Regression Analysis Report

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University of Houston *

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3360

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Statistics

Date

Feb 20, 2024

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pdf

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4

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Nguyen Bui PSID: 1987401 MECE 3360 Experimental Method Submission date: 02/13/2024 Regression Analysis Report I. Linear 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 and insert a scatter plot of Time vs. Linear Mean. 3. Display linear trendline on the plot. 4. Display the least squared value and equation for the best fit curve. 5. 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. 6. Dispaly the error bars for each y-value using the calculated uncertainty. Discussion Out of all data points, six are below and seven are above the best fit curve. However, they are in very close proximity to the curve and the rest of the data points are on the curve, indicating that the curve is a good representation of the output. The errors are also relatively small . y = 0.4243x + 1.2277 R² = 0.9978 0 2 4 6 8 10 12 0 5 10 15 20 25 Linear Mean Time Linear Regression Figure 1. Linear Regression
II. Cubic 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 and insert a scatter plot of Time vs. Linear Mean. 3. Display linear trendline on the plot. 4. Display the least squared value and equation (3 rd order polynomial) for the best fit curve. 5. 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. 6. Display the error bars for each y-value using the calculated uncertainty. Discussion As in the case of linear regression, some data points are above and below the best fit curve, but they are in very close proximity to the best fit curve. Having the R 2 close to 1 is another indication that this curve is a good prediction of the output values. y = 0.0246x 3 + 0.246x 2 + 0.3031x + 0.5971 R² = 0.996 0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Cubic Mean Time Cubic Regression Figure 2. Cubic Regression
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