Math 1 · Unit 10 · Lesson 2
The Line of Best Fit
A model is a family member that fits the data best. The line of best fit, the least squares regression line, makes the total squared error as small as possible, and technology finds its slope and y-intercept. Then read it the Unit 3 way: the slope and the y-intercept each mean something in the story. Use the model to predict, forward and backward, and always ask whether the prediction makes sense: inside the data is fairly safe, far outside can be nonsense.
The big idea
A model is a family member that fits the data best. For data that looks like a line, the line of best fit, the least squares regression line, is the one that makes the total of the squared misses as small as possible, squared so that misses above and below the line cannot cancel. Technology finds its numbers; you ask the same three questions as always: what family, what are its numbers, and what does each mean in the story. The slope is the change in y for each 1 of x, and the y-intercept is the value when x is 0, both said with the word about because the points are not exactly on the line. A model predicts forward by putting x in, and backward by setting it equal to a value and solving the Unit 1 way. Predicting inside the data, interpolating, is fairly safe. Predicting outside it, extrapolating, gets riskier the farther you go, so always ask whether the answer makes sense.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with least squares and why you square, reading slope and y-intercept in the story, forward and backward predictions, and interpolation against extrapolation. Plus a worksheet with an answer key and a short lesson plan.
Where this goes next
NC Math 1 standards in this lesson: NC.M1.S-ID.6a (fit a least squares regression line with technology and use it), NC.M1.S-ID.7 (interpret slope and intercept in context; interpolate and extrapolate; judge predictions), NC.M1.F-LE.5 (interpret the parameters in context).