Exercise 2 A corporation sells computer parts and performs maintenance and repair service. The data below have been collected from 18 recent calls to perform maintenance service; for each call, 1 is the number of repairs and y is the total number of minutes spent by the service person. Moreover, it is also available the information about the type of computer: in particular, the first 12 observations refer to business computers, while the last 6 refer to personal computers. Specifically, business computers i 1 2 3 4 5 6 7 8 9 10 11 12 number of repairs total minutes 7 6 5 5 4 7 7 4 2 8 5 5 97 86 78 75 62 101 105 53 33 118 65 71 personal computers i 13 14 15 16 17 18 number of repairs total minutes 2 1 3 1 4 3 25 10 39 17 49 28 with 18 Στα = 1112 i=1 = 1040.889 18 Στ1 = 79 i=1 R² = 0.9808 = 4.4869 a) Formulate an appropriate Gaussian linear model ("model A") to study how the total min- utes of intervention depend on the number of repairs and the type of computer. Write the model formulation and assumptions. b) State the decomposition of the sum of squares and specify each term for the fitted model. c) Test the hypothesis about the overall significance of the model and interpret its result. d) Specify a new model ("model B") which assumes that there is an interaction effect between the number of repairs and the type of computer. Write the model formulation. e) Can you choose between the two models (model A and model B) by simply comparing their coefficients of determination R²? Explain. f) In the model that includes the interaction term (model B) it is obtained a residual (error) sum of squares equal to SSEB = 285.657. Perform a test to compare this model with model A using a significance level 0.05. Which model do you prefer?
Exercise 2 A corporation sells computer parts and performs maintenance and repair service. The data below have been collected from 18 recent calls to perform maintenance service; for each call, 1 is the number of repairs and y is the total number of minutes spent by the service person. Moreover, it is also available the information about the type of computer: in particular, the first 12 observations refer to business computers, while the last 6 refer to personal computers. Specifically, business computers i 1 2 3 4 5 6 7 8 9 10 11 12 number of repairs total minutes 7 6 5 5 4 7 7 4 2 8 5 5 97 86 78 75 62 101 105 53 33 118 65 71 personal computers i 13 14 15 16 17 18 number of repairs total minutes 2 1 3 1 4 3 25 10 39 17 49 28 with 18 Στα = 1112 i=1 = 1040.889 18 Στ1 = 79 i=1 R² = 0.9808 = 4.4869 a) Formulate an appropriate Gaussian linear model ("model A") to study how the total min- utes of intervention depend on the number of repairs and the type of computer. Write the model formulation and assumptions. b) State the decomposition of the sum of squares and specify each term for the fitted model. c) Test the hypothesis about the overall significance of the model and interpret its result. d) Specify a new model ("model B") which assumes that there is an interaction effect between the number of repairs and the type of computer. Write the model formulation. e) Can you choose between the two models (model A and model B) by simply comparing their coefficients of determination R²? Explain. f) In the model that includes the interaction term (model B) it is obtained a residual (error) sum of squares equal to SSEB = 285.657. Perform a test to compare this model with model A using a significance level 0.05. Which model do you prefer?
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 14CR
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For context, the image provided below is a question from a September, 2024 past paper in statistical modeling
Transcribed Image Text:Exercise 2
A corporation sells computer parts and performs maintenance and repair service. The data
below have been collected from 18 recent calls to perform maintenance service; for each call,
1 is the number of repairs and y is the total number of minutes spent by the service person.
Moreover, it is also available the information about the type of computer: in particular, the
first 12 observations refer to business computers, while the last 6 refer to personal computers.
Specifically,
business computers
i
1
2
3
4
5
6
7
8
9
10 11 12
number of repairs
total minutes
7 6 5
5
4
7
7
4
2
8
5
5
97 86 78
75
62
101
105
53
33
118
65
71
personal computers
i
13
14
15
16
17
18
number of repairs
total minutes
2
1
3
1
4
3
25
10 39
17
49
28
with
18
Στα = 1112
i=1
= 1040.889
18
Στ1 = 79
i=1
R² = 0.9808
= 4.4869
a) Formulate an appropriate Gaussian linear model ("model A") to study how the total min-
utes of intervention depend on the number of repairs and the type of computer. Write the
model formulation and assumptions.
b) State the decomposition of the sum of squares and specify each term for the fitted model.
c) Test the hypothesis about the overall significance of the model and interpret its result.
d) Specify a new model ("model B") which assumes that there is an interaction effect between
the number of repairs and the type of computer. Write the model formulation.
e) Can you choose between the two models (model A and model B) by simply comparing
their coefficients of determination R²? Explain.
f) In the model that includes the interaction term (model B) it is obtained a residual (error)
sum of squares equal to SSEB = 285.657. Perform a test to compare this model with
model A using a significance level 0.05. Which model do you prefer?
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