Find the variance/covariance matriz for the following data set \[\

podnescijy 2021-11-16 Answered

Find the variance/covariance matriz for the following data set

\begin{array}{cc} S t u d e n t & A l g e b r a & C o m b i n a t o r i c s & A n a l y s i s \\ 1 & 90 & 80 & 90 \\ 2 & 30 & 60 & 30 \\ 3 & 60 & 60 & 50 \\ 4 & 90 & 60 & 30 \\ 5 & 40 & 70 & 40 \end{array}

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Expert Answer

Harr1957

Answered 2021-11-17 Author has 18 answers

Step 1

\begin{array}{cc} 90 & 80 & 90 \\ 30 & 60 & 30 \\ 60 & 60 & 50 \\ 90 & 60 & 30 \\ 40 & 70 & 40 \\ V a r i a n c e, f r o m E x c e l f u n c t i o n & 770 & 80 & 620 \end{array}

Correlations, from Excel function:
Corr(Algebra, Combinatorics)=0.3225=CORREL(E1:E5,F1:F5)
Corr(Algebra, Analysis)=0.5138=CORREL(E1:E5,G1:G5)
Corr(Combinatorics, Analysis)=0.8531=CORREL(F1:F5,G1:G5)
Corr(Algebra, Algebra)=1=CORREL(E1:E5,E1:E5)
Corr(Analysis, Analysis)=1=CORREL(G1:G5,G1:G5)
Corr(Combinatorics, Combinatorics)=1=CORREL(F1:F5,F1:F5)
Step 2
Variance/correlation matrix:

\begin{array}{cc} A l g e b r a & C o m b i n a t o r i c s & A n a l y s i s \\ A l g e b r a & 1 & 0.3225 & 0.5138 \\ C o m b i n a t o r i c s & 0.3225 & 1 & 0.8531 \\ A n a l y s i s & 0.5138 & 0.8531 & 1 \end{array}

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