Explanation The explanatory variable and the response variable are given as follows. x 25 13 16 19 29 19 16 30 y 40 20 33 30 50 37 34 37 The slope of the least-square regression line ( b 1 ) is found to be 1.0565 . This is the point estimator of β 1 Calculation: The hypotheses are given as, H 0 ; β 1 = 0 H 1 ; β 1 ≠ 0 For the level of confidence ( 1 − α ) 100 % where α = 0.01 . Then, the confidence interval can be expressed as, b 1 ± t α / 2 ⋅ s b Where s b = s e ∑ ( x − x ¯ ) 2 and s e = ∑ ( y − y ¯ ) n − 2 . The confidence interval is decided upon the point estimator and the margin of error. In this case, the computed slope of the line is considered as the point estimator. Then the margin of error is given by t α / 2 ⋅ s b . Following table shows the relevant calculations as a summary. x y x − x ¯ y − y ¯ ( x − x ¯ ) 2 ( y − y ¯ ) 2 25 40 4.125 4.875 17.0156 23.7656 13 20 − 7.875 − 15.125 62.0156 228.7656 16 33 − 4.875 − 2.125 23.7656 4.5156 19 30 − 1.875 − 5.125 3.5156 26

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ISBN: 9781260373561

Author: Navidi, William

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Elementary Statistics

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To test: The hypothesis for β 1 .

Solution Summary: The author explains how to test the hypothesis and the null hypothesis. The slope of the least-square regression line is 1.0565.

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Chapter 13 Solutions