Transcript TwMM 2.1 Modeling Linear Data Patterns.pptx

Math CC7/8 – Be Prepared
On Desk:
Learning Log:
1. Pencil
1.
2. Calculator
3. Math Journal
4. TwMM Learning Log
HW: p. 45, #1-3, #35 (ACE worksheet)
Tasks for Today
• Warm Up –
• Lesson 2.1 – A-B (C?)
– Modeling Linear Data Patterns
Warm Up
Are the following patterns linear or non linear?
Give the equation if they are a linear relationship
Linear, y = 7x + 2
Non-linear
Linear, y = 1.5x + 2.3
Labsheet 2.1
12 22 33 43 54
0
Model #1
-4
-1 -3 -6
64
0
10 20 30 40 50
60
2
4
2
Model #2
-2
0
-2
Using the model y = 10.4x + 1.6
gives predictions consistently at
or above the actual data, a
trend that is shown by the
many 0 or negative residuals.
Yes, the line y = 10x passes through
(4,40), (5, 50), and (6, 60). The line
shown passes very close to those
points.
The residuals for Sally’s model are a mix of over and
underestimates of the actual breaking weights.
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•
•
•
Both equations produce small residuals.
The first model consistently give overestimates.
The second model’s predictions are a mix of over- and underestimates.
The second model (y = 10x) gives better predictions, so it is a better fit!
Which is x and which is y?
Graph:
Mathematical Model:
Answers vary…
y = 2.4x + 0.42
Residuals are small and
some are positive and
some are negative… Linear
model makes sense!