Regression Analysis Report

III. Sine Regression Procedures 1. Compute Mean and Standard Deviation of each row. 2. Copy-paste Time values (first column), Mean, and Standard Deviation into another sheet. 3. Calculate the uncertainty of each row by using the equation t*(st dev)/sqrt(n) where t = 2 for 95% confidence interval and n = 40 is the number of data points. 4. Estimate C 1 , C 2 , C 3 , and C 4 values in the best fit curve function C 1 -eC 2 x sin(C 3 x + C 4 ) where C 1 is the initial amplitude of the sine wave, C 2 is the reciprocal of the time constant (time constant is the time where the amplitude decays to 1/e^(initial amplitude)), C 3 is the angular frequency, and C 4 is the phase shift pi/2. 5. Calculate predicted values using the C’s values and above equation. 6. Calculate the square error with function = (Sine Mean – Predicted Value)^2 and add up the square error values. 7. Use Excel Solver to minimize the sum of the square error values and therefore determine new predicted values and C’s values. 8. Insert a scatter plot of Time vs. Linear Mean and use the new predicted values to construct the best fit curve on the plot. 9. Calculate the uncertainty of each row by using the equation t*(st dev)/sqrt(n) where t = 2 for 95% confidence interval and n = 40 is the number of data points. 10. Display the error bars for each y-value using the calculated uncertainty. -1 -0.5 0 0.5 1 1.5 0 5 10 15 20 25 Sine Mean Time Decaying Sine Wave Regression y = 1.00189e -0.25208x sin(3.00069x + 1.57265) Figure 3. Sine Regression