regression lines. today’s aim: to learn the method for calculating the most accurate line of best...
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![Page 1: Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data](https://reader035.vdocument.in/reader035/viewer/2022062408/56649f145503460f94c28a49/html5/thumbnails/1.jpg)
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
![Page 3: Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data](https://reader035.vdocument.in/reader035/viewer/2022062408/56649f145503460f94c28a49/html5/thumbnails/3.jpg)
Make a Scatterplot of the following data:
X Y
23 81
25 80
27 90
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![Page 5: Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data](https://reader035.vdocument.in/reader035/viewer/2022062408/56649f145503460f94c28a49/html5/thumbnails/5.jpg)
Lets guess where the Line of Best
Fit should go
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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
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![Page 9: Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data](https://reader035.vdocument.in/reader035/viewer/2022062408/56649f145503460f94c28a49/html5/thumbnails/9.jpg)
Now, lets try with a different line…
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We can also measure with numbers the vertical
distances between the Scatterplot points and
the Line of Best Fit
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Actual y
values:
81
80
90
81
80
90Predicted y
values:
79.1
83.6
88.2
79.1
83.6
88.2
Difference in y
values:
.9
3.6
1.8
.9
3.6
1.8
.9
3.6
1.8
6.3
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For the first possible Line of Best Fit, the sum of the vertical
distances (errors) was 6.3
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81
80
90
79.6
83
85.2
.4
3
4.8
.4
3
4.8
8.2
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The sum of the vertical distances
(errors) on the second possible line was 8.2.
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The correct Line of Best Fit is called a Regression Line.
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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.
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To Calculate the Error:
Error = actual y value - predicted y 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.
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For example…
X YPredicted Y values (Line A)
Vertical Distances
(errors)
Distances Squared
3 7 7.2 - 0.2 .04
4 9 9.6 - 0.6 .036
7 12 9.5 2.5 6.25
SUM:6.35
X YPredicted Y values (Line B)
Vertical Distances
(errors)
Distances Squared
3 7 7.5 - 0.5 .25
4 9 9.2 - 0.2 .04
7 12 11.3 .7 .49
SUM:.78
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