2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de...
26
Transcript of 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de...
![Page 1: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/1.jpg)
![Page 2: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/2.jpg)
![Page 3: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/3.jpg)
Var(X) = E[X2] – E[X]2 = 12 . P[X=1] – p2
= p – p2 = p(1-p) Exercise!
![Page 4: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/4.jpg)
var(∑ixi)=∑ivar(xi) for independent xi
![Page 5: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/5.jpg)
pe = p if e = 1pe = 1 if e = 0
Result: we have transformed a single categorical variable taking one of m values ai into an m-dimensional numeric variable taking value 1 in the ith column and 0 elsewhere
![Page 6: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/6.jpg)
![Page 7: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/7.jpg)
Bins -> Categorical attributes {a1, a2, a3, a4}
![Page 8: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/8.jpg)
![Page 9: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/9.jpg)
One categorial variable Ai for each possible attribute value ai
![Page 10: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/10.jpg)
= n! / (n1! n2!...nm!) = #ways of choosing m subsets of sizes n1, n2,…,nm
![Page 11: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/11.jpg)
![Page 12: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/12.jpg)
![Page 13: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/13.jpg)
![Page 14: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/14.jpg)
![Page 15: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/15.jpg)
![Page 16: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/16.jpg)
![Page 17: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/17.jpg)
![Page 18: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/18.jpg)
![Page 19: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/19.jpg)
![Page 20: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/20.jpg)
![Page 21: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/21.jpg)
![Page 22: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/22.jpg)
![Page 23: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/23.jpg)
![Page 24: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/24.jpg)
![Page 25: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/25.jpg)
![Page 26: 2 = p –p - CESGcesg.tamu.edu/wp-content/uploads/2016/02/chap3.pptx.nd_.pdfUniversidade Federal de Minas Gerais, Belo Horizonte, Brazil Chapter 3: Categorical Attributes Zaki & Jr.](https://reader034.fdocuments.in/reader034/viewer/2022042314/5f029fa47e708231d4053073/html5/thumbnails/26.jpg)