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Linear Models…zing Gauss Lesson 1.5 Finite Differences • The differences between each y-value and the preceding one in a table of values • Basically tells if the line is good for the model • Example #1 on page 44 Leibniz Residual • Measure of the error between the actual value of the data, r, and the value of y given by the model. • Vertical distance between actual point and model point on a graph • Example2 on page 46 Galois Least Regression Lines • For any set of data there is one and only one line for which the sum of the squares of the residuals is as small as possible. • Linear Regression is the name of the process Calculator • r correlation coefficient • The closer to 1 the better fit the line. Close to zero is a poor fit with perhaps no correlation • r2 Coefficient of Determination • A statistical measure that is the proportion of variation between x and y in a data set. Example • The lengths of the radii of the inscribed circles in regular polygons whose sides have length one unit are given Number of sides Radius 3 4 5 6 7 0.289 0.500 0.688 0.866 1.038 8 9 1.207 1.374 1. Draw a scatter plot 2. Calculate the finite differences for the data points 3. Find the model that best fits the data using the regression feature on the calculator 4. What does the correlation coefficient indicate about the data? I think that is it! • Get to work you little whippersnappers! Newton