Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics...
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Transcript of Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics...
![Page 1: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/1.jpg)
Data Analysis in Mathematical Modeling
Dan TeagueNC School of Science and Mathematics
![Page 2: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/2.jpg)
Wind Chill Table
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20 mph row
![Page 4: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/4.jpg)
Residuals for 20 mph Wind Velocity
![Page 5: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/5.jpg)
Residuals for 5-20 mph lines
![Page 6: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/6.jpg)
Residuals for 25-45 mph lines
![Page 7: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/7.jpg)
Fit a line to each row
![Page 8: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/8.jpg)
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“Wind velocities greater than 45 mph have little additional cooling effect”.
![Page 10: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/10.jpg)
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Semi-log Re-expression
![Page 12: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/12.jpg)
Flip the Residual Curvature
![Page 13: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/13.jpg)
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Difference Quotients
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Logistic Models
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What is the probability a test tube needs to be retested?
• The probability of an individual testing positive is p.
• The probability of an individual testing negative, then, is 1 – p.
• The probability of two individuals both testing negative is (1 – p)(1 – p).
• The probability of G individuals all testing negative is (1 – p)^G.
• The probability of at least on of G individuals testing positive is 1 – (1 – p)^G.
![Page 31: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/31.jpg)
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Why Calculus Fails
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Data Analysis to the Rescue
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The Data Falling on the Solution
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We see double asymptotes, so try log-log
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Vertical Shift?
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Minimize Sums of Squares
![Page 38: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/38.jpg)
Two Potential Models
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Should we always group?
![Page 40: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/40.jpg)
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CO2 in the Atmostphere
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sinC t f t a b t c
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Is it exponential?
ln 300 0.0399 0.437C t 0.0399( ) 1.548 300tF t e
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Residuals?
0.0399( ) 1.548 300tF t e
sinC t f t a b t c
![Page 46: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/46.jpg)
The residuals from the exponential model
1
3sin 224
S t t
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0.0399 1( ) 1.548 3sin 2 300
24tC t F t e t
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Data Analysis in Mathematical Modeling
Dan TeagueNC School of Science and Mathematics
![Page 49: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/49.jpg)
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Which model captures the underlying functional relationship?
![Page 56: Data Analysis in Mathematical Modeling Dan Teague NC School of Science and Mathematics teague@ncssm.edu.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649d1f5503460f949f264f/html5/thumbnails/56.jpg)
Data Analysis in Mathematical Modeling
Dan TeagueNC School of Science and Mathematics