An abrasion test was performed using n = 14 moulded ceramic pieces. The following are the test results, where for the i-th piece, the result of the test was recorded (one of Survived, Broken). The data also gives x₁, the porosity index of the piece, which is a numerical quantity: (Survived, 8), (Broken,16), (Broken, 19), (Survived,26), (Survived,49), (Survived,54), (Survived,66), (Survived, 79), (Survived, 102), (Broken,111), (Survived,114), (Broken,151), (Survived,163), (Broken,199) We want to study the resistance of pieces to abrasion as function of porosity. To this end, consider the following logistic regression model, log (1₁) where the observations follow the distribution Y; Bernoulli(;). A data value yi = 1 indicates that the piece survived the test and y₁ = 0 indicates that the piece broke. Fit this model in R using the function glm (). Examine your output and then answer the following questions. A) What is the value of Bo? B) If the porosity of a piece was X15 = = Bo + B₁xi, 37, what is the predicted survival 15?
An abrasion test was performed using n = 14 moulded ceramic pieces. The following are the test results, where for the i-th piece, the result of the test was recorded (one of Survived, Broken). The data also gives x₁, the porosity index of the piece, which is a numerical quantity: (Survived, 8), (Broken,16), (Broken, 19), (Survived,26), (Survived,49), (Survived,54), (Survived,66), (Survived, 79), (Survived, 102), (Broken,111), (Survived,114), (Broken,151), (Survived,163), (Broken,199) We want to study the resistance of pieces to abrasion as function of porosity. To this end, consider the following logistic regression model, log (1₁) where the observations follow the distribution Y; Bernoulli(;). A data value yi = 1 indicates that the piece survived the test and y₁ = 0 indicates that the piece broke. Fit this model in R using the function glm (). Examine your output and then answer the following questions. A) What is the value of Bo? B) If the porosity of a piece was X15 = = Bo + B₁xi, 37, what is the predicted survival 15?
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:An abrasion test was performed using n = 14 moulded ceramic pieces. The following are the test results,
where for the i-th piece, the result of the test was recorded (one of Survived, Broken). The data also gives Xi,
the porosity index of the piece, which is a numerical quantity:
(Survived,8), (Broken,16), (Broken,19), (Survived,26), (Survived,49), (Survived,54), (Survived,66),
(Survived,79), (Survived,102), (Broken,111), (Survived,114), (Broken,151), (Survived,163), (Broken,199)
We want to study the resistance of pieces to abrasion as function of porosity. To this end, consider the
following logistic regression model,
log
πi
1/727 ) = B₁ + B₁x₁₂
πi
where the observations follow the distribution Y; Bernoulli(;). A data value y; = 1 indicates that the
piece survived the test and yi 0 indicates that the piece broke. Fit this model in R using the function
glm (). Examine your output and then answer the following questions.
=
A) What is the value of Bo?
B) If the porosity of a piece was X15 = 37, what is the predicted survival î15?
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