Problem #5: Suppose three tests are administered to a random sample of college students. Let X₁, ..., Xy be observationvectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let xj denote a student's score on the jthexam. Suppose the covariance matrix of the data isProblem #5:S. =130556855 6825 262640Let y = C₁x1 + ₂x2 + c3x3 be an "index" of student performance with c + c3 + c3 = 1 and c₁ ≥ 0. Find theconstants C1, C2, C3 so that the variance of y over the data set is as large as possible.Enter the values of C₁, C2, C3 into the answer box below, separated by commas.numbers correct to 2 decimals

Let be an "index" of student performance with .

Answered: Problem #5: Suppose three tests are…

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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9) O Points: 0 of 1 Part 1 of 3 Save Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have on r? Row 1 19 23 31 49 51 70 79 ID. Row 2 156 155 190 141 202 191 181 Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. r= (Round to three decimal places as needed.)
Consider the following table of data X у a. Calculate the least squares line and the correlation coefficient b. Repeat part (a), but this time delete the last point. c. Draw a graph of the data, and use it to explain the dramatic difference between the answers to parts (a) and (b). 1 3 1 1 2 3 2 10 D 11 10 a. The least squares line is Y=x+ (Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.)
1.The least squares estimate of β0 is i. 2.3176 ii. 0.7176 iii. 0.8824 iv. 1.8990 2. The least squares estimate of β1 is i. 0.4773 ii. 0.2990 iii. 0.2061 iv. 0.9265 3. The linear correlation coefficient r is i. 0.4122 ii. 0.1700 iii. 0.2990 iv. 0.5683
10
A Of two personnel evaluation techniques available, the first requires a 2-hour test-interview while the second can be completed in less than an hour. The scores for each of the eight individuals who took both tests are given in the table below. Applicant Test 1 (x) Test 2 (y) 1 75 38 2 90 56 60 35 71 46 92 58 3 4 5 7 8 106 55 87 69 30 52 (a) Find the correlation coefficient r to describe the relationship between the two tests. (Round your answer to three decimal places.) r= (b) Would you be willing to use the second and quicker test rather than the longer test-interview to evaluate personnel? Explain. O The correlation coefficient is close to -1, indicating that the second and quicker test could be used in place of the longer test-interview. O The correlation coefficient is close to 1, indicating that the second and quicker test could be used in place of the longer test-interview. O The correlation coefficient is close to 1, indicating that the second and quicker test could not be…
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.
1 Professor Yema conducted a research to determine factors that influence environmental attitude. Table 1 below is a matrix of Pearson’s r correlation coefficients for the following variables used in the study: Environmental attitude (En), level of education (Le), and income (In). Table 1: Factors that influence environmental attitude ____________________________________________________________________ Variable En Le In ____________________________________________________________________ Environmental attitude (En) 1.0 Level of education (Le) 0.6** 1.0 Income (In) –0.3* 0.9*** 1.0 ____________________________________________________________________ ***Correlation is…
Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data,
I need help on Part D
An investigator has a data set which contains a response variable(y) and four explanatory variables(xı, x2, X3, X4). A correlation matrix was produced from the data set and is provided below. Correlations Y X1 X2 X3 X1 0.785 X2 0.731 0.690 X3 0.603 0.343 0.771 Х4 0.745 0.742 0.500 0.630 Does the correlation matrix provide evidence that multicollinearity may be an issue? Explain your reasoning.
3. The following table shows the scores made by six randomly selected student nurses on final examinations in three subject areas: Subject Area Student Number Fundamentals Physiology Anatomy 98 95 77 95 71 79 76 80 91 95 81 84 83 77 80 99 70 93 1 236 4 5 Test whether they perform equally well in all three subject areas at 5% level (Use Non-Parametric Methods).
4. Areal estate company wants to study the relationship between Home price in OMR 1000) and the following variables: Floor size (in 100 square feet (X 1 ) , Type of Heating (X 2 =1 if electricity and X 2 =0,if Gas) , Location of home (X 3 =1 if in town and X 3 =0 , if in village). Use this to answer the following questions: Then the degrees of freedom of Fstatistic for finding critical value is A . r 1 =3,r 2 =10 B. None C. r 1 =11,r 2 =3 D. r 1 =3,r 2 =11 E. r 1 =10; r 2 =3

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