Manual Linear Function Fitting Task

A Manual Linear Function Fitting Task is a linear regression task that is a manual function fitting task.

• AKA: Manual Linear Regression.
  • …
• Counter-Example(s):
  • an Automated Linear Regression Task.
• See: Linear Regression System.

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References

2015

• (Allain, 2015) ⇒ Rhett Allain. (2015). “An Ode to the Graph, Physics’ Underappreciated Workhorse.” In: Wired, 2015-06-03
  • QUOTE: … if you fit a linear equation to that data, what would the slope represent? ...
    • Plotting data as a linear graph is a great way to examine the validity of a model.
    • Sometimes you will have to do something to the variables in order to make the plot a linear function (like squaring both sides of the model).
    • The slope of the linear function that fits the data actually means something. Find the slope and find out what it represents (and check it).

2011

• (Allain, 2011) ⇒ Rhett Allain. (2011). “Linear Regression by Hand.” In: Wired, 2011-01-16
  • QUOTE: It only makes sense. I did linear regression in google docs and I did it for python. But what if you neither of those? Can you do it by hand? Why yes. Suppose I take the same data from the pylab example and I imagine trying to add a linear function to represent that data. …

    … you have to make up some criteria for choosing the best line. Commonly, it is chosen to pick the line such that the value of the sum of [math]\displaystyle{ d^2 }[/math] is minimized. … typically, the horizontal variable is your independent variable – so these might be some set values. The vertical data is typically the one with the most error (but not always). …

    There. That is the the basic form of linear regression by hand. Note that there ARE other ways to do this – more complicated ways (assuming different types of distributions for the data). Also, the same basic idea is followed if you want to fit some higher order polynomial. Warning, it gets complicated (algebraically) real quick.

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