Title: Calculating the Variance/Covariance Matrix for a Data Set---## Data SetThe table below presents scores from five students across three subjects: Algebra, Combinatorics, and Analysis.| Student | Algebra | Combinatorics | Analysis ||---------|---------|---------------|----------|| 1 | 90 | 80 | 90 || 2 | 30 | 60 | 30 || 3 | 60 | 60 | 50 || 4 | 90 | 60 | 30 || 5 | 40 | 70 | 40 |## ObjectiveThe task is to determine the variance/covariance matrix for the data set provided.The variance/covariance matrix is a statistical measure that helps analyze the relationships and variations between different data sets—in this case, the scores in the three subjects. Each element in the matrix represents the covariance between two different subjects or the variance within one subject.

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Description: Title: Calculating the Variance/Covariance Matrix for a Data Set---## Data SetThe table below presents scores from five students across three subjects: Algebra, Combinatorics, and Analysis.| Student | Algebra | Combinatorics | Analysis ||---------|-

90 80 90 30 60 30 60 60 50 90 60 30 40 70 40 Variance, from Excel function 770…

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Title: Calculating the Variance/Covariance Matrix for a Data Set

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## Data Set

The table below presents scores from five students across three subjects: Algebra, Combinatorics, and Analysis.

| Student | Algebra | Combinatorics | Analysis |
|---------|---------|---------------|----------|
| 1 | 90 | 80 | 90 |
| 2 | 30 | 60 | 30 |
| 3 | 60 | 60 | 50 |
| 4 | 90 | 60 | 30 |
| 5 | 40 | 70 | 40 |

## Objective

The task is to determine the variance/covariance matrix for the data set provided.

The variance/covariance matrix is a statistical measure that helps analyze the relationships and variations between different data sets—in this case, the scores in the three subjects. Each element in the matrix represents the covariance between two different subjects or the variance within one subject.

Expert Solution

Step 1

	90	80	90
	30	60	30
	60	60	50
	90	60	30
	40	70	40
Variance, from Excel function	770	80	620

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)

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