Explanation Given information: The provided points are ( − 2 , − 1 ) , ( − 1 , 1 ) , ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 4 ) and ( 3 , 3 ) Formula used: The regression line is the line which gives the minimum sum-of-square error for the data points ( x 1 , y 1 ) , ( x 2 , y 2 ) ,……, ( x n , y n ) and given by, y = m x + b Where, m and b are the regression coefficients and calculated as, m = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 And, b = ∑ y − m ( ∑ x ) n Where n is the number of data points. 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. Calculation: Consider the given points are ( − 2 , − 1 ) , ( − 1 , 1 ) , ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 4 ) and ( 3 , 3 ) . Make the table for the values of xy and x 2 on substituting the values of x and y . Then, the table is as follows, x y x y x 2 y 2 − 2 − 1 2 4 1 − 1 1 − 1 1 1 0 1 0 0 1 1 2 2 1 4 2 4 8 4 16 3 3 9 9 9 ∑ ( Sum ) 3 10 20 19 32 Hence, n = 6 , ∑ x = 3 , ∑ y = 1 0 , ∑ ( x y ) = 20 , ∑ ( x 2 ) = 19 and ∑ ( y 2 ) = 32

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 1, Problem 26RE

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To calculate: The line which best fits the points (−2,−1), (−1,1), (0,1), (1,2), (2,4) and (3,3) also calculates the correlation coefficient.

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Chapter 1, Problem 25RE

Chapter 1, Problem 27RE

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The line which best fits the points ( − 2 , − 1 ) , ( − 1 , 1 ) , ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 4 ) and ( 3 , 3 ) also calculates the correlation coefficient.

Solution Summary: The author calculates the regression line which gives the minimum sum-of-square error for the data points.

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To calculate: The line which best fits the points (−2,−1), (−1,1), (0,1), (1,2), (2,4) and (3,3) also calculates the correlation coefficient.

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