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How to find Chi-squared and Quantitative estimate of the quality of the fit line

How to find Chi-squared and Quantitative estimate of the quality of the fit line

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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How to find Chi-squared and Quantitative estimate of the quality of the fit line

### Experimental Data Analysis: Relationship Between Stretch and Force This educational resource provides an analysis of the experimental relationship between the stretch of a material (in centimeters) and the force required to achieve that stretch (in Newtons). The data includes measurements taken by a student, labeled Student D, and is accompanied by a calculated uncertainty metric for the force measurements. #### Table of Observations | Stretch (cm) | Force (N) | Uncertainty in Force (N) | |--------------|-----------|--------------------------| | 1 | 1 | 1 | | 2 | 7 | 1 | | 3 | 17 | 1 | | 4 | 16 | 8 | | 5 | 22 | 8 | | 6 | 33 | 8 | | 7 | 61 | 1 | | 8 | 70 | 1 | | 9 | 90 | 8 | The table displays the measured stretch in centimeters, the corresponding force in Newtons, and the uncertainty in the force measurement for each stretch value. #### Graphical Analysis Below the table, a graph plots the force (N) versus the extension (cm). Key elements of the graph include: - **Title:** "Student D" - **Axes:** The x-axis represents Extension (cm) and the y-axis represents Force (N). - **Data Points:** Observations from the table are marked with blue dots. - **Error Bars:** Vertical gray lines through each point indicate the uncertainty in force measurements. - **Trend Line:** An orange curved line fitting the data is labeled with the equation \( y = x^2 + 6 \). #### Conclusion The plotted data and fitted trend line suggest a quadratic relationship between the stretch and the force, described by the equation \(y = x^2 + 6\). This indicates that as the stretch increases, the force increases non-linearly. The inclusion of error bars highlights the variability and uncertainty in the measurements, particularly noting that some measurements have higher uncertainty than others, which is critical when interpreting the accuracy and reliability of the observed trend. This analysis helps in understanding material properties and is essential for applications that require precise control of force and stretch, such as in engineering and material science experiments.
Transcribed Image Text:### Experimental Data Analysis: Relationship Between Stretch and Force This educational resource provides an analysis of the experimental relationship between the stretch of a material (in centimeters) and the force required to achieve that stretch (in Newtons). The data includes measurements taken by a student, labeled Student D, and is accompanied by a calculated uncertainty metric for the force measurements. #### Table of Observations | Stretch (cm) | Force (N) | Uncertainty in Force (N) | |--------------|-----------|--------------------------| | 1 | 1 | 1 | | 2 | 7 | 1 | | 3 | 17 | 1 | | 4 | 16 | 8 | | 5 | 22 | 8 | | 6 | 33 | 8 | | 7 | 61 | 1 | | 8 | 70 | 1 | | 9 | 90 | 8 | The table displays the measured stretch in centimeters, the corresponding force in Newtons, and the uncertainty in the force measurement for each stretch value. #### Graphical Analysis Below the table, a graph plots the force (N) versus the extension (cm). Key elements of the graph include: - **Title:** "Student D" - **Axes:** The x-axis represents Extension (cm) and the y-axis represents Force (N). - **Data Points:** Observations from the table are marked with blue dots. - **Error Bars:** Vertical gray lines through each point indicate the uncertainty in force measurements. - **Trend Line:** An orange curved line fitting the data is labeled with the equation \( y = x^2 + 6 \). #### Conclusion The plotted data and fitted trend line suggest a quadratic relationship between the stretch and the force, described by the equation \(y = x^2 + 6\). This indicates that as the stretch increases, the force increases non-linearly. The inclusion of error bars highlights the variability and uncertainty in the measurements, particularly noting that some measurements have higher uncertainty than others, which is critical when interpreting the accuracy and reliability of the observed trend. This analysis helps in understanding material properties and is essential for applications that require precise control of force and stretch, such as in engineering and material science experiments.
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