10192021 Variability in Several Dimensions Instructor Ron S

10/19/2021 Variability in Several Dimensions Instructor: Ron S. Kenett Email: ron@kpa. co. il Course Website: www. kpa. co. il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998 (c) 2000, Ron S. Kenett, Ph. D. 1

10/19/2021 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 (c) 2000, Ron S. Kenett, Ph. D. 2

10/19/2021 Scatter Plots Y Y X X Y Y X (c) 2000, Ron S. Kenett, Ph. D. X 3

A Case Study - 1 10/19/2021 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. (c) 2000, Ron S. Kenett, Ph. D. 4

A Case Study - 2 10/19/2021 Figure 1: Scatter plot of y deviations versus x deviations (c) 2000, Ron S. Kenett, Ph. D. 5

A Case Study - 3 10/19/2021 Figure 2: Box plots of x deviations by board number (c) 2000, Ron S. Kenett, Ph. D. 6

A Case Study - 4 10/19/2021 Figure 3: Scatter plot of y deviations versus x deviations with coding variable (c) 2000, Ron S. Kenett, Ph. D. 7

The Correlation Coefficient 10/19/2021 Y X Mean St. Dev X 2 3 1 4 3 5 Y 2 1 2 3 5 4 XY 4 3 2 12 15 20 3. 00 1. 41 2. 83 1. 47 9. 33 (c) 2000, Ron S. Kenett, Ph. D. r = (9. 33 - 3. 00*2. 83) / (1. 41*1. 47) = 0. 41 8

The Balloon’s Rule 10/19/2021 Y H h X X 2 3 1 4 3 5 Y 2 1 2 3 5 4 (c) 2000, Ron S. Kenett, Ph. D. r ~ Sqrt[ 1 - (2. 7/3. 1)^2] = 0. 36 9

10/19/2021 The Linear Regression Model Y = 2. 07+. 424 b*X+e R 2 = 94% Y Confidence Limits Predicted Y X (c) 2000, Ron S. Kenett, Ph. D. 10

Anscombe’s Data Sets (c) 2000, Ron S. Kenett, Ph. D. 10/19/2021 11