want a curve that quickly heads up and over the line. In our case, there are false positives to start with, and then the line heads up and over properly:
Finally, use Scikit-learn's [`roc_auc_score` API](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_auc_score.html?highlight=roc_auc#sklearn.metrics.roc_auc_score) to compute the actual 'Area Under the Curve' (AUC):
The result is `0.9749908725812341`. Given that the AUC ranges from 0 to 1, you want a big score, since a model that is 100% correct in its predictions will have an AUC of 1; in this case, the model is _pretty good_.
In future lessons on classifications, you will learn how to iterate to improve your model's scores. But for now, congratulations! You've completed these regression lessons!
There's a lot more to unpack regarding logistic regression! But the best way to learn is to experiment. Find a dataset that lends itself to this type of analysis and build a model with it. What do you learn? tip: try [Kaggle](https://www.kaggle.com/search?q=logistic+regression+datasets) for interesting datasets.
Read the first few pages of [this paper from Stanford](https://web.stanford.edu/~jurafsky/slp3/5.pdf) on some practical uses for logistic regression. Think about tasks that are better suited for one or the other type of regression tasks that we have studied up to this point. What would work best?
