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Unformatted text preview: Chapter 12 Bivariate Regression 12.1 H : ρ = 0 versus H 1 : ρ ≠ 0 for a twotailed test. Summary Table Sample df r t t α r α Decision a 18 .45 2.138 ±2.101 ±.444 Reject b 28 −.35 −1.977 ±1.701 ±.306 Reject c 5 .6 1.677 2.015 .669 Fail to Reject d 59 −.3 −2.416 −2.39 −.297 Reject 12.2 a. The scatter plot shows a positive correlation between hours worked and weekly pay. b. Hours Worked (X) Weekly Pay (Y) 2 ( ) i x x 2 ( ) i y y ( )( ) i i x x y y 10 93 100 7056 840 15 171 25 36 30 20 204 729 20 156 441 35 261 225 7056 1260 20 177 350 15318 2130 x y SSxx SSyy SSxy 2130 .9199 350 15318 r = = c . t .025 = 3.182 d . 2 5 2 .9199 4.063 1 (.9199) t = = . We reject the null hypothesis of zero correlation. e. pvalue = .0269. 110 12.3 a. The scatter plot shows a negative correlation between operators and wait time. b. Operators (X) Wait (Y) 2 ( ) i x x 2 ( ) i y y ( )( ) i i x x y y 4 385 4 1444 −76 5 335 1 144 12 6 383 1296 7 344 1 9 −3 8 288 4 3481 −118 6 347 10 6374 −185 x y SSxx SSyy SSxy 185 .7328 10 6374 r = =  c . t .025 = ±3.183 d . 2 5 2 .7328 1.865 1 ( .7328) t =  =   . We fail to reject the null hypothesis of zero correlation. e. pvalue = .159. 12.4 a. The scatter plot shows little correlation between age and amount spent. b. r calculated = −.292 c. t .025 = ±2.306 d. 2 10 2 .292 .864 1 ( .292) t =  =   e. critical 2 2.306 .632 2.306 10 2 r = ± = ± + . f. Because r calculated (−.292) > −.632, we fail to reject the null hypothesis of zero correlation. 111 12.5 a. The scatter plot shows a positive correlation between returns from last year and returns from this year. b. r calculated = .5313 c. t .025 = ±2.131 d. 2 17 2 .5313 2.429 1 (.5313) t = = e. critical 2 2.131 .482 2.131 17 2 r = ± = ± + f. Because r calculated (.5313) > .482, we reject the null hypothesis of zero correlation. 12.6 a. The scatter plot shows a positive correlation between orders and ship cost. b. r calculated = .820 c. t .025 = ±2.228 d. 2 12 2 .820 4.530 1 (.820) t = = e. critical 2 2.228 .576 2.228 12 2 r = ± = ± + f. Because r calculated (.820) > .576, we reject the null hypothesis of zero correlation. 12.7 a. Correlation Matrix 1Year 10Year 1Year 1.000 3Year.095 5Year .014 10Year .341 1.000 12 sample size ± .576 critical value .05 (twotail) ± .708 critical value .01 (twotail) d. There were positive correlations between years 3 and 5 and years 5 and 10. Higher returns in Year 3 lead to higher returns in Year 5 and also in Year 10. 12.8 a. An increase in the price of $1, reduces its expected sales by 37.5 units. b. Sales = 842 – (20)*37.5 = 92 c. From a practical point of view no. A zero price is unrealistic....
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 Spring '08
 HEATHERADAMS
 Statistics, Regression Analysis, Statistical hypothesis testing, Correlation and dependence, Pearson productmoment correlation coefficient, a. b. c.

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