Question

Suppose the correlation between two variables is $r=0.23 .$ What will the new correlation be if 0.14 is added to all values of the $x$ -variable, every value of the $y$ -variable is doubled, and the two variables are interchanged? (A) 0.74 (B) 0.37 (C) 0.23 (D) -0.23 (E) -0.74

Name: Problem 7, Chapter 2: AP Statistics with 6 Practice Tests
Uploaded: 2021-05-03T23:37:21-08:00
Duration: 1 min 31 s
Channel: Jerrah Biggerstaff
Description: Suppose the correlation between two variables is r=0.23 . What will the new correlation be if 0.14 is added to all values of the x -variable, every value of the y -variable is doubled, and the two variables are interchanged? (A) 0.74 (B) 0.37 (C) 0.23 (D) -0.23 (E) -0.74

   Suppose the correlation between two variables is $r=0.23 .$
What will the new correlation be if 0.14 is added to all values
of the $x$ -variable, every value of the $y$ -variable is doubled, and the two variables are interchanged?
(A) 0.74
(B) 0.37
(C) 0.23
(D) -0.23
(E) -0.74

AP Statistics with 6 Practice Tests

Martin Sternstein 11th Edition

Chapter 2, Problem 7

Instant Answer

Solved by Expert Jerrah Biggerstaff

05/03/2021

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It is not affected by changes in the center or scale of the variables. Show more…

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Suppose the correlation between two variables is $r=0.23 .$ What will the new correlation be if 0.14 is added to all values of the $x$ -variable, every value of the $y$ -variable is doubled, and the two variables are interchanged? (A) 0.74 (B) 0.37 (C) 0.23 (D) -0.23 (E) -0.74

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Key Concepts

Correlation Coefficient

The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is a standardized measure that ranges between -1 and 1, where values close to 0 indicate weak linear relationships and values near -1 or 1 indicate strong negative or positive linear relationships, respectively.

Linear Transformations

Linear transformations, such as adding a constant to a variable or multiplying it by a positive constant, do not affect the correlation between two variables. These operations change the position and scale of the data but preserve the linear relationship, leaving the coefficient unchanged.

Symmetry of Correlation

The correlation coefficient is symmetric with respect to the two variables; that is, the correlation between x and y is the same as the correlation between y and x. Interchanging the roles of the variables does not affect the value of the correlation coefficient.

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