Explanation Given information: The provided points are ( − 1 , 1 ) , ( 1 , 2 ) and ( 2 , 0 ) . 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 that the points are ( − 1 , 1 ) , ( 1 , 2 ) and ( 2 , 0 ) . 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 − 1 1 − 1 1 1 1 2 2 1 4 2 0 0 4 0 ∑ ( Sum ) 2 3 1 6 5 Hence, n = 3 , ∑ x = 2 , ∑ y = 1 , ∑ ( x y ) = 3 , ∑ ( x 2 ) = 6 and ∑ ( y 2 ) = 5

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 1, Problem 25RE

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

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Chapter 1, Problem 24RE

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

Solution Summary: The author explains the formula used to calculate the correlation coefficient. The regression line is the 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 $(−1,1)$ , $(1,2)$ and $(2,0)$ also calculates the correlation coefficient.

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