Experimental uncertainty (error) in simple linear data plot

A typical set of linear data can be described by the change of the pressure, p, (in pascals) of an ideal gas as a function of the temperature, T, in degrees kelvin.

T /K

298

328

358

388

418

448

478

508

p/Pa

5606

5890

6405

6997

7172

8160

8518

9218

Important Note:
Regression calculations to find the line of ‘best-fit’ assume that the main errors (uncertainties) occur in the y-values with negligible error in the x-values.

This data is analysed using:

X-Y plot of data including:  - see video Regression Analysis A

  • Trendlines projected back to the y-axis
  • Forcing the trendline through the origin of the graph
  • Error bars based on a specified value

Functions to calculate:  - see video Regression Analysis A

  • Slope of the trendline using SLOPE(y-data,x-data)
  • Intercept (on the y-axis) of the trendline using INTERCEPT(y-data,x-data)
  • Slope of a trendline which is forced through the origin using LINEST(y-data,x-data,FALSE) 
  • Standard deviation of the experimental data using STEYX(y-data,x-data)

Data Analysis tools to perform a Regression analysis to calculate:  - see video Regression Analysis A

  • The same values as obtained by the functions above
  • Uncertainties in the values for slope and intercept

Excel demonstration of the effect of random experimental variations, including - see video Regression Analysis B 

  • Error bars based on a data range