Find the variance/covariance matriz for the following data set

$$\begin{array}{|cccc|}\hline Student& Algebra& Combinatorics& Analysis\\ 1& 90& 80& 90\\ 2& 30& 60& 30\\ 3& 60& 60& 50\\ 4& 90& 60& 30\\ 5& 40& 70& 40\\ \hline\end{array}$$

podnescijy
2021-11-16
Answered

Find the variance/covariance matriz for the following data set

$$\begin{array}{|cccc|}\hline Student& Algebra& Combinatorics& Analysis\\ 1& 90& 80& 90\\ 2& 30& 60& 30\\ 3& 60& 60& 50\\ 4& 90& 60& 30\\ 5& 40& 70& 40\\ \hline\end{array}$$

You can still ask an expert for help

Harr1957

Answered 2021-11-17
Author has **18** answers

Step 1

$$\begin{array}{|cccc|}\hline & 90& 80& 90\\ & 30& 60& 30\\ & 60& 60& 50\\ & 90& 60& 30\\ & 40& 70& 40\\ Variance,\text{}from\text{}Excel\text{}function& 770& 80& 620\\ \hline\end{array}$$

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:

$$\begin{array}{cccc}& Algebra& Combinatorics& Analysis\\ Algebra& 1& 0.3225& 0.5138\\ Combinatorics& 0.3225& 1& 0.8531\\ Analysis& 0.5138& 0.8531& 1\end{array}$$

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:

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What is the maximum monthly profit realizable?

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$\text{Var}\left(\hat{\mu}\right)=\frac{{\sigma}^{2}({n}_{1}+2{n}_{2})}{{({n}_{1}+{n}_{2})}^{2}}.$

where$\sigma}^{2$ is a constant.

Can we say that$\text{Var}\left(\hat{\mu}\right)\approx \frac{1}{{n}_{1}+{n}_{2}}$ and then conclude that $\text{Var}\left(\hat{\mu}\right)\to 0$ as $n}_{1}\to \mathrm{\infty$ and $n}_{2}\to \mathrm{\infty$ ?

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where

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A company charges $\mathrm{\$}2.50}$ per bottle when a certain beverage is bought in lots of 120 bottles or less, with a price per bottle of $\mathrm{\$}2.25}$ if more than 120 bottles are purchased. Let $C\left(x\right)$ represent the cost of x bottles. Find the cost for the following numbers of bottles.

a) 90

b) 120

c) 150

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b) 120

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