Fitting Data To A
Mathematical Function
BlackBoard Notes

======================= Photo - Click for a Larger Version =============================

======================= First Board Section =============================

• A lab practical skill!
• (Note to Jeff: keep to the color scheme for the graphs below) 

• Model: x = v_ot + x_o
• Do the data support the model?
• What are the best values of the model's parameters, (x_o, v_o)?

======================= Second Board Section =============================

• SSR = Sum of the Square of the Residuals (also known as Chi Square: χ²)

======================= Third Board Section =============================

• Calculating the best value of v_o:  (where Σ means "sum")

• Calculating the Standard Error (S.E.)
  •           (where N is the number of data points)

• Calculating the Uncertainty of a value 
  • Uncertainty = (S.E.) 2

======================= Fourth Board Section =============================

• Use calculation table (pg. 3) to keep track of your numbers
• Avoid rounding errors - use the memory functions of your calculator
• State the slope as: v_o = ___ +/- ___ {units}     (point to and label value and uncertainty fields)
• Stay on track:
  • 2:00 pm – start hand calculations
  • 3:00 pm – start KaleidaGraph exercise

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Revised: 12 Sep 2023

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