2. Danford et al. (1960) gave an example of a covariance matrix on41 degree of freedom.; the variable was time (in days) after radiation. Thevariances and covariances wereS =4685 4522 5096 5202 5035 4746 5026 5090 4847 49334799 5287 5408 5250 5026 5323 5280 5238 522861516192 6055 5773 6120 6092 6027 61326525 6231 5923 6285 6204 6137 62526171 5850 6185 6150 6105 61755745 5941 6000 5950 595964796332 6371 63826523 6398 63906798 65666753(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.

Step 1:(a) Intraclass Correlation Model:The intraclass correlation coefficient (ICC) assesses the…

Answered: 2. Danford et al. (1960) gave an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Example 2. Calculate the covariance of the following pairs of observations of the two variates X and Y. (1, 6), (2, 9), (3, 6), (4, 7), (5, 8). (6, 5), (7, 12), (8, 3), (9, 17), (10, 1). Cs Scanned with CamScanner
Here are the summary statistics (sample covariance matrix and sample means) for the Dutch and Spanish returns from the countries data set: Covariances spain 0.0013035 netherlands netherlands spain 0.0014360 0.0013035 0.0036288 What is the sample correlation between the Dutch and Spanish returns? 0.00144 0.00104 0.57168 0.03789 Cannot be determined A) D) E)
How to interpret the following correlation matrix X1 X2 X3 X4X1 1 X2 -0.026651075 1 X3 -0.251215273 0.478429673 1 X4 0.009303729 0.185917439 -0.126481433 1
Suppose the random variables X,, X,,X3 have the population variance/covariance matrix: -2 0 E=-2 5 1 Calculate the principal components and interpret their meaning. What can be gained from knowing these values?
Ensure the RaceResults worksheet is active, then use the FREQUENCY function to calculate the frequency distribution of the race results in column D. Place your results in the range G4:G9. Enter a function in cell F22 to calculate the correlation between age (Columns C) and race time (Column D). Enter a function in cell G22 to calculate the covariance between age and race time. Enter a function in cell H22 to calculate the variance of the ages in the data set. Note this is a sample of data not a population. Enter a function in cell 122 to calculate the standard deviation of the ages in the data set.
4. According to the information given below, compute the correlation coefficient and the covariance coefficient between stock A and stock B. Standard deviation of the portfolio (stock A and stock B) :0.37 Standard deviation of the stock A : 0.38 Standard deviation of the stock B :0.43 Weight for stock A : 0.60 Weight for stock B :0.40 NOTE: PLEASE SHOW HOW YOU COMPUTE EACH OF THE ITEMS.
How would I solve this assuming the population variances are equal?
Let Rand S denote the sample correlation matrix and the sample covariance matrix, respectively. Let D= diag(s.22. Ann). Show that S-DRD/2 Under what conditions can we conclude from the equation above that R D-1/2SD-1/2? Justify your answer.
prove
Question 4Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained: d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
If we reject the null hypothesis, H0: ρ = 0, what can we conclude about the population correlation coefficient? A) It is zero. B) It could be zero. C) It is not zero. D) It equals the computed sample correlation.
Five observations taken for two variables follow. xi 4 5 12 4 13 yi 50 50 30 50 20 Compute the sample covariance (to 1 decimal and enter negative value as negative figure). Compute the sample correlation coefficient (to 3 decimals and enter negative value as negative figure)

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