To determine the temperature dependence of a pressure transducer, one student de

Question

To determine the temperature dependence of a pressure transducer, one student decides to immerse a pressure transducer in a fluid bath of variable temperature. He obtains the following results:

(a) Calculate the linear correlation coefficient. Can the student be 95% confident that there is a trend

between the output of the pressure transducer and the temperature? Explain why or why not. To what

confidence level (given with 3 signicant digits) is there a trend in the data?

(b) Perform a linear least-square fit through the data.

To determine the temperature dependence of a pressure transducer, one student decides to immerse a pressure transducer in a fluid bath of variable temperature. He obtains the following results: alculate the linear correlation coefficient. Can the student be 95% confident that there is a trend between the output of the pressure transducer and the temperature? Explain why or why not. To what confidence level (given with 3 signicant digits) is there a trend in the data? Perform a linear least-square fit through the data.

Explanation / Answer

the result of regression on excel is as

SUMMARY OUTPUT Regression Statistics Multiple R 0.83205 R Square 0.692308 Adjusted R Square 0.589744 Standard Error 0.007303 Observations 5 ANOVA df SS MS F Significance F Regression 1 0.00036 0.00036 6.75 0.08051 Residual 3 0.00016 5.33E-05 Total 4 0.00052 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4.172 0.005657 737.5124 5.5E-09 4.153997 4.190003 4.153997 4.190003 X Variable 1 0.0006 0.000231 2.598076 0.08051 -0.00013 0.001335 -0.00013 0.001335

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