04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 1

Variability in Several Dimensions

Instructor: Ron S. KenettEmail: ron@kpa.co.il

Course Website: www.kpa.co.il/biostatCourse textbook: MODERN INDUSTRIAL STATISTICS,

Kenett and Zacks, Duxbury Press, 1998

04/10/23

(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

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 3

Y

X

Y

X

Y

X

Y

X

Scatter Plots

04/10/23

(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.

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.

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 5

A Case Study - 2

-0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 0.005

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

x_dev

y_de

v

Figure 1: Scatter plot of y deviations versus x deviations

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 6

A Case Study - 3

Figure 2: Box plots of x deviations by board number

1 2 3 4 5 6 7 8 91011121314151617181920212223242526

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

Board_n

x_de

v

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 7

A Case Study - 4

1 2 3

-0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 0.005

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

x_dev

y_de

v

Figure 3: Scatter plot of y deviations versus x deviations with coding variable

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 8

YX

YXYXr

YX

YXYXr

X Y

2 2

3 1

1 2

4 3

3 5

5 4

3.00 2.83

1.41 1.47

XY

4

3

2

12

15

20

9.33

Y

XX

Y

X6

Y6

Mean

StDev

r = (9.33 - 3.00*2.83) / (1.41*1.47) = 0.41

The Correlation Coefficient

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 9

2

1

H

hr

2

1

H

hr

X Y

2 2

3 1

1 2

4 3

3 5

5 4

Y

XX

Y

X6

Y6

r ~ Sqrt[ 1 - (2.7/3.1)^2] = 0.36

The Balloon’s Rule

HHhh

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 10

2.0

4.0

6.0

8.0

10.0

2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Y

X

Predicted Y

X Y7.6 5.64.2 3.9

10.2 6.713.8 7.913.6 7.714.5 8.43.2 3.27.9 5.9

13.4 7.14.7 4.95.9 4.43.5 3.73.4 3.25.0 3.15.6 4.5

X Y7.6 5.64.2 3.9

10.2 6.713.8 7.913.6 7.714.5 8.43.2 3.27.9 5.9

13.4 7.14.7 4.95.9 4.43.5 3.73.4 3.25.0 3.15.6 4.5

Y = 2.07+.424b*X+Y = 2.07+.424b*X+

RR22 = 94% = 94%Confidence Limits

The Linear Regression Model

04/10/23

(c) 2000, Ron S. Kenett, Ph.D. 11

Anscombe’s Data Sets