2. Danford et al. (1960) gave an example of a covariance matrix on 41 degree of freedom.; the variable was time (in days) after radiation. The variances and covariances were S = 4685 4522 5096 5202 5035 4746 5026 5090 4847 4933 4799 5287 5408 5250 5026 5323 5280 5238 5228 6151 6192 6055 5773 6120 6092 6027 6132 6525 6231 5923 6285 6204 6137 6252 6171 5850 6185 6150 6105 6175 5745 5941 6000 5950 5959 6479 6332 6371 6382 6523 6398 6390 6798 6566 6753 (a) Can an intraclass correlation model be assumed? Test at α = 0.05. (b) Are the scores for each time period independent? Test at a = = 0.05. (c) Does the result of (b) seem reasonable? (d) Perform an equicorrelation test for the covariance matrix. (e) Perform a sphericity test for the covariance matrix.

A random sample for five exam scores produced the following (hours of study, grade) data values:Hours Studied (x)       Test Grade (y)3.5                                         882.4                                         764                                            925                                            851.1                                         60a. Compute the covariance.b. Compute the correlation coefficient

Given that the σ_AB= σ_BA, then the variance-covariance matrix for a portfolio with 50 stocks requires the calculations of ____ variances and ____ covariances.

1. Generate random 100 MVN data, p=20. The covariance matrix should be positive semi- definite symmetric matrix. (1) Show the generated data matrix. (2) Plot the scatter plot to show the correlation among variables.

The covariance matrix of an image with three spectral components is shown below. Let x₁, x₂, and x3 denote the spectral components of each pixel in the image. Find a new variable of the form y₁ = C₁X₁ + C₂X₂ + C3x3 that has maximum possible variance, subject to the constraint that c3 + c3 + c3 = 1. What percentage of the total variance in the data is explained by y₁? 27.22 19.55 6.00 S= 19.55 21.88 13.36 6.00 13.36 25.32 (...) Which of the following could be the new variable y₁? O A. Y₁ = -0.56x₁ +0.06x2 -0.83x3 O C. y₁ = 0.62x₁ +0.62x2 +0.62x3 O B. y₁ = -0.54x₁ -0.78x2 +0.32x3 ⒸD. y₁=0.54x₁1 -0.78x2 + 0.32x3 O F. y₁ = 0.62x₁ +0.63x2 +0.47x3 y₁ = 0.62x₁ +0.63x2 -0.47x3 O E. y₁=0.54x₁1 -0.78x2 -0.32x3 O G. y₁ = 0.56x₁ +0.06x2 -0.83x3 O H.

The following matrix shows the bivariate correlations for houses with garages.   Baths Beds Sqft Age Price Baths 1         Beds 0.591 1       Sqft 0.696 0.626 1     Age -0.427 -0.133 -0.069 1   Price 0.643 0.374 0.767 -0.099 1 Baths: # of bathrooms in the house Beds: # of bedrooms in the house Sqft: # of square feet in the house Age: age of the house in years Price: selling price of house Answer the following: a) Do older houses with garages sell for lower or higher prices than newer houses with garages on average? Are older houses with garages smaller or larger than newer houses with garages on average? b) Is the correlation between baths and age weaker or stronger than correlation between beds and price? c) Is the correlation between age and sqft weaker or stronger than the correlation between age and price?

You are given the following course metrics from the 1000 students thatcompleted 'Introduction to the Matrix' for the Fall 2021 semester thatresulted in a perfectly normal distribution: Mean Course Grade - 75.0Standard Deviation of Course Grades - 5.0 You are asked to evaluate the following Course Grades from an unidentifiedclass of students:# Grade # Grade # Grade # Grade # Grade1 75       6 60      11 55     16 90      21 952 55       7 70      12 80     17 65      22 603 60       8 75      13 85     18 80      23 904 75       9 65      14 70     19 75      24 755 60      10 90     15 95     20 80      25 95(a) Is this class 25 student class representative of an 'Introduction to theMatrix' class?  Provide statistical analysis (Table, Graphs, metrics, etc.) and anexplanation of the rationale used for comparison between this classof 25 students and the 1000 'Introduction to the Matrix' students.