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The article “Mathematical Modeling of the Argon-Oxygen

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 13E Chapter 7.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 13E

The article “Mathematical Modeling of the Argon-Oxygen Decarburization Refining Process of Stainless Steel: Part II. Application of the Model to Industrial Practice” (J. Wei and D. Zhu, Metallurgical and Materials Transactions B, 2001:212-217) presents the carbon content (in mass %) and bath temperature (in K) for 32 heats of austenitic stainless steel. These data are shown in the following table.

Carbon %

Temp.

Carbon %

Temp.

Carbon %

Temp.

Carbon %

Temp.

19

1975

17

1984

18

1962

17

1983

23

1947

20

1991

19

1985

20

1966

22

1954

19

1965

19

1946

21

1972

16

1992

22

1963

15

1986

17

1989

17

1965

18

1949

20

1946

18

1984

18

1971

22

1960

22

1950

23

1967

12

2046

20

1960

15

1979

13

1954

24

1945

19

1953

15

1989

15

1977

a. Compute the least-squares line for predicting bath temperature (y) from carbon content (x).

Step-by-Step Solution:
Step 1 of 3

Review Notes for Calculus I Symmetry:  A graph is symmetric with respect to the y-axis if whenever (x, y) is a point on the graph then (-x, y) is also a point on the graph. Some even functions (y=x , y=x , etc.) have symmetry with respect to the y-axis. These graphs usually are parabolas (u-shaped graphs). To figure out if a graph has y-axis symmetry, then you replace all x’s with the opposite of x (ex: x would become –x).  A graph is symmetric with respect to the x-axis if whenever (x, y) is a point on the graph then (x, -y) is also a point on the graph. These graphs can look like a parabola turned on its side. To figure out if a graph has x-axis symmetry, you replace all y’s with the opposite of y (ex: y wo

Step 2 of 3

Chapter 7.4, Problem 13E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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