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## Regression Lines

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**Today’s Aim:To learn the method for calculating the most**accurate Line of Best Fit for a set of data**Now we want to measure the distance between the actual Y**values for each point and the predicted Y value on our possible Line of Best Fit**We can also measure with numbers the vertical distances**between the Scatterplot points and the Line of Best Fit**Actual y values:**Predicted y values: Difference in y values: 90 1.8 88.2 81 80 90 79.1 .9 3.6 1.8 1.8 83.6 6.3 88.2 3.6 83.6 .9 3.6 81 .9 80 79.1**For the first possible Line of Best Fit, the sum of the**vertical distances (errors) was 6.3**90**4.8 4.8 85.2 8.2 3 83 .4 3 81 79.6 .4 80**The sum of the vertical distances (errors) on the second**possible line was 8.2.**A Regression Line is the line that makes the sum of the**squares of the vertical distances (errors) of the data points from the line as small as possible.**To Calculate the Error:**Error = actualy value - predictedy value Note: If the predicted value is larger than the actual value, the error will be a negative number. This is why we square the errors - to turn them into positive numbers.**For example…**SUM: 6.35 SUM: .78