Judging Model Fit with Least Squares Method (v2)
Lesson
Judging Model Fit with Least Squares Method When modeling a relationship between two numerical attributes, more than one line can appear to fit the data reasonably well. Different people may draw different lines, each claiming a “best fit,” which makes comparison difficult. Tuva’s Show Squares feature makes the idea of least squares visible. By displaying the squared distances between data points and a fitted line, it helps you judge model fit using a clear, visual criterion rather than guesswork. [---cta ⚡ Ready to practice? Jump straight into the interactive tool. ---]{border-left:#ecb606;buttons:[{"type":"enroll","text":"Enroll in series","bg":"#682D8A","color":"#ffffff","border":"#682D8A","icon":"ti ti-add"},{"type":"modeltool","text":"Try It Out Now","bg":"#ffffff","color":"#682D8A","icon":"ti ti-external","border":"#682D8A"}];} !![tuva]560x315 How It Works Judge model fit using least squares in four quick actions: [---card Create a scatter plot Drag one numerical attribute to the x-axis and another to the y-axis. ---]{border-color:#DADFE5;} [---card Add a Movable Line From the toolbar, choose :ti[movable-line] to place a line on the graph. ---]{border-color:#DADFE5;} [---card Show the squares (residuals) From the toolbar, choose :ti[show-squares]. Squares are drawn on each residual Each square represents a squared distance ---]{border-color:#DADFE5;} [---card Compare the sum of squares View the total in the :ti[ti-summary-view] or by hovering on the line Drag the line to see the sum update Smaller totals indicate a better fit ---]{border-color:#DADFE5;} [---card In a Nutshell The best-fitting line is the one that makes the total area of the squares as small as possible. ---]{border-color:#DADFE5;} [---cta ⚡ Try It Out Jump straight into the interactive tool. ---]{border-left:#ecb606;buttons:[{"type":"enroll","text":"Enroll in series","bg":"#682D8A","color":"#ffffff","border":"#682D8A","icon":"ti ti-add"},{"type":"modeltool","text":"Try It Out Now","bg":"#ffffff","color":"#682D8A","icon":"ti ti-external","border":"#682D8A"}];}
Topics and standards: Line Of Best Fit, Scatter Plots, Fitting Data, Tutorial