solmidterms06

Solmidterms06 - PSTAT 120C Midterm Solutions May 9 2006 1(a The dependent variable is the height from the floor and the independent variable is the

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Unformatted text preview: PSTAT 120C: Midterm Solutions May 9, 2006 1. (a) The dependent variable is the height from the floor and the independent variable is the mass on the spring. (b) In our typical regression equation, height = β + β 1 mass where β is the height when there is no mass on the spring and- β 1 = k . ˆ β 1 = r s y s x =- . 9867 14 . 523 64 . 55 =- . 222 . The value for k = 0 . 222 The 95% confidence interval depends on an estimate of the residual variance s 2 e = n- 1 n- 2 ( 1- r 2 ) s 2 y = 3 2 ( 1- . 9867 2 ) 14 . 523 2 = 8 . 3596 . The standard error of ˆ β 1 is s e p ( n- 1) s 2 x = s 8 . 3596 3(64 . 55) 2 = 0 . 02586 Leading to the confidence interval, ( t critical value with 2 degrees of freedom is 4.303), . 222- 4 . 303(0 . 02586) = 0 . 111 . 222 + 4 . 303(0 . 02586) = 0 . 333 [0 . 111 , . 333] (c) The estimate for ˆ β is ˆ β = ¯ y- ˆ β 1 ¯ x = 81 . 25 + 0 . 222(125) = 109 ....
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This note was uploaded on 04/09/2008 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.

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Solmidterms06 - PSTAT 120C Midterm Solutions May 9 2006 1(a The dependent variable is the height from the floor and the independent variable is the

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