# ismch10 - Chapter 10 Simple Regression 153 Chapter 10...

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Unformatted text preview: Chapter 10: Simple Regression 153 Chapter 10: Simple Regression 10.1 Let x = Project and y = Examination. 2 10, 767, 767/10 76.7, 59497 n x X x = = = = = ∑ ∑ 2 786, 786/10 78.6, 62604, 60862 y Y y xy = = = = = ∑ ∑ ∑ 2 2 60862 (10)(76.7)(78.6) (59497 10(76.7) )(62604 (10)(78.6) ) r- =-- =.7759 10-2 a. 2 13, 7.2, 7.2/13 .5538, 80.06 n x X x = = = = = ∑ ∑ 2 153.6, 153.6/13 11.8154, 3718.76, 69.67 y Y y xy = = = = = - ∑ ∑ ∑ 2 2 69.67 (13)(.5538)(11.8154) (80.06 (13)(.5538) )(3718.76 (13)(11.8154) ) r-- =-- = - .4066 b. 1 : 0, : o H H ρ ρ = ≠ 2 .4066 1.4761 [1 ( .4066) ]/11 t- = = -- - t 11,.10 = 1.363, t 11,.05 = 1.796 Therefore, do not reject Ho at the 10% level 10.3a. Let x = Instructor Rating and y = Expected Grade 2 12, 46.2, 46.2/12 3.85, 182.22 n x X x = = = = = ∑ ∑ 2 35.4, 35.4/12 2.95, 105.86, 138.09 y Y y xy = = = = = ∑ ∑ ∑ 2 2 138.09 (12)(3.85)(2.95) (182.22 12(3.85) )(105.86 (12)(2.95) ) r- =-- =.7217 b. 1 : 0, : o H H ρ ρ = 2 .7217 3.2971 [1 (.7217) ]/10 t = =- Therefore, reject Ho at the 10% level since 3.2971 > 1.372 = t 10,.10 10-4 1 : 0, : o H H ρ ρ = ≠ 2 17, 67.83, 67.83/17 3.99, 365.3705 n x X x = = = = = ∑ ∑ 2 2716.07, 2716.07/17 159.7688, 485,829.5153, 10,964.5397 y Y y xy = = = = = ∑ ∑ ∑ 2 2 10,964.5397 (17)(3.99)(159.7688) (365.3705 17(3.99) )(485,829.5153 (17)(159.7688) ) r- =-- =.0575 2 .0575 .2230 [1 (.0575) ]/15 t = =- Therefore, do not reject Ho at the 20% level since .2230 < 1.341 = t 15,.10 154 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 10-5 1 : 0, : o H H ρ ρ = 2 .75 7.7736 [1 (.75) ]/ 47 t = =- Therefore, reject Ho at all common levels of alpha 10-6 1 : 0, : o H H ρ ρ = 2 .11 2.07 [1 (.11) ]/351 t = =- Therefore, reject Ho at the 2.5% level since 2.07 > 1.96 = z .025 ≈ t 351,.025 10-7 1 : 0, : o H H ρ ρ = 2 .51 4.8168 [1 (.51) ]/ 66 t = =- Therefore, reject Ho at the 5% level since 4.8168 > 2.66 ≈ t 66,.05 10.8 A population regression equation consists of the true regression coefficients ' i s β and the true model error i ε . By contrast, the estimated regression model consists of the estimated regression coefficients b i ’s and the residual term i e . The population regression equation is a model that purports to measure the actual value of Y while the sample regression equation is an estimate of the predicted value of the dependent variable Y. 10.9 While the true model error i ε is the random error term for the model, the residual i e is the difference between the predicted value of Y ( ˆ Y ) from the regression line and the observed value of Y. The residual term is a combined measure of both the model error and the errors that are encountered in estimating b o and b 1 ....
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ismch10 - Chapter 10 Simple Regression 153 Chapter 10...

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