Explanation Given: The accompanying table lists the average SAT scores and teachers’ salaries for certain states. 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 2 901 44 39644 811801 1936 903 35 31605 815409 1225 1040 30 31200 1081600 900 994 29 28826 988036 841 993 26 25818 986049 676 ∑ x = 4831 ∑ y = 164 ∑ x y = 157093 ∑ x 2 = 4682895 ∑ y 2 = 5578 Since there are five pairs of ( x , y ) , the n value is 5

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ISBN: 8220103632027

Author: Pirnot

Publisher: Pearson Education (US)

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Chapter 14.5, Problem 16E

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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 15E

Chapter 14.5, Problem 17E

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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 two variables x and y and determines whether there is significant correlation between the 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.