3. A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime y (thousands of holes drilled) of four bits at each of five speeds x. The data were: x: 60 | 60 | 60 60 | 80 80 80 80 100 100 y: 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5 x: 100 100 120 120 120 120 140 140 | 140 140 y: 3.2 4.8 4.1 4.5 4.0 3.8 3.6 | 3.0 3.5 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? a. Is there any evident outlier? If so, does it have high influence? b. Test the paired data for lack of fit at 5% level of significance. c. d. Fit the best regression model on Y based on X. Provide justifications.
3. A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime y (thousands of holes drilled) of four bits at each of five speeds x. The data were: x: 60 | 60 | 60 60 | 80 80 80 80 100 100 y: 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5 x: 100 100 120 120 120 120 140 140 | 140 140 y: 3.2 4.8 4.1 4.5 4.0 3.8 3.6 | 3.0 3.5 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? a. Is there any evident outlier? If so, does it have high influence? b. Test the paired data for lack of fit at 5% level of significance. c. d. Fit the best regression model on Y based on X. Provide justifications.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.6: Higher-degree Polynomials And Rational Functions
Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...
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Transcribed Image Text:3. A manufacturer of cases for sound equipment requires drilling holes
for metal screws. The drill bits wear out and must be replaced; there
is expense not only in the cost of the bits but also for lost production.
Engineers varied the rotation speed of the drill and measured the
lifetime y (thousands of holes drilled) of four bits at each of five
speeds x. The data were:
x: 60 60 60 60 80 80
80 80 100 100
y: 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5
x: 100 100 120 120 120 120 140 140 140 140
y: 3.2 4.8 4.1 | 4.5 4.0 | 3.8 | 3.6 | 3.0
3.5 3.4
Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear?
а.
Is there any evident outlier? If so, does it have high influence?
b.
Test the paired data for lack of fit at 5% level of significance.
C.
Fit the best regression model on Y based on X. Provide justifications.
d.
Optimize lifetime y by identifying the best value for speed x.
е.
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