Theoretical Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover Theoretical and links to relevant pages within the course.
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| The Least Squares Line According the the method of least squares, the line of best fit is the one that minimizes the squares of the differences between the data points' observed (experimental) y-values and their expected (theoretical) y-values. This line is known as the least squares regression line. To calculate the sum of squares of a line, find the difference between and the true y value for each point. is found by substituting the corresponding x value into the linear regression equation. Then square those differences, and then sum them. Line A is done below: Point x y Difference y- Difference Squared (y-)2 1 10 5.0 8.0 -3.0 9.00 2 18 24 14.4 9.6 92.16 3 38 27.5 30.4 -2.9 8.41 4 50 60.0 40.0 20.0 400.00 5 63 50.0 48.0 2.0 4.00 The total sum of squares for this line is 513.57. As said before, the line that minimizes this value is the line of best fit according to the least squares method. | View Page |
| Standard Error of Estimate The sum of squares of the deviations can also be used to provide an estimate of how closely the data cluster around the line. The Standard Error of Estimate (Se) is one such estimate, and is calculated according to the following formula, where S denotes summation, and the yi and i are the observed and theoretical y-values of the datapoints, respectively: For example, the Standard Error of Estimate of the preceding example is the following: | View Page |