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Last modified by Mengting Qiu on 2024/09/02 17:23
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edited by Mengting Qiu
on 2024/09/02 17:23
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edited by Mengting Qiu
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49 49  When x=8 mA, y=2.5 meters
50 50  
51 51  
52 -**A more general formular:**
52 +A more general formular:
53 53  
54 -(% style="color:blue" %)**Y=(y2-y1)/(x2-x1)* (x-x1) + y1**
54 +(% style="color:#4f81bd" %)**Y=(y2-y1)/(x2-x1)* (x-x1) + y1**
55 55  
56 56  
57 57  Calibration Curve Schematic：
58 58  
59 -[[image:image-20240902114541-1.png||height="336" width="596"]]
59 +[[image:image-20240902114541-1.png||height="479" width="851"]]
60 60  
61 61  
62 62  == 2.2 Performing linear calibration curves in Excel ==
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64 64  
65 65  In addition, we can also perform calibration curves in Excel and directly obtain linear equations by statistics of X and Y values.
66 66  
67 -Citing the same example above, (% style="color:#4f81bd" %)**X**(%%) and (% style="color:#4f81bd" %)**Y**(%%).
68 68  
69 69  
70 -=== Step 1: Create chart ===
71 71  
72 72  
73 -A simple spreadsheet with two columns: X values and Y values.
74 74  
75 -[[image:image-20240902160516-1.png||height="404" width="561"]]
76 76  
77 -* Start by selecting the data you want to plot in the chart.
78 -* First, select the X-Value column cell, then press the Ctrl key, and finally click the Y-value column cell.
79 79  
80 -[[image:image-20240902160755-2.png||height="394" width="562"]]
81 -
82 -* Go to the "(% style="color:#4f81bd" %)**Insert**(%%)" TAB, navigate to the "(% style="color:#4f81bd" %)**Chart**(%%)" menu, and then select the first option in the "(% style="color:#4f81bd" %)**Scatter**(%%)" drop-down list.
83 -* A chart will appear with the data points in the two columns.
84 -
85 -[[image:image-20240902161202-3.png||height="453" width="824"]]
86 -
87 -* Right-click on one of the blue dots and select the (% style="color:#4f81bd" %)**"Add Trendline" **(%%)option.
88 -
89 -[[image:image-20240902161711-4.png||height="490" width="681"]]
90 -
91 -* A straight line will appear on the chart.
92 -
93 -On the right side of the screen, the Format Trendline menu will appear. Check the boxes next to (% style="color:#4f81bd" %)**"Show formulas on chart" **(%%)and (% style="color:#4f81bd" %)**"Show R-squared values on chart"**(%%).
94 -
95 -The R-squared value is a statistic that tells you how well the line fits the data. The best R-squared value is **1.000**, which means that every data point touches the line.
96 -
97 -Because the ideal data example is used, the R-squared value in this case is 1.
98 -
99 -As the difference between the data points and the line increases, the R-squared value decreases, with **0.000** being the lowest possible value.
100 -
101 -The equation is of the form (% style="color:blue" %)**"y = kx + b"**(%%),(% style="color:blue" %)** **(%%)where (% style="color:blue" %)**k**(%%) is the slope and (% style="color:blue" %)**b**(%%) is the y-intercept of the line.
102 -
103 -[[image:image-20240902161857-5.png||height="559" width="1103"]]
104 -
105 -* Calibration is complete. The user can customize the chart by editing the title and adding the axis title.
106 -
107 -[[image:image-20240902163527-7.png||height="349" width="656"]]
108 -
109 -
110 -=== Step 2: Calculate the line equation and R-squared statistic ===
111 -
112 -* Write the (% style="color:#4f81bd" %)**Slope formula**(%%) in the formula bar according to the original x and y values statistics table.
113 -
114 -[[image:image-20240902164104-8.png||height="503" width="492"]]
115 -
116 -* Write (% style="color:#4f81bd" %)**Intercept formula**(%%) in the formula bar according to the original x and y value statistics table.
117 -
118 -[[image:image-20240902164156-9.png||height="525" width="488"]]
119 -
120 -* Write (% style="color:#4f81bd" %)**CORREL's squared formula**(%%) in the formula bar based on the original x and y statistics table.
121 -
122 -The CORREL function returns "R", so we have to square it to compute "R squared".
123 -
124 -[[image:image-20240902164503-11.png||height="523" width="743"]]
125 -
126 -* These values match those shown in the chart.
127 -
128 -[[image:image-20240902164910-12.png||height="420" width="897"]]
129 -
130 -
131 -=== Step 3: Set up formulas to quickly calculate X and Y values. ===
132 -
133 -
134 -* The equation of the best fitting line is "Y-value = SLOPE * x-value + INTERCEPT", so the solution of "y-value" is obtained by multiplying X value and SLOPE, and then INTERCEPT is added.
135 -
136 -A simple formula table for calculating Y value automatically with input X value is obtained.
137 -
138 -[[image:image-20240902171627-15.png||height="440" width="754"]]
139 -
140 -
141 -* The X value based on the Y value is solved by subtracting INTERCEPT from the Y value and dividing the result by SLOPE: "x-value = (y-value-intercept)/SLOPE".
142 -
143 -A simple formula table for automatically calculating X value based on the input Y value is obtained.
144 -
145 -[[image:image-20240902171909-16.png||height="604" width="756"]]
146 -
147 -
148 148  = 3. Case examples =
149 149  
150 150  
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168 168  
169 169  (% style="color:red" %)**Notice for Linear Calibrate:**
170 170  
171 -(% style="color:red" %)**1. k(Slope) is very important, We can measure more points to calculate the most accuracy k. **
97 +1. k(Slope) is very important, We can measure more points to calculate the most accuracy k.
98 +1. Make sure the mapping is linear, and choose two calibrate points as "far" as possible.
172 172  
173 -(% style="color:red" %)**2. Make sure the mapping is linear, and choose two calibrate points as "far" as possible.**
174 174  
175 -
176 -
177 -
178 -
179 179  
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