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).

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