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TEAC-MEOH 2500 2000 1500 1000 500 FR NF -8 100 Tea Samples of Methanol 150 200 TPC-MEOH 250 fermented correlation coefficient:0.6907772111770509 error: 0.10124972471697807 p: 8.9463696660193e-12 **** 300 350 48 nonfermented correlation coefficient: 0.21863626031266953 error: 0.14233599637989416 p: 0.12452430345122018 a. Which type(s) of tea samples (fermented or unfermented) show correlations between the two variables? How is the correlation (or non-correlation) of the two types related to the shape of the ellipses in the figure? b. Suppose that you want to distinguish fermented and unfermented samples based only one of the two variables (TPC or TEAC). Based on what the graph shows, which variable should you choose in order to best distinguish between the two? Justify your answer.

TEAC-MEOH 2500 2000 1500 1000 500 FR NF -8 100 Tea Samples of Methanol 150 200 TPC-MEOH 250 fermented correlation coefficient:0.6907772111770509 error: 0.10124972471697807 p: 8.9463696660193e-12 **** 300 350 48 nonfermented correlation coefficient: 0.21863626031266953 error: 0.14233599637989416 p: 0.12452430345122018 a. Which type(s) of tea samples (fermented or unfermented) show correlations between the two variables? How is the correlation (or non-correlation) of the two types related to the shape of the ellipses in the figure? b. Suppose that you want to distinguish fermented and unfermented samples based only one of the two variables (TPC or TEAC). Based on what the graph shows, which variable should you choose in order to best distinguish between the two? Justify your answer.

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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Please do part B and Exercise 4. Please make sure you explain

**Tea Samples of Methanol** The graph displays the relationship between TPC-MEOH (Total Phenolic Content in Methanol) and TEAC-MEOH (Trolox Equivalent Antioxidant Capacity in Methanol) for two types of tea samples: Fermented (FR) and Non-Fermented (NF). - **Key:** - **FR (Fermented):** Represented by blue ellipses and points. - **NF (Non-Fermented):** Represented by orange ellipses and points. - **Observations:** - The graph shows two clusters of data points, each enclosed by an ellipse, indicating the distribution of each tea type's samples. - The x-axis represents the TPC-MEOH values ranging from 50 to 400. - The y-axis represents the TEAC-MEOH values ranging from 500 to 2500. **Correlation Details:** - **Fermented Tea Samples:** - Correlation Coefficient: 0.690777211177059 - Error: 0.1012497247169787 - p-value: 8.946396668193e-12 - **Non-Fermented Tea Samples:** - Correlation Coefficient: 0.218632603126953 - Error: 0.14233959637989416 - p-value: 0.12452430345210218 **Analysis Questions:** a. **Correlation in Tea Samples:** - Fermented tea samples show a stronger correlation (0.6908) between TPC-MEOH and TEAC-MEOH than non-fermented samples (0.2186). - This difference is visually represented by the tighter clustering and more elongated shape of the ellipse around the fermented samples. b. **Distinguishing Between Tea Types:** - Based on the graph, TEAC-MEOH is a more distinguishing variable between the two types. The separation between the clusters is more defined along the TEAC-MEOH axis, which would make it easier to discriminate between fermented and non-fermented samples.
Transcribed Image Text:**Tea Samples of Methanol** The graph displays the relationship between TPC-MEOH (Total Phenolic Content in Methanol) and TEAC-MEOH (Trolox Equivalent Antioxidant Capacity in Methanol) for two types of tea samples: Fermented (FR) and Non-Fermented (NF). - **Key:** - **FR (Fermented):** Represented by blue ellipses and points. - **NF (Non-Fermented):** Represented by orange ellipses and points. - **Observations:** - The graph shows two clusters of data points, each enclosed by an ellipse, indicating the distribution of each tea type's samples. - The x-axis represents the TPC-MEOH values ranging from 50 to 400. - The y-axis represents the TEAC-MEOH values ranging from 500 to 2500. **Correlation Details:** - **Fermented Tea Samples:** - Correlation Coefficient: 0.690777211177059 - Error: 0.1012497247169787 - p-value: 8.946396668193e-12 - **Non-Fermented Tea Samples:** - Correlation Coefficient: 0.218632603126953 - Error: 0.14233959637989416 - p-value: 0.12452430345210218 **Analysis Questions:** a. **Correlation in Tea Samples:** - Fermented tea samples show a stronger correlation (0.6908) between TPC-MEOH and TEAC-MEOH than non-fermented samples (0.2186). - This difference is visually represented by the tighter clustering and more elongated shape of the ellipse around the fermented samples. b. **Distinguishing Between Tea Types:** - Based on the graph, TEAC-MEOH is a more distinguishing variable between the two types. The separation between the clusters is more defined along the TEAC-MEOH axis, which would make it easier to discriminate between fermented and non-fermented samples.
**Understanding Correlated Variables in Classification** Generally, if two variables are correlated, they provide similar information about the samples. When two variables are employed for classification, and the correlation differs across classes, this can aid in distinguishing between the classes by reducing the overlap between confidence ellipses. **Exercise 4:** Sketch (on paper or using a computer application) a 2-D plot illustrating the confidence ellipses for two classes with two variables. In your sketch, demonstrate a scenario where the two individual variables have similar distributions in the two classes, but the overlap area between confidence ellipses is minimized. This occurs because the variables are correlated differently in the different classes.
Transcribed Image Text:**Understanding Correlated Variables in Classification** Generally, if two variables are correlated, they provide similar information about the samples. When two variables are employed for classification, and the correlation differs across classes, this can aid in distinguishing between the classes by reducing the overlap between confidence ellipses. **Exercise 4:** Sketch (on paper or using a computer application) a 2-D plot illustrating the confidence ellipses for two classes with two variables. In your sketch, demonstrate a scenario where the two individual variables have similar distributions in the two classes, but the overlap area between confidence ellipses is minimized. This occurs because the variables are correlated differently in the different classes.
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