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# 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.1 Variability in Several Dimensions Instructor: Ron S. Kenett Course Website:

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1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.1 Variability in Several Dimensions Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website: www.kpa.co.il/biostatwww.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.2 Course Syllabus Understanding Variability Variability in Several Dimensions Basic Models of Probability Sampling for Estimation of Population Quantities Parametric Statistical Inference Computer Intensive Techniques Multiple Linear Regression Statistical Process Control Design of Experiments

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.3 Y X Y X Y X Y X Scatter Plots

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.4 A Case Study - 1 Example 3.1, p. 45, in Kenett and Zacks (1998) involves the development of a placement machine that picks components from a tray and positions them on printed circuit boards. The customer requirements involve precision in the x-y position. The developers of the system collected data from 26 boards, with 16 components on each. For each board the deviations in x and y, from the required nominal values, were recorded, producing 416 values for x_dev and y_dev.

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.5 A Case Study - 2 Figure 1: Scatter plot of y deviations versus x deviations

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.6 A Case Study - 3 Figure 2: Box plots of x deviations by board number

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.7 A Case Study - 4 Figure 3: Scatter plot of y deviations versus x deviations with coding variable

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.8 XY 22 31 12 43 35 54 3.002.83 1.411.47 XY 4 3 2 12 15 20 9.33 Y X Mean StDev r = (9.33 - 3.00*2.83) / (1.41*1.47) = 0.41 The Correlation Coefficient

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.9 XY 22 31 12 43 35 54 Y X r ~ Sqrt[ 1 - (2.7/3.1)^ 2 ] = 0.36 The Balloon s RuleH h

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.10 Y X Predicted Y Y = 2.07+.424b*X+ Y = 2.07+.424b*X+ R 2 = 94% Confidence Limits The Linear Regression Model

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.11 Anscombe s Data Sets

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