HW4_SolutionSet - Homework#4 Solution Set Problem 1...

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- 1 - Homework #4 Solution Set Problem 1 Solution: (a) The scatter plot shows a pretty strong negative linear association between the line speed and the number of defective parts. The equation of the least squares regression line is y ˆ = 22.174 – 0.1478 x (b) x Predicted y 20 19.218 20 19.218 40 16.262 30 17.740 60 13.306 40 16.262 (c) i i i y y e predicted observed - = Observed y Predicted y Residual e 21 19.218 1.782 19 19.218 –0.218 15 16.262 –1.262 16 17.740 –1.740 14 13.306 0.694 17 16.262 0.738 (d) The mean is approximately 0. This result is not surprising because the mean of residuals is always zero. (e) ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 1 2 738 . 0 694 . 0 740 . 1 262 . 1 218 . 0 782 . 1 2 6 1 2 1 + + - + - + - + - = - = = n i i e e n s 489 . 1 2175 . 2 ) 870 . 8 )( 25 . 0 ( = = = (f) -2 -1 0 1 2 0 20 40 60 80 Residuals Line Speed Line Speed Residual Plot
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- 2 - (g) The residual plot shows an approximately symmetrical random scatter around the zero line with no apparent pattern. Thus, the linear mathematical model is appropriate. (With only six points it is hard to assess the normality assumption.) (h) SSR = 25.13 SSE = 8.87 SST = SSR + SSE = 34 (i) 7391 . 0
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