Explanation Given Information: The points are ( 0 , 0 ) , ( − a , a ) and ( a , a ) . 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 slope of the regression line, calculated as: m = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 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. Proof: Consider that the points are ( 0 , 0 ) , ( − a , a ) and ( a , a ) . 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 xy x 2 y 2 0 0 0 0 0 − a a − a 2 a 2 a 2 a a a 2 a 2 a 2 ∑ ( Sum ) 0 2 a 0 2 a 2 2 a 2 Hence, n = 3 , ∑ x = 0 , ∑ y = 2 a , ∑ ( x y ) = 0 , ∑ ( x 2 ) = 2 a 2 and ∑ ( y 2 ) = 2 a 2

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ISBN: 9781337514309

Author: Waner

Publisher: Cengage

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Chapter 1.4, Problem 41E

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To prove: The slope of the regression line for the point (0,0), (−a,a) and (a,a) is 0 also calculate the value of correlation coefficient r.

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Chapter 1.4, Problem 40E

Chapter 1.4, Problem 42E

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Applied Calculus

Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - Prob. 8E Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...

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To prove: The slope of the regression line for the point ( 0 , 0 ) , ( − a , a ) and ( a , a ) is 0 also calculate the value of correlation coefficient r.

Solution Summary: The author explains the formula used to calculate the coefficient of correlation r.

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To prove: The slope of the regression line for the point (0,0), (−a,a) and (a,a) is 0 also calculate the value of correlation coefficient r.

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