Explanation Given: The accompanying table is based on data from the National Center for Health Statistics (Based on data from The National Center for Health Statistics). 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 8 62.7 501.6 64 3931.29 10 61.1 611 100 3733.21 12 65.5 786 144 4290.25 16 57.6 921.6 256 3317.76 18 53.7 966.6 324 2883.69 ∑ x = 64 ∑ y = 300.6 ∑ x y = 3786.8 ∑ x 2 = 888 ∑ y 2 = 18156.2 Since there are five pairs of ( x , y ) , the n value is 5

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ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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Chapter 14.5, Problem 18E

To determine

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 17E

Chapter 14.5, Problem 19E

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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 calculates the linear correlation coefficient for two variables x and y, based on the National Center for Health Statistics.

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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.

Want to see the full answer?

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.