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Unformatted text preview: Chapter 12 Bivariate Regression 12.1 H : = 0 versus H 1 : 0 for a twotailed test. Summary Table Sample df r t t r 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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This note was uploaded on 12/13/2010 for the course LEEDS BCOR 1020 taught by Professor Heatheradams during the Spring '08 term at Colorado.
 Spring '08
 HEATHERADAMS

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