Explanation Given: The following table lists the number of years of education past high school and the annual income of five people. Definition used: If we have pairs of data for two variables x and y , the linear correlation coefficient for these data, denoted by r , is given by the formula r = n ∑ x y − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 n ( ∑ y 2 ) − ( ∑ y ) 2 , where n is the number of pairs of data we have for x and y . Calculation: Consider the given xy pairs. The computations to calculate correlation coefficient is shown below x y xy x 2 y 2 0 23 0 0 529 1 22 22 1 484 2 27 54 4 729 2 28 56 4 784 5 35 175 25 1225 ∑ x = 10 ∑ y = 135 ∑ x y = 307 ∑ x 2 = 34 ∑ y 2 = 3751 Since there are five pairs of ( x , y ) , the n value is 5

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ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Chapter 14.5, Problem 15E

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To find:

The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

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Chapter 14.5, Problem 14E

Chapter 14.5, Problem 16E

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The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

Solution Summary: The author explains the linear correlation coefficient for x and y and determines whether we can be 95% or 99% confident that there is significant correlation between the two variables.

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To find: The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.

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Chapter 14 Solutions

To find:

The linear correlation coefficient for the data and also to determine whether we can be 95% or 99% confident that there is significant linear correlation between the two variables.