Ask a question from expert

Ask now

Statistical Methods in Engineering Assignment

8 Pages1027 Words277 Views
   

Added on  2020-05-28

Statistical Methods in Engineering Assignment

   Added on 2020-05-28

BookmarkShareRelated Documents
Statistical Methods in EngineeringStudent Name:University15th January 2018
Statistical Methods in Engineering Assignment_1
Task 1: OrthogonalizationAccording to the Gram-Schmidt Process. If we letV to be an inner product spaceand{v1,v2,...,vn}to be a set of linearly independent vectors that are inV. Then there exists anorthonormalsetofvectors{e1,e2,...,en}ofVsuchthatspan(v1,v2,...,vj)=span(e1,e2,...,ej)foreachj=1,2,...,n.The proof is done by induction.Supposej=1; we can then lete1=v1v1. But v10sincev10bearing in mind that a set oflinearly independent vectors has no zero vector. From this it is clear thatspan(v1)=span(e1)based on the fact thatv1ande1differ only byv1as such they are scalar multiples of eachother. Again,e1=v1v1=1.Next considering the case whenj>1, and assuming a set of orthonormal vectors of j1,{e1,e2,...,ej1}such thatspan(v1,v2,...,vj1)=span(e1,e2,...,ej1).Now since{v1,v2,...,vn}is a linearly independent set of vectors, we have thatvjspan(v1,v2,...,vj1). Thus we definethe vectorejas:ej=vj¿vj,e1>e1¿vj,e2>e2...¿vj,ej1>ej1vj¿vj,e1>e1¿vj,e2>e2...¿vj,ej1>ej1Clearlyej=1. Next is to show thatejis orthonormal toe1,e2,...,ej1. Given any integerksuchthat1k<j,weconsidertheinnerproductofejwithek.LetN=vj¿vj,e1>e1¿vj,e2>e2...¿vj,ej1>ej1. Then we have that:ej,ek=vj¿vj,e1>e1¿vj,e2>e2...¿vj,ej1>ej1N,ek¿1Nvj¿vj,e1>e1¿vj,e2>e2...¿vj,ej1>ej1,ek¿1N(vj,ekvj,ek)=0Now it is clear that the set of vectors{e1,e2,...,ej}is orthonormal. It is therefore evidentthatspan(v1,v2,...,vj)=span(e1,e2,...,ej)
Statistical Methods in Engineering Assignment_2
Task 2: Linear models by handa)observation vector y and evidence matrix XSolutionObservation vector is;y=[0124]Evidence matrix is;X=[11101112]b)We sought to find the equation y=β0+β1x of the least-squares line that best fits the given data points.Solution^β=[β0β1]=(X'X)1X'y=([11111012][11101112])1[11111012][0124]=[0.80000.7429]Thus the equation is;y=0.8000+0.7429x
Statistical Methods in Engineering Assignment_3

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
Anova Assignment | Answers
|22
|2126
|25

Quantitative Analysis 1
|15
|1568
|2

Statistics - Desklib Online Library for Study Material
|8
|726
|67

Regression Analysis of Relationship between Annual Income and Credit Card Charges
|7
|1017
|404

Regression Analysis in Statistics
|11
|1898
|65

SEO Suggestions for Desklib Online Library
|4
|530
|447