Least Squares Curve Fitting

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Least Squares Curve Fitting

• Trendline Analysis

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Curve Fitting

• For a given collection of data, we would like to
  determine the best choice for
  to represent the data.
• The form of f(x) is suggested by the appearance
  of the data or intuition based on the underlying
  physics. For example, for spring stiffness
  relations, we know that the deflection must be
  zero with zero applied force and we expect the
  deflection curve to be linear. Therefore, for
  f(x) we choose a linear function with a zero
  intercept.
• Options for general curve fits

• The problem is to find the appropriate
  coefficient values.

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In least squares curve fitting, the objective is
to minimize the overall deviation of the curve
fit with respect to the data points.
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Linear Curve Fit
Linear (1st Order Polynomial) curve fit
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Pressure Transducer Calibration

• Pressure transducer is used to transform the
  parameter of interest (pressure) into a form that
  is convenient for measurement (voltage)
• Wish to determine the relationship between the
  input pressure and output voltage of the
  transducer, i.e., calibrate the transducer.
• Create an experiment in which known values of
  pressure are applied and output voltages are
  measured.

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Pressure Transducer Calibration

• Right-click on any one of the data points and
  select Add-Trendline

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Pressure Transducer Calibration
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Pressure Transducer Calibration

• Enter a descriptive curve fit title for use in
  the plot legend
• Display the equation on the chart
• Display R-squared value on the chart

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Pressure Transducer Calibration

• Right-click on the trendline results and select
  Format Data Labels
• 10pt Arial, regular type face, no autoscaling
• white background
• medium-weight black border

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Pressure Transducer Calibration

• Right-click on the trendline and select Format
  Trendline
• Black, light-weight, solid line

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Pressure Transducer Calibration

• Use the Chart Options to add a legend to the plot

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Pressure Transducer Calibration

• Use the Source Data dialog to change the legend
  description for the data

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Pressure Transducer Calibration

• Use the Format Legend dialog to format the legend
  to match the trendline data
• 10pt Arial, regular type face, no autoscaling
• white background, medium-weight, black border

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Pressure Transducer Calibration
By calibrating a pressure transducer, we are
establishing the relationship between the applied
pressure and the voltage output.
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Pressure Measurements

• With the transducer calibration established,
  measurements of unknown pressures can be
  performed.