12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x) has the form yi bo+bixi + Ei where the b; are regression coefficients that estimate the B; parameters. The safe range of x values is limited to the interval 20≤ x ≤ 40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95% confidence interval for the slope parameter ẞ₁ should have the form P(b₁-8< ß₁
12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x) has the form yi bo+bixi + Ei where the b; are regression coefficients that estimate the B; parameters. The safe range of x values is limited to the interval 20≤ x ≤ 40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95% confidence interval for the slope parameter ẞ₁ should have the form P(b₁-8< ß₁
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 4E
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Transcribed Image Text:12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to
estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x)
has the form
yi bo+bixi + Ei
where the b; are regression coefficients that estimate the B; parameters. The safe range of x values is
limited to the interval 20≤ x ≤ 40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the
experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95%
confidence interval for the slope parameter ẞ₁ should have the form
P(b₁-8< ß₁ <b₁ + 8) = 0.95
where 6 = 0.6. The standard deviation of the noise is expected to be σ = 24. Determine the total
number of observations required under each of the following experiment designs:
a. All of the observations are concentrated at the two extreme levels of x in a balanced manner.
b. Observations are distributed uniformly between 20 and 40.
c. An equal number of observations are taken at each of x = 20, 30, and 40.
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