chapter 1

Chapter 12: Simple Linear Regression and Correlation65.a. Although the normal probability plot of the x’s appears somewhat curved, such a patternis not terribly unusual when n is small; the test of normality presented in section 14.2 (p.625) does not reject the hypothesis of population normality. The normal probability plotof the y’s is much straighter.b. : ρ = 10H will be rejected in favor of : ρ ≠ 0oH at level .01 if22t ≥ t .= 3.355 . Σ = 864, Σx= 78,142, Σy= 138.0, Σy= 1959. 1005,8iiax andΣ x y i i= 12,322.4 , so 3992== .913( 186.8796)( 23.3880).913( 2.8284)t == 6.33 ≥ 3.355.4080relationship.r andi, so reject H o . There does appear to be a lineari66.a. We used Minitab to calculate the r i ’s: r 1 = 0.192, r 2 = 0.382, and r 3 = 0.183. It appearsthat the lag 2 correlation is best, but all of them are weak, based on the definitions givenin the text.2b. . 2100= . We reject H o if r ≥ . 2i. For all lags, r i does not fall in the rejectionregion, so we cannot reject H o . There is not evidence of theoretical autocorrelation at thefirst 3 lags.c. If we want an approximate .05 significance level for the simultaneous hypotheses, wewould have to use smaller individual significance level. If the individual confidencelevels were .95, then the simultaneous confidence levels would be approximately(.95)(.95)(.95) = .857.67.a. Because p-value = .00032 < α = .001, H o should be rejected at this significance level.b. Not necessarily. For this n, the test statistic t has approximately a standard normaldistribution when H : ρ = 10 is true, and a p-value of .00032 corresponds toz = 3.60 (or –3.60). Solvingor 4983.60r12= − for r yields r = .159. This rsuggests only a weak linear relationship between x and y, one that would typically havelittle practical import.c. t = .20 ≥ t 1. 96 , so H o is rejected in favor of H a . The value t = 2.20 is2. 025, 9998=statistically significant -- it cannot be attributed just to sampling variability in the caseρ = 0 . But with this n, r = .022 implies ρ = . 022extremely weak linear relationship., which in turn shows an382