Data Analysis in Mathematical Modeling
Dan TeagueNC School of Science and Mathematics
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
Which model captures the underlying functional relationship?
Data Analysis in Mathematical Modeling
Dan TeagueNC School of Science and Mathematics