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Regression Analysis and Control Chart Analysis

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1. Quality Control

Eastsound operates round-trip flights between two cities using a fleet of three planes: the Viper, the Tiger, and the Eagle. The budgeted quantity of fuel for each round trip is the average fuel usage, which over the past 12 months has been 150 gallons. Eastsound has set the upper control limit at 180 gallons. The operations manager received the following report for round-trip fuel
Usage for the period by the three planes.

a. Create quality control charts for round-trip fuel usage for each of the three planes for the period. What inferences can you draw from them?

b. Some managers propose that Eastsound present its quality control charts in monetary terms rather than in physical quantities (gallons). What are the advantages and disadvantages of using monetary fuel costs rather than gallons in the quality control charts?

2. Cost behavior when costs are semi variable

Data from the payroll department of Dominguez Company for the past two months follow:

a. Sketch a line describing these costs as a function of the number of employees paid.

b. What is the apparent variable cost per employee paid?

c. The line should indicate that these costs are semi-variable. What is the apparent fixed cost per month of running the payroll department during November and December?

3. Cost Estimation using Regression Analysis:

Milky Chocolates has observed the following overhead costs for the past 12 months:

The results of the regression analysis are:
TC ¬ = $8,781 + ($0.63 X Number of Boxes)

a. Plot the data and the regression line--see sample graph below:

b. Estimate total monthly costs for a month when 10,200 boxes of chocolate are
Produced.

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Solution Summary

Control chart is used to determine if a process is within statistical control. Also, regression analysis is used to create a total cost function and to determine the total cost based on changing the x variable, fixed cost and variable cost.

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Question 1
An experiment involves three treatment groups; group A, group B and a control group
(i.e. no treatment). Three hundred subjects are randomly assigned to the groups creating
three groups of one hundred.
a. If the experimenter wants the regression slopes to compare each treatment mean
to the control group mean, how should the codes be set up? Are they orthogonal?
b. If the experimenter wants to perform the following comparisons, how should the
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1. Treatment vs No Treatment
2. Treatment A vs Treatment B

Question 2
The school board of a particular town wants to compare the three high schools in the
town. A multiple regression analysis is conducted using the contrasts shown below. Use
the means table also shown to find the prediction equation: ) 2 c ( b ) 1 c ( b b Yˆ i = 0 + 1 + 2 , i.e.
find the values of b0, b1, and b2. Describe (in a sentence each) the meaning of the
coefficient of c1 and c2.
c1 c2 Mean SAT N
School 1 1 1 School 1 992 100
School 2 -2 0 School 2 988 100
School 3 1 -1 School 3 986 100

Question 3
A researcher is interested to know if playing a musical instrument has a significant effect
on grade point average (gpa). She records whether or not a student plays an instrument
and their gender.
Using the data, run the appropriate analysis and interpret the results. Include the group
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interpretation as well as a separate effects ANOVA table.

Question 4
A company is interested in ways of improving employee production. The management
decided to attempt to increase company pride and moral by providing one day a month
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include some sort of work related activities (such as training or other workshops, group
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