Uncertainty Calculations in the Gradient and Y-intercept
Upon inspection, you will notice that you have the following information for your best fit line:
1. Best Fit Gradient:
2. Manual Fit Highest Gradient:
3. Manual Fit Lowest Gradient:
1.992 °C/m
2.242 °C/m
1.849 °C/m
Best Fit Y-intercept:
45.59 °C
Manual Fit Lowest Y-intercept: 33.09 °C
Manual Fit Highest Y-intercept: 52.48 °C
With this information you may now calculate the uncertainties in both the slope and the y-intercept of your data. Note
that you must report your data and calculations from Logger Pro with the appropriate number of significant figures. The
slope must be rounded to 3 significant figures because of the rule of division and the Y-intercept to the tenths decimal
place because of the precision in the raw data. One can make Logger Pro display this data appropriately by changing the
precision manually within the Manual Fit boxes on the graph. Just as you accessed the Enable Line Drag function by
right-clicking, do this for all three boxes and change the Displayed Precision so the graph ends up looking like the image
shown below:
In your lab reports you would have to indicate, as part of your analysis of data, the following information:
The uncertainties were determined by taking the difference between the high and low values of the slope and dividing
by 2.. These calculations are shown below.
Uncertainty in the Slope:
Uncertainty in the Y-Intercept:
Congratulations! You have just learned how to use Logger Pro to plot and label data, present it in a suitable graphical
format and analyze it for its slope and y-intercept while also working out the error analysis aspects that you will have
to do undoubtedly for all individual lab reports you will be assigned on occasion.
Let this also be a word of caution that this is not the end of Data Collection and Processing. Usually one has to use the
slope and y-intercept to calculate some other quantity, for which the lab report will have to indicate the mathematics
involved in the calculations as well as the error propagation that occurs when you add, subtract, multiply or divide.