BOOKCH11ANSWERS - Chapter 12: Simple Regression 12.1 a....

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Unformatted text preview: Chapter 12: Simple Regression 12.1 a. Compute the sample correlation x y ( ) i x x- 2 ( ) i x x- ( ) i y y- 2 ( ) i y y- ( )( ) i i x x y y-- 2 5-1.8 3.24-2.4 5.76 4.32 5 8 1.2 1.44 0.6 0.36 0.72 3 7-0.8 0.64-0.4 0.16 0.32 1 2-2.8 7.84-5.4 29.16 15.12 8 15 4.2 17.64 7.6 57.76 31.92 19 37 30.8 93.2 52.4 x = 19/5 = 3.8, y = 37/5 = 7.4, 2 ( ) 1 i x x x s n- =- ∑ = 30.8 4 = 2.7749, 2 ( ) 1 i y y y s n- =- ∑ = 93.2 4 = 4.827, ( )( ) 1 i i xy x x y y s n-- =- ∑ = 52.4/4 = 13.1 xy x y s r s s = = 13.1/(2.7749)(4.827) = .97802 b. Compute the sample correlation x y ( ) i x x- 2 ( ) i x x- ( ) i y y- 2 ( ) i y y- ( )( ) i i x x y y-- 7 5-1.8 3.24-2.4 5.76 4.32 10 8 1.2 1.44 0.6 0.36 0.72 8 7-0.8 0.64-0.4 0.16 0.32 6 2-2.8 7.84-5.4 29.16 15.12 13 15 4.2 17.64 7.6 57.76 31.92 44 37 30.8 93.2 52.4 x = 44/5 = 8.8, y = 37/5 = 7.4, 2 ( ) 1 i x x x s n- =- ∑ = 30.8 4 = 2.7749, 2 ( ) 1 i y y y s n- =- ∑ = 93.2 4 = 4.827, ( )( ) 1 i i xy x x y y s n-- =- ∑ = 52.4/4 = 13.1 xy x y s r s s = = 13.1/(2.7749)(4.827) = .97802 c. Compute the sample correlation 229 Statistics for Business & Economics, 6 th edition x y ( ) i x x- 2 ( ) i x x- ( ) i y y- 2 ( ) i y y- ( )( ) i i x x y y-- 12 4-3.6 12.96-1.8 3.24 6.48 15 6-0.6 0.36 0.2 0.04-0.12 16 5 0.4 0.16-0.8 0.64-0.32 21 8 5.4 29.16 2.2 4.84 11.88 14 6-1.6 2.56 0.2 0.04-0.32 78 29 45.2 8.8 17.6 x = 78/5 = 15.6, y = 29/5 = 5.8, 2 ( ) 1 i x x x s n- =- ∑ = 45.2 4 = 3.36155, 2 ( ) 1 i y y y s n- =- ∑ = 8.8 4 = 1.48324, ( )( ) 1 i i xy x x y y s n-- =- ∑ = 17.6/4 = 4.4 xy x y s r s s = = 4.4/(3.36155)(1.48324) = .88247 d. Compute the correlation coefficient x y ( ) i x x- 2 ( ) i x x- ( ) i y y- 2 ( ) i y y- ( )( ) i i x x y y-- 2 8-1.8 3.24-5 25 9 5 12 1.2 1.44-1 1-1.2 3 14-0.8 0.64 1 1-0.8 1 9-2.8 7.84-4 16 11.2 8 22 4.2 17.64 9 81 37.8 19 65 30.8 124 56 x = 19/5 = 3.8, y = 65/5 = 13, 2 ( ) 1 i x x x s n- =- ∑ = 30.8 4 = 2.77488, 2 ( ) 1 i y y y s n- =- ∑ = 124 4 = 5.56776, ( )( ) 1 i i xy x x y y s n-- =- ∑ = 56/4 = 14 xy x y s r s s = = 14/(2.77488)(5.56776) = .90615 Chapter 12: Simple Regression 230 12.2 a. 1 : 0, : o H H ρ ρ = ≠ , 2 ( 2) (1 ) r n t r- =- = 2 .35 38 2.303 (1 .35 ) t = =- , t 38,.05 ≈ 2.021, t 38,.01 ≈ 2.704. Reject H at the 5% level. Insufficient evidence to reject H 0 at the 1% level. b. 1 : 0, : o H H ρ ρ = ≠ , 2 ( 2) (1 ) r n t r- =- = 2 .5 58 4.397 (1 .5 ) t = =- t 58,.05 ≈ 2.000, t 58,.01 ≈ 2.660. Therefore, reject H 0 at the 1% level. c. 1 : 0, : o H H ρ ρ = ≠ , 2 ( 2) (1 ) r n t r- =- = 2 .62 43 5.182 (1 .62 ) t = =- t 43,.05 ≈ 2.021, t 43,.01 ≈ 2.704. Therefore, reject H 0 at the 1% level. d. 1 : 0, : o H H ρ ρ = ≠ , 2 ( 2) (1 ) r n t r- =- = 2 .60 23 3.597 (1 .60 ) t = =- t 23,.05 ≈ 2.069, t 23,.01 ≈ 2.807. Therefore, reject H 0 at the 1% level....
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This note was uploaded on 04/26/2010 for the course ECO 329 taught by Professor K during the Spring '08 term at University of Texas.

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BOOKCH11ANSWERS - Chapter 12: Simple Regression 12.1 a....

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