Plotting data & Regression using the parallelogram method Annika Lohstroh 17 BB 03...
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Plotting data & Regression using the parallelogram method Annika Lohstroh 17 BB 03 [email protected]
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Transcript of Plotting data & Regression using the parallelogram method Annika Lohstroh 17 BB 03...
Plotting data &
Regression using the parallelogram method
Annika Lohstroh
17 BB 03
Outline
• Plotting data
• Taking the data
•Choosing the graph scales
• Formatting the graph
• Parallelogram method
• Drawing the best fit line
• Drawing the parallelogram
• Determining the gradient and
intercept
• Using your result
• Adding error bars to your graph
• Quoting the fit results
Taking data – table & graph
Power supplyTX Ltd
Model 832
Multimeter Fluke 73Series II
20 V scale
MultimeterFluke 73Series II
1 mA scale
Sample
V [V]
0.01.02.03.04.05.0
I [mA]
64.887365.150265.0376………
Uncertainty in the instrument ?
Plotting the graph
-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300
20
40
60
80
100
120
Axis label & units
Axi
s la
bel &
uni
tsTitle
Scale not ideal
Choosing the scale & labeling
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
•Plot as you go along•Your graph does not have to show the coordinate (0/0)
Drawing the best fit line
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
Drawing the parallelogram
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
The best fit line is in the centre of the two parallel lines above and below it
2/3 of the data points should lie within the parallelogramm
Determining the gradient
• Section1
• Subsection
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
Use a large triangle to determine the gradient mbest
V24
mA .92 64mA 65.80 bestm
mS 0.0367
Determining the gradient
• Section1
• Subsection
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
Draw the diagonals in the parallelogram and determine their gradients
mS 0.0238minm
mS 0.0483maxm
mS 0.0367bestm
Determining the intercept
• Section1
• Subsection
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
Determine the intercept c for all 3 lines
Cmin = 64.78 mA
Cbest = 64.92 mA
Cmax = 65.08 mA
Using those results…
Quoting your results:
Never use more than 2 digits of precision for the uncertainty – round the values accordingly:
mS 0.005321
mS 0.0238 - mS 0.0483
n
minmax mm
m
Calculating the uncertainties, where n is the #data points:
mA 0.06521
mA 64.78 -mA 65.08
n
minmax ccc
mS 0.005)0.037 (mmm best
mA 0.07)64.92 (ccc best
Adding error bars…
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
The error bars have the height of the parallelogram.
mS 0.005)0.037 (m
mA 0.07)64.92 (c
Fig 1: Current vs Voltage
Voltage [V]
-2 0 2 4 6 8 10 12 14 16 18 20 22
Cu
rren
t [m
A]
64.8
65.0
65.2
65.4
65.6
65.8
66.0
66.2
Adding error bars…
In a formal report you may choose not to show the helping lines(parallelogram, grid lines…)
mS 0.005)0.037 (m
mA 0.07)64.92 (c
Questions ?
