Suppose three tests are administered to a random sample of college students. Let X1, ..., XN 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 j th exam.Suppose the covariance matrix of the data is26.Let y be an “index" of student performance, withy = c,x1 + C2X2 + C3X3 and cỉ + c² + c = 1. Choose c1, C2, C3%3D%3Dso that the variance of y over the data set is as large as possible. [Hint: The eigenvalues of the sample covariance matrixare 1 = 3, 6, and 9.1

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Answered: Suppose three tests are administered to…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
Given data points (1, 3), (0, -1). (2. 1). (4. 1). (-2. 1), center the data and compute the sample covariance matrix. Record the entries of the covariance matrix row by row, separated by commas.
Create a correlation matrix Table in APA style to report the correlations among these variables, along with their Ms and SDs.
Which of the scatter diagrams below suggests a strong positive linear relationship between the x and y variables?
The following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night. Intercept 52.536016 9.353956 5.616449 0.000802 Hours Unsupervised 7.173889 1.656518 4.330703 0.003435 Hours Playing Video Games 2.025042 1.731352 1.169631 0.280429 Step 1 of 2:Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Step 2 of 2:Indicate if any of the independent variables could be eliminated at the 0.010.01 level of significance. (x1, x2, or keep all variables)
The following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 62.711817 4.607133 13.611896 0.000010 Hours Unsupervised 0.635048 0.915495 0.693666 0.513836 Hours Playing Video Games 7.528738 1.296727 5.805955 0.001145 Copy Data Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Answer 田 Tables 国 Keypad How to enter your answer (opens in new window) Keyboard Shortcuts X +
The following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 62.711817 4.607133 13.611896 0.000010 Hours Unsupervised 0.635048 0.915495 0.693666 0.513836 Hours Playing Video Games 7.528738 1.296727 5.805955 0.001145 Copy Data Step 2 of 2: Indicate if any of the independent variables could be eliminated at the 0.05 level of significance. E Tables E Keypad Answer Keyboard Shortcuts O x2 O Keep all variables
The following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per nigh, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 50.375000 7.719473 6.525704 0.000326 Hours Unsupervised 6.682500 1.484194 4.502444 0.002790 Hours Playing Video Games 1.535000 1.145568 1.339947 0.222124 Step 1: Write the multiple regression equation for the computer output given. y=_+_x1+_x2 Step 2: Indicate if any of the independent variables could be eliminated at the 0.05 level of significance. A) x1 B) x2 C) Keep all variables
The coefficient of correlation will be zero if if the relationship between two variables x and y is non-linear. if there is no linear relationship between two variables. if the covariance between two variables x and y is 1. None of the above.
If the correlation coefficient (r) is equal to 1.00, then all the data points must fall exactly on a straight line with a slope that equals 1.00. O all the data points must fall exactly on a straight line with a negative slope. O all the data points must fall exactly on a straight line with a positive slope. all the data points must fall exactly on a horizontal straight line with a zero slope.
What does it mean if the linear correlation coefficient is A) 0? B) -1?
Are any of the variables significantly correlated? If so, which ones and in which direction (positive or negative)? Correlation matrix: Health Score Anxiety Score Anxiety 0.13994335 Score (0.5047) Stress Score 0.38584335 0.010340294 (0.0568) (0.9609)

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