data analysis in mathematical modeling dan teague nc school of science and mathematics...

Data Analysis in Mathematical Modeling

Dan TeagueNC School of Science and Mathematics

teague@ncssm.edu

Wind Chill Table

20 mph row

Residuals for 20 mph Wind Velocity

Residuals for 5-20 mph lines

Residuals for 25-45 mph lines

Fit a line to each row

“Wind velocities greater than 45 mph have little additional cooling effect”.

Semi-log Re-expression

Flip the Residual Curvature

Difference Quotients

Logistic Models

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.

Why Calculus Fails

Data Analysis to the Rescue

The Data Falling on the Solution

We see double asymptotes, so try log-log

Vertical Shift?

Minimize Sums of Squares

Two Potential Models

Should we always group?

CO2 in the Atmostphere

sinC t f t a b t c

Is it exponential?

ln 300 0.0399 0.437C t 0.0399( ) 1.548 300tF t e

Residuals?

0.0399( ) 1.548 300tF t e

sinC t f t a b t c

The residuals from the exponential model

1

3sin 224

S t t

0.0399 1( ) 1.548 3sin 2 300

24tC t F t e t

Data Analysis in Mathematical Modeling

Dan TeagueNC School of Science and Mathematics

teague@ncssm.edu

Which model captures the underlying functional relationship?

Data Analysis in Mathematical Modeling

Dan TeagueNC School of Science and Mathematics

teague@ncssm.edu