讲解Statistics 106、辅导Java、Python，c/c++程序语言、讲解Box-Cox
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Winter 2019
Homework 4
Due date : February 22 (Friday)
The work must be submitted in class on the due date. Please write your
name and last 4 digits of student ID on the first page. Any resource used in
solving the problems (other than textbook, lecture notes, and discussions with
instructor and/or TAs) must be mentioned.
1. Problem 18.9 (modified): Refer to Premium distribution problem 16.12 in
Homework 3.
(a) Obtain the residuals prepare aligned residual dot plots by agent. What departures
from the standard ANOVA model can be studied from these plots ? What are
your findings ?
(b*) Prepare a normal probability plot of the residuals. Does the normality assumption
appear reasonable here ?
(c) The observations within each factor level are in time order. Prepare residual
sequence plots and interpret them. What are your findings ?
(d*) Obtain the studentized residuals and check how many fall outside the interval
[3, 3]. Do you see presence of an outlier ?
2. Problem 18.17 (modified): In a completely randomized design to study the effect
of the speed of winding thread (1:slow, 2:normal, 3:fast, 4:maximum) onto 75-yard
spools, 16 runs of 10,000 spools each were made at each of the four winding speeds.
The response variable is the number of thread breaks during the production run. Since
the responses are counts, the researcher was concerned about the normality and equal
variance assumptions of the ANOVA model.
[Use the data set CH18PR17.txt (first column = response, second column = treatment
index (i), third column = replicate index (j)).]
(a) Obtain the fitted values and residuals of the ANOVA model.
(b) Prepare suitable residual plots to study whether or not the error variances are
equal for the four winding speeds. What are your findings ?
(c) Test by means of Brown-Forsythe test whether or not the treatment error variances
are equal, at α = 0.05. What is the P-value of the test ? Are your results
consistent with the diagnosis in part (b) ?
(d*) Perform Hartley’s test to see whether or not the treatment error variances are
equal, at α = 0.05. Are your results consistent with the findings in part (c) ?
1(e*) For each winding speed, calculate Y i· and si
. Based on these, examine which of
the following possibilities seems most reasonable:
(i) σ
i ∝ μi
; (ii) σi ∝ μi
; (iii) σi ∝ μi.
Determine the transformation that is most appropriate here.
(f*) Use the Box-Cox procedure to find an appropriate power transformation of Y .
Evaluate SSE for values of λ in the set {1, 0.8, 0.6, · · · , 0.6, 0.8, 1}. Does
λ = 0 (corresponds to logarithmic transformation) appear to be reasonable, based
on the Box-Cox procedure ?
Winter 2019
Homework 4
Due date : February 22 (Friday)
The work must be submitted in class on the due date. Please write your
name and last 4 digits of student ID on the first page. Any resource used in
solving the problems (other than textbook, lecture notes, and discussions with
instructor and/or TAs) must be mentioned.
1. Problem 18.9 (modified): Refer to Premium distribution problem 16.12 in
Homework 3.
(a) Obtain the residuals prepare aligned residual dot plots by agent. What departures
from the standard ANOVA model can be studied from these plots ? What are
your findings ?
(b*) Prepare a normal probability plot of the residuals. Does the normality assumption
appear reasonable here ?
(c) The observations within each factor level are in time order. Prepare residual
sequence plots and interpret them. What are your findings ?
(d*) Obtain the studentized residuals and check how many fall outside the interval
[3, 3]. Do you see presence of an outlier ?
2. Problem 18.17 (modified): In a completely randomized design to study the effect
of the speed of winding thread (1:slow, 2:normal, 3:fast, 4:maximum) onto 75-yard
spools, 16 runs of 10,000 spools each were made at each of the four winding speeds.
The response variable is the number of thread breaks during the production run. Since
the responses are counts, the researcher was concerned about the normality and equal
variance assumptions of the ANOVA model.
[Use the data set CH18PR17.txt (first column = response, second column = treatment
index (i), third column = replicate index (j)).]
(a) Obtain the fitted values and residuals of the ANOVA model.
(b) Prepare suitable residual plots to study whether or not the error variances are
equal for the four winding speeds. What are your findings ?
(c) Test by means of Brown-Forsythe test whether or not the treatment error variances
are equal, at α = 0.05. What is the P-value of the test ? Are your results
consistent with the diagnosis in part (b) ?
(d*) Perform Hartley’s test to see whether or not the treatment error variances are
equal, at α = 0.05. Are your results consistent with the findings in part (c) ?
1(e*) For each winding speed, calculate Y i· and si
. Based on these, examine which of
the following possibilities seems most reasonable:
(i) σ
i ∝ μi
; (ii) σi ∝ μi
; (iii) σi ∝ μi.
Determine the transformation that is most appropriate here.
(f*) Use the Box-Cox procedure to find an appropriate power transformation of Y .
Evaluate SSE for values of λ in the set {1, 0.8, 0.6, · · · , 0.6, 0.8, 1}. Does
λ = 0 (corresponds to logarithmic transformation) appear to be reasonable, based
on the Box-Cox procedure ?