A temperature measurement system is calibrated against a standard system certifi

Question

A temperature measurement system is calibrated against a standard system certified to an uncertainty of +0.05°C The system sensor is immersed alongside the standard within a temperature bath so that the two are separated by~10mm. The temperature uniformity of the bath is estimated at -5°C/m. The temperature system sensor is connected to a readout that indicates the temperature in terms of voltage. The following are calibration results between the temperature indicated by the standard and the indicated voltage Temperature T (? 0.5 9.8 21.2 39.7 76.4 99.2 Voltage E (mV 0.02 0.45 1.30 2.00 6.00 a. Perform a linear regression on the data to find the best-fit linear response function. You may use any package, or do it manually, but either way give details. b. Find Syx, the standard error of the fit. Calculate and report the total uncertainty in a Temperature measurement using the c. above system - include the systematic uncertainties (stated standard accuracy bath non-uniformity) and the error of the fit.

Explanation / Answer

Solution:

go to data >data analysis>regression

regression eq is

volatge=-0.2334+0.0497*temperature.

slope=0.0497

y intercept=-0.2334

R sq=0.8075=0.8075*100=80.75%

80.75% varaition in volatge is explained by temperature.

Solutionb:

standard error of estimate=

SUMMARY OUTPUT Regression Statistics Multiple R 0.898628 R Square 0.807532 Adjusted R Square 0.759415 Standard Error 1.061331 Observations 6 ANOVA df SS MS F Significance F Regression 1 18.90439 18.90439 16.78267 0.014894 Residual 4 4.505693 1.126423 Total 5 23.41008 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.23341 0.661016 -0.35311 0.741831 -2.06869 1.601867 Temperature 0.049718 0.012136 4.096666 0.014894 0.016023 0.083414

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