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: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Chapter 14.5, Problem 18E

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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 17E

Chapter 14.5, Problem 19E

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Chapter 14 Solutions

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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.

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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.