Explanation Calculation: Consider the set of data points of part (a) as ( 1 , 3 ) , ( − 2 , 9 ) , ( 2 , 1 ) . The coefficient of correlation r is calculated as; r = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 ⋅ n ( ∑ y 2 ) − ( ∑ y ) 2 Where n is the number of data points. Make the table for the values of xy , x 2 and y 2 on substituting the values of x and y . Then, the table is as follows: x y xy x 2 y 2 1 3 3 1 9 − 2 9 − 18 4 81 2 1 2 4 1 ∑ ( Sum ) 1 13 − 13 9 91 Hence, n = 3 , ∑ x = 1 , ∑ y = 13 , ∑ ( x y ) = − 13 , ∑ ( x 2 ) = 9 and ∑ ( y 2 ) = 91 . Compute the correlation coefficient r by substituting the values in the formula, as; r = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 ⋅ n ( ∑ y 2 ) − ( ∑ y ) 2 = ( 3 ) ( − 13 ) − ( 1 ) ( 13 ) ( 3 ) ( 9 ) − ( 1 ) 2 ⋅ ( 3 ) ( 91 ) − ( 13 ) 2 = − 39 − 13 27 − 1 ⋅ 273 − 169 Solve further as, r = − 52 26 ⋅ 104 = − 52 52 = − 1 Consider the set of data points of part (b) as ( 0 , 1 ) , ( 1 , 0 ) , ( 2 , 1 ) . Make the table for the values of xy , x 2 and y 2 on substituting the values of x and y . Then, the table is as follows: x y xy x 2 y 2 0 1 0 0 1 1 0 0 1 0 2 1 2 4 1 ∑ ( Sum ) 3 2 2 5 2 Hence, n = 3 , ∑ x = 3 , ∑ y = 2 , ∑ ( x y ) = 2 , ∑ ( x 2 ) = 5 and ∑ ( y 2 ) = 2

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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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 1.4, Problem 14E

To determine

The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient:

(a)(1,3), (−2,9), (2,1)

(b)(0,1), (1,0), (2,1)

(c)(0,0), (5,−5), (2,−2.1)

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Chapter 1.4, Problem 13E

Chapter 1.4, Problem 15E

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The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient : (a) ( 1 , 3 ) , ( − 2 , 9 ) , ( 2 , 1 ) (b) ( 0 , 1 ) , ( 1 , 0 ) , ( 2 , 1 ) (c) ( 0 , 0 ) , ( 5 , − 5 ) , ( 2 , − 2.1 )

Solution Summary: The author analyzes the correlation coefficients of the data sets to determine the best, worst, and perfect fit for the associated regression line.

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The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient:

(a)(1,3), (−2,9), (2,1)

(b)(0,1), (1,0), (2,1)

(c)(0,0), (5,−5), (2,−2.1)

Want to see the full answer?

Chapter 1 Solutions

The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient : (a) ( 1 , 3 ) , ( − 2 , 9 ) , ( 2 , 1 ) (b) ( 0 , 1 ) , ( 1 , 0 ) , ( 2 , 1 ) (c) ( 0 , 0 ) , ( 5 , − 5 ) , ( 2 , − 2.1 )

Solution Summary: The author analyzes the correlation coefficients of the data sets to determine the best, worst, and perfect fit for the associated regression line.

Concept explainers

Videos

The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient: (a)(1,3), (−2,9), (2,1) (b)(0,1), (1,0), (2,1) (c)(0,0), (5,−5), (2,−2.1)

Want to see the full answer?

Chapter 1 Solutions

The data set which best fits, worst fits and a perfect fit for the associated regression line from the following data sets by using the correlation coefficient:

(a)(1,3), (−2,9), (2,1)

(b)(0,1), (1,0), (2,1)

(c)(0,0), (5,−5), (2,−2.1)