Example 17.4 In a problem involving three variables X₁, X₂ and X3, we find thatr12 = 0.8, r13 = 0.6, 23 = 0.5Find the values of coefficients of partial correlation r23.1 and r13.2.

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Answered: Example 17.4 In a problem involving…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter9: Solving Quadratic Functions

Section: Chapter Questions

Problem 4CA

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
1 The coefficient of correlation between X and Y is and 3 Var(X) = o,? = a, Var(Y) = o,? = 4a and Var(Z) =0,? = 114, where Z = 3X- 4Y. What is a? O a. 4 b. 2 O .3 O d. 5
3. Two lists of numbers, X and Y, have a correlation of 0.3; X and Z have a correlation of - 0.7 We know that: A. the stronger correlation is the correlation of X and Y, since it is positive. B. the stronger correlation is the correlation of X and Z. C. the two correlations are equally strong, since 1.0 - 0.7 = 0.3 D. We cannot tell which is stronger without more information. 4. Which of the following sets of variables is most likely to have a negative association? A. the number of bedrooms and the number of bathrooms in a house B. the number of rooms in a house and the time it takes to vacuum the house C. the age of a house and the cleanliness of the carpets inside D. the size of a house and its selling price
A. Describe the strength and direction of correlation of the following pairs of variables. Complete the table bellows and compute the value of correlation coefficient (r). Using the formula --- r= n(Exy)-(Ex)(Ey) √InEx²-(Ex)²] [nEy²-(Ey)²] 2. It is hypothesized that the number of hours that a student studies (X) is related to the examination grade (Y) obtained. The following are data obtained from ten students. Determine if there is a relationship between the two variables. Baby X Y A 8 56 B 5 44 C 11 79 T D 13 72 E 10 70 F 5 54 G 18 94 H 15 85 J 2 8 33 65
A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values are multiplied by 2 and the correlation is computed for the new scores, which value will be obtained for the new correlation?
Two lists of numbers, X and Y, have a correlation of 0.4; X and Z have a correlation of - 0.6. We know that: A. the stronger correlation is the correlation of X and Y, since it is positive. B. the stronger correlation is the correlation of X and Z. C. the two correlations are equally strong, since 1.0 - 0.6 = 0.4 D. We cannot tell which is stronger without more information. Would the answer be D?
If a linear relation exists between the variables x and y, then the coefficient of correlation between them is + 1 or – 1. |
Which of the following is true of the correlation r? It measures the strength of the straight-line relationship between two quantitative variables. It cannot be greater than 1 or less than 1. A correlation of +1 or –1 can only happen if there is a perfect straight-line relationship between two quantitative variables. Correlation is 0 only when there is no association between the variables. Correlation changes when the explanatory and response variables are switched.
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.
A. Describe the strength and direction of correlation of the following pairs of variables. Complete the table bellows and compute the value of correlation coefficient (r). Using the formula --- n(Exy) - (Ex)(Ey) √InEx²-(Ex)²] [nEy²-(Ey)²] 1. The following are the ages of (X) of the babies in months and their heights (Y) in centimeters. Determine if there is a relationship between their ages and heights. Baby X Y 36 86 48 90 51 91 54 93 57 94 60 95 ABCDEF
2. (a) If simple correlation between the variables X,, X, and X, are same (+ 1), then show that i. all the partial correlation coefficients will be same and ii. multiple correlations will also be same.
If the coefficient of determination is equal to 1, then the correlation coefficient A. must also be equal to 1 B. can be either -1 or +1 C. must be -1 D. can be any value between -1 to +1

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Example 17.4 In a problem involving three variables X₁, X₂ and X3, we find that r12 = 0.8, 13 = 0.6, 723 = 0.5 Find the values of coefficients of partial correlation 23.1 and 13.2.