Interactive Regression Builder MicroSim

Run the Interactive Regression Builder MicroSim Fullscreen
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About This MicroSim

The scatter plot is yours to edit. Click to add a point, drag a point to move it, and double-click a point to remove it. After every change the model is fitted again by ordinary least squares, the same calculation that scikit-learn's LinearRegression performs.

The panel reports:

the equation \(\hat{y} = \beta_0 + \beta_1 x\) with the current coefficients
the slope and the intercept in plain language with units, and a caution when \(x = 0\) is far outside the data
R², the share of the variation in \(y\) that the line explains, \(R^2 = 1 - \text{SSE}/\text{SST}\), with a bar from 0 to 1
RMSE, \(\sqrt{\text{SSE}/n}\), the typical size of a prediction error (the value of np.sqrt(mean_squared_error(y, y_pred)))
a prediction for the \(x\) you type, with a warning when that \(x\) is outside your data (extrapolation)

The residual plot under the scatter plot shows \(y - \hat{y}\) at each \(x\) on the same horizontal scale.

Four starting data sets are provided. Study hours vs score is the chapter's eight-student example, and its fit matches what scikit-learn returns for that data: \(\hat{y} = 47.04 + 5.71x\) with \(R^2 = 0.997\). House size vs price, Car age vs value, and Random come from a seeded generator, so they are the same on every load. In the two money data sets the y-axis is in thousands of dollars.

Not included: a confidence band, a confidence interval for the prediction, a noise slider, and assumption indicators. The residual plot uses \(x\) on its horizontal axis. With one predictor this shows the same pattern as a plot against fitted values.

How to Use

Choose a Data set. Read the equation and the two interpretation sentences.
Drag one point far from the line and watch the slope, R², and RMSE change. Drag it back.
Click empty space to add a point. Double-click a point to remove it. Clear All gives a blank plot for your own data.
Type a value in Predict at x to see the predicted value as a green diamond on the line. Try a value outside your data to see the extrapolation warning.
Uncheck Show residuals to hide the red residual segments in the scatter plot.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://dmccreary.github.io/data-science-course/sims/interactive-regression-builder-microsim/main.html"
        height="622"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

High School (11-12) and College Freshman

Duration

15-20 minutes

Prerequisites

The regression equation, residuals, and the idea that least squares picks the line with the smallest sum of squared errors.

Bloom's Taxonomy Level

Create (L6)

Learning Objective

Students will be able to construct data sets with a required slope, strength of fit, or outlier, and interpret the fitted model's coefficients, R², RMSE, and predictions.

Activities

Interpret (4 min): Students load each data set and write the slope and intercept interpretations in their own words, noting where the intercept has no real meaning.
Build (8 min): Starting from Clear All, students build three data sets: one with R² above 0.9, one with a negative slope, and one with R² below 0.1. They sketch each one and record its equation.
Break (5 min): Students load the study-hours data, add one outlier, and record how far the slope, R², and RMSE move. They compare an outlier near the middle of the x range with one at the end.

Assessment

Students build a data set of at least eight points whose fitted slope is between 2 and 3 and whose R² is above 0.8. They write the equation, interpret both coefficients, and explain whether a prediction at an x value of their choice is an interpolation or an extrapolation.

References

scikit-learn documentation. LinearRegression.
scikit-learn documentation. r2_score.
Wikipedia. Coefficient of determination.