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+b₁x; + € i = where the b; are regression coefficients that estimate the ẞ; 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 B₁ should have the form P(b₁-8
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+b₁x; + € i = where the b; are regression coefficients that estimate the ẞ; 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 B₁ should have the form P(b₁-8
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 5PPS
Related questions
Question
Solve with minitab software
Answer. N =64
N=192
N=96
Transcribed Image Text: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+b₁x; + € i
=
where the b; are regression coefficients that estimate the ẞ; 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 B₁ should have the form
P(b₁-8<B₁ <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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning