Question

Data for a force sensor is given in the table below (Force is the input, x, Voltage is the output, y.). a. Find the slope and y-intercept of the least-squares best-fit line through the data. b. Estimate the standard error of the fit. C. Find the 95% confidence interval of the best-fit line. Force (N) Vout (V) 62.0 1.05 63.0 1.41 64.0 1.93 65.0 2.46 66.0 3.03 67.0 3.59 68.0 3.88 69.0 4.48 70.0 5.04 71.0 5.51

Answer 1

64 (a) The procedure in Excel to perform the regression analysis is: 1. Enter the data in Excel as shown below: A B 1 Force (N) Vout (V) 1.05 1.41 1.93 2.46 3.03 3.59 3.88 4.48 70 5.04 5.51 2. Click on Data->Data Analysis->Regression. 3. Enter the input and output as shown below: Regression mnoooo 71 Input Input Y Range: OK Cancel Input X Range: $B$1:$BS111 SA$1:$A$111 Constant is Zero 95 % Help Labels Confidence Level: SDS Output options O Qutput Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

4. Click on OK. The output is: SUMMARY OUTPUT Regression Statistics Multiple R 0.999046197 R Square 0.998093304 Adjusted R Square 0.997854967 Standard Error 0.070706392 Observations 10 ANOVA df Regression Residual Total 1 8 S MS 20.93616485 20.93616 4187.740575 0.039995152 0.004999 20.97616 Significance F 3.61672E-12 9 Intercept Force (N) Coefficients -30.26187879 0.503757576 Standard Error Stat P-value 0.51815307 -58.4034 8.20451E-12 0.007784518 64.71275 3.61672E-12 Lower 95% Upper 95% -31.45674191 -29.06701567 0.485806446 0.521708706 The Regression equation is: Vout=-30 26 +0.50x Force The slope is 0.50 and the y-intercept is -30.26. (b) The standard error of the fit is 0.07. (c) The 95% confidence interval of the best-fit line is 0.48 to 0.52. Note: If you don't have Data Analysis plugin installed in your Excel then you install it by clicking on File->Options->Addins->Under Excel Add-ins Click on Go...- >Check Analysis ToolPak and click OK. Now you will have Data Analysis option under Data Tab. Good luck with your studies!!!