1. The Height and Span Juxtaposition
Unit 4 – Bivariate Data
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Algebra 1 Institute

2. Another TED Talk
Hans Rosling
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Algebra 1 Institute

3. Bivariate Data Association between two variables
Positive: an increase in one variable generally produces an increase in the other.
Example: association between a student's grades and the number of hours per week that student spends studying
Negative: an increase in one variable generally produces a decrease in the other.
Example: association between the number of doctors in a country and the percentage of the population that dies before adulthood is generally a negative one.
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Algebra 1 Institute

4. Collect Data
In groups of 2
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Algebra 1 Institute

5. Compile the Data
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6. Scatterplot in GeoGebra
Enter the Arm Span information in Column A and the Height in Column B.
Highlight the cells in Column A and B that contain the information.
Click on the tool “Two Variable Regression Analysis”
On the pop-up window, click “Analyze”
A Scatterplot will be produced
2/24/2019
Algebra 1 Institute

7. Association?
Does an increase in arm span generally lead to an increase in height? How strong is the association (correlation)?
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Algebra 1 Institute

8. Find the Means
Is your arm span and height above the average of these 40 adults?
How many of the 40 people have above-average arm spans?
How many of the 40 people have above-average heights?
It is possible to divide the 40 people into four categories:
Above-average arm span and above-average height;
Above-average arm span and below-average height;
Below-average arm span and above-average height; and
Below-average arm span and below-average height.
2/24/2019
Algebra 1 Institute

9. Use the Means to add Lines
Regression is about the mean, but you could ask the students what would change if you replace those lines with the medians instead of the means?
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Algebra 1 Institute

10. How Many People in each Quadrant?
Do most people with below-average arm spans also have below-average heights?
Do most people with above-average arm spans also have above-average heights?
What do these answers suggest?
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Algebra 1 Institute

11. Height – Arm Span
How many of the 40 people have heights that are greater than their arm spans?
How many of the 40 people have heights that are less than their arm spans?
How many of the 40 people have heights that are equal to their arm spans?
Which six people are the closest to being square without being perfectly square?
Which five are the farthest from being square?
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Algebra 1 Institute

12. Draw Line y = x in Scatterplot
What do the points above the line represent?
What do the points on the line represent?
What do the points below the line represent?
Why is it helpful to draw the line height = arm span? How does this line help us analyze differences?
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Algebra 1 Institute

13. Draw More Lines Which one is a better fit? Y = x Y = x + 1 Y = x – 1
Any other?
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14. Distance = |Y - YL| = |Error|
Error = Y - YL
Y = actual observed height (Y)
YL = predicted height (on the line)
Error =
Actual Observed Height - Predicted Height
Distance = |Y - YL| = |Error|
2/24/2019
Algebra 1 Institute

15. Square of the Error
When comparing two lines, the line with the smaller total of the sum of the squared errors (SSE) is the "better" line in terms of how well it describes the linear relationship between the two variables. |Y-YL|2
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16. For our Data
Judging on the basis of the SSE, which is the best line? Which is the worst?
What other ways could we change the line equation in an attempt to further reduce the SSE?
Is it possible to reduce the SSE to 0? Why or why not?
2/24/2019
Algebra 1 Institute