The following data were collected to determine therelationship between two processing variables and thehardness of a certain kind of steel: AnnealingHardness Copper content temperature(Rockwell 30-T) (percent) (degrees F)y x1 x278.9 0.02 1,00055.2 0.02 1,20080.9 0.10 1,00057.4 0.10 1,20085.3 0.18 1,00060.7 0.18 1,200Fit a plane by the method of least squares, and use it toestimate the average hardness of this kind of steel when the copper content is 0.14 percent and the annealing tem-perature is 1,100◦F.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The following data were collected to determine the
relationship between two processing variables and the
hardness of a certain kind of steel:
Annealing
Hardness Copper content temperature
(Rockwell 30-T) (percent) (degrees F)
y x1 x2
78.9 0.02 1,000
55.2 0.02 1,200
80.9 0.10 1,000
57.4 0.10 1,200
85.3 0.18 1,000
60.7 0.18 1,200
Fit a plane by the method of least squares, and use it to
estimate the average hardness of this kind of steel when
the copper content is 0.14 percent and the annealing tem-
perature is 1,100◦F.
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