Why is it important to use a \"least squares fit\" line for a standard curve rat
ID: 637278 • Letter: W
Question
Why is it important to use a "least squares fit" line for a standard curve rather than the plot of all data? (For the following curves.Concentration vs absorbances of a solution to obtain its Molarity for an experiment entitled-Colorimetric determination of an equilibrium constant in aqueous solution) Data Collected' Plot of ALL DATA 0.030 0.15 0.28 10033 0.55 1.24 | 0,046 ? 2.05 | 0.068 | 2.56 4.10 4.50 6.50 9.80 0,520 13.86 0.8001 17.000.959 0.040 Chart Area 0 0.800 0.103 0.167 0.270 0.347 b 0.600 E 0200 0.000 5.00 15.00 20.00 25.00 20.00 1.100 25.00 27.00 30.00 1.250 275 Least Squares Fit of all the data ? ? ? ? ? 1st 6 points y 0.0472x+0.026 R2 = 0.9769 A 1.200 1.000 00.800 b 0.600 10.00 15.000 25.00 30.00Massaged Data 0.00 5.00 A 1.200 1000 0.800 b 0.600 y = 0.058x-0.0353 R2 0.9959 C 0.200 0.00 25.00Explanation / Answer
The least square fit method gives linear approximation of the given data. Most of the chemical processes are analysed using linear sensors. Linear sensors are preferred in many industrial applications too. This is because mostly all the circuits designed to measure the output are based upon linear relationship between the input and output. The output is majorly voltage that gives indication of the desired chemical parameter. The data that we get from initial experiments of these sensors very rarely follows an exact linear plot. Hence, we introduce a least square fit curve. Also, we are interested in finding how much the output deviates from the linear approximation. The deviation is found out by measuring non-linearity corresponding to the least square fit plot. If multiple observations are made using the same apparatus, though we may not get the same data values, we are bound to get least square fit plots that tend to be coincident.
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