ISYE412HW2

.docx

School

University of Wisconsin, Madison *

*We aren’t endorsed by this school

Course

412

Subject

Industrial Engineering

Date

Apr 3, 2024

Type

docx

Pages

4

Uploaded by MinisterThunderLemur27

Report
ISYE 412 Fundamentals of industrial data analytics Homework 2 Problem 1 (25 points): Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 11, 13, 14, 17, 18, 19, 19, 22, 22, 25, 25, 26, 26, 28, 30, 31, 32, 32, 35, 35, 36, 41, 43, 45, 47, 54, 72. Use smoothing by bin means to smooth the data above with an equal bin depth of 3. Illustrate your steps. Comment on the e ff ect of this technique for the given data. We group up the age values in groups of 3 values and find the mean of the bin group 1. 11, 13, 14 → Mean = 12.67 2. 17, 18, 19 → Mean = 18 3. 19, 22, 22 → Mean = 21 4. 25, 25, 26 → Mean = 25.33 5. 26, 28, 30 → Mean = 28 6. 31, 32, 32 → Mean = 31.67 7. 35, 35, 36 → Mean = 35.33 8. 41, 43, 45 → Mean = 43 9. 47, 54, 72 → Mean = 57.67 Then each value in each group will be replaced by the mean which will result in smoothened data 12.67, 12.67, 12.67, 18, 18, 18, 21, 21, 21, 25.33, 25.33, 25.33, 28, 28, 28, 31.67, 31.67, 31.67, 35.33, 35.33, 35.33, 43, 43, 43, 57.67, 57.67, 57.67 This smoothened data reduces the variability of the age day are less possible values within the list Problem 2 (25 points): Use the methods below to normalize the following group of data: 200, 800, 500, 400, 1000 (a) min-max normalization by setting min = 0 and max = 1 (b) z-score normalization (c) normalization by decimal scaling
Problem 3 (25 points) Suppose a hospital tested the age and body fat data for 18 randomly selected adults with the following result Age 21 22 26 27 37 41 44 46 51 %Fat 9.6 26 7.4 17.9 32.8 24.4 29 27 31 Age 54 55 55 58 59 61 61 63 64 %Fat 35.9 42.2 27.1 31.5 30.5 36 42 37.5 36.5 (a) Use R to normalize the two attributes based on z-score normalization. Show your code and result. Age_norm Result: -1.76267097 -1.69473076 -1.42296993 -1.35502972 -0.67562763 - 0.40386680 -0.20004617 -0.06416575 0.27553529 0.47935592 0.54729613 0.54729613 0.75111675 0.81905696 0.95493738 0.95493738 1.09081780 1.15875800 Fat_pct_norm Result: -2.01357199 -0.32251523 -2.24042107 -1.15773229 0.37865465 - 0.48749638 -0.01317558 -0.21940201 0.19305086 0.69830562 1.34791889 -0.20909069 0.24460747 0.14149425 0.70861694 1.32729625 0.86328677 0.76017355 (b) Calculate the correlation coe ffi cient (Pearson’s product moment coe ffi cient). Are these two attributes positively or negatively correlated? Compute their covariance. Using sample covariance Covariance: 116.6134 Correlation: 0.8169391 From these values, we can say that the data is positively correlated. This suggests that as age increases, there tends to be an increase in body fat percentage. This aligns with the positive covariance value which suggests a positive relationship between age and body fat percentage.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help