A pressure transducer has been statically calibrated and the results are shown i

Question

A pressure transducer has been statically calibrated and the results are shown in the table table below.

a) Is there a linear trend between Voltage (y-axis) and Pressure, to the standard engineering confidence level of 95%?

b) To what confidence level can you state there a linear trend between Voltage (y-axis) and Pressure?

c) Determine the linear correlation and regression between Voltage (y-axis) and Pressure?

d) How well do the coefficients fit this data? You must use results from the regression analysis. A subjective discussion is not allowed.

e) What is the sensitivity of this transducer assuming a linear model?

f) Can any of the data points be removed as outlier? Support your answer with results from the regression analysis.

g) Plot the following with Voltage (y-axis) and Pressure: Raw Data, Linear calibration, The upper and lower 90% confidence intervals on the data.

Pressure Voltage [kpsi] [mV] 0.00 780.00 0.50 815.50 1.00 798.00 1.50 767.50 2.00 705.00 2.50 725.00 3.00 612.00 3.50 522.50 4.00 498.00 4.50 485.50 5.00 464.00 5.50 450.00 6.00 341.00 6.50 397.50 7.00 365.00 7.50 308.50 8.00 231.00 8.50 245.50 9.00 187.00 9.50 181.50 10.00 167.00 10.50 83.50 11.00 95.00 11.50 25.50 12.00 43.00

Explanation / Answer

-0.990

(a) Yes, there is a linear trend between Voltage (y-axis) and Pressure, to the standard engineering confidence level of 95%

(b) Since the p- value for the slope is almost 0, we can say that there is a linear correlation between voltage and pressure at 99.5% confidence also.

(c) The regression equation is Voltage = 823.57 - 68.63 * Pressure

The correlation coefficient is -0.990, which implies an almost perfect negative correlation between Voltage and Pressure

(d) Coefficient of determination is r^2 = 0.98, which means 98% of the variation in Voltage is explained by the variation in Pressure. The model is a very good fit to the data.

Regression Analysis r² 0.980 n   25 r   -0.990 k   1 Std. Error   37.272 Dep. Var. Voltage ANOVA table Source SS   df   MS F p-value Regression 1,531,015.2069 1   1,531,015.2069 1102.11 6.19E-21 Residual 31,950.8531 23   1,389.1675 Total 1,562,966.0600 24   Regression output confidence interval variables coefficients std. error    t (df=23) p-value 95% lower 95% upper std. coeff. Intercept 823.5723 0.000 Pressure -68.6354 2.0675 -33.198 6.19E-21 -72.9122 -64.3585

-0.990

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