What quantity did you change?
Labs / Mathematics
Least Squares Fit
Every point casts a little square whose area is its squared distance from your line. Grab the two handles and tilt the line until the total shaded area is as small as it can be — that is exactly what “least squares” means. Add your own points by clicking, then hit snap to see the true best fit.
Labs / Mathematics / Least Squares Fit
Least Squares Fit
Every point casts a little square whose area is its squared distance from your line. Grab the two handles and tilt the line until the total shaded area is as small as it can be — that is exactly what “least squares” means. Add your own points by clicking, then hit snap to see the true best fit.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
y = 0.30x + 5.00SSR 0r 0
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Can you get the total SSR lower by hand than the “Snap to best fit” button does?
- Turn on the best-fit ghost. Which way should you tilt the line to shrink the biggest square?
- Add one far-off point to the “Cloud” data. How much does a single outlier drag the best-fit line?
- What arrangement of points pushes r closest to +1 or −1, and what does that scatter look like?
- Can you place points so the correlation r is nearly 0 even though there is a clear pattern?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.