Explanation Given: The given xy pairs are (3, 5), (7, 8), (4, 6), (6, 7). 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 3 5 15 9 25 7 8 56 49 64 4 6 24 16 36 6 7 42 36 49 ∑ x = 20 ∑ y = 26 ∑ x y = 137 ∑ x 2 = 110 ∑ y 2 = 174 Substitute the known values in r = n ∑ x y − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 n ( ∑ y 2 ) − ( ∑ y ) 2

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Correlation

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.

Regression Analysis

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 7E

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Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

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Chapter 14.5, Problem 6E

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Whether we can be 95% or 99% confident that there is significant linear correlation between x and y .

Solution Summary: The author explains that they can be 95% or 99% confident that there is significant linear correlation between x and y.

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To find:

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

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Chapter 14 Solutions

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y .

Solution Summary: The author explains that they can be 95% or 99% confident that there is significant linear correlation between x and y.

Concept explainers

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To find: Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

Want to see the full answer?

Chapter 14 Solutions

To find:

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.