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## Linear regression

Demo 1:
• Use default data, or paste in data and click "Use Data".
• Click "Show Movable line". Use the square green dots on the line to move it around (center green dot moves it up and down; endpoints change slope).
• Click "Show Squared Residuals". Move the line some more. Try to manually minimize SSE (sum of squared errors).
• Click "Show Regression Line", the "Show Squared Residuals" under it, and see how close you get to the optimal SSE.
• Click "Correlation" and "R-squared".
• Note: Using "Show Residuals" instead of "Show Squared Residuals"
minimizes SAE = sum of absolute values of residuals
instead of SSE = sum of squared residuals,
so it doesn't match what we're doing.
Demo 2:
• Click on a bunch of points on the grid to create data (blue points). Make it have a linear tendency, but not a perfect line. Alternately, paste a dataset into the coordinates box and hit "Update Plot".
• Click BOTH "Fit your own line" and "Move Your Fit Line" and then drag the big green dots to move the line.
• Click "Show Residuals" and move the line around some more. Try to collectively minimize the residuals. (It would be better if it gave the sum of squared errors, like SSE in demo 1.)
• Click "Display line of best fit" and see how close you got.