Formulae Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover Formulae and links to relevant pages within the course.
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| Determining the Least Squares Line Least squares would be a tedious process if we had to draw four of five lines of best fit and then determine which line had the least sum of squares, and then we still would have no way of knowing whether the line we had chosen was truly the best out of all possible lines. Consider the data in the following figure. The least squares formulae automatically provided the slope and y-intercept where the sum of squares (and therefore the Standard Error of Estimate) is smallest. | View Page |
| Formulae for Determining the Slope and Intercept To find the slope, calculate the deviation of each x from mean, , and calculate the deviation of each y from its mean, . The numerator is the product of the deviation of each x and y pair, the denominator is the sum of the squared deviations of all of the x-values. Thus the formula is: The y-intercept, a, is calculated by substituting and into the equation of a line and solving for a: To draw this line on a graph, substitute two or three values for x, calculate the corresponding y values, plot these x-y pairs as points on the graph, and draw a line through these points. | View Page |
| Using the Least Squares Formulae Using the totals from the previous table, we can calculate the slope of the regression line: We can also calculate the y intercept of the regression line: Therefore, the least squares regression line is: Here is the calculated line, plotted on the original data points: | View Page |
| Formulae for Confidence Intervals The formulae for regression confidence intervals are: at the 95% confidence level, where: Evaluating the plus sign in the above expressions gives the upper bound of the interval, and the minus sign gives the lower bound of the interval. | View Page |