Take-home Portion of Exam 2
75 points
STAT 310
Name_____SOLUTION______________
Due: Monday, April 22nd @ 1pm
Spring 2013
Please turn in a hard copy of the take-home portion of Exam 2 when you come to take class on Monday, April
22, 2013 @ 1pm. Your notes, homework and practice problems may be used to answer the questions on this
exam. You must include all the JMP output used to answer each question and make sure to show all work in
order to receive full credit. You may ask questions of the instructor however this exam is to be completed by
ONLY you and may NOT be discussed with anyone else in the class or outside of the class (e.g. other professors,
other students). Failure to comply will result in a zero for this portion of the exam.
1. The file ManHours.jmp found on the course website contains data concerning the manpower and
workload for US Navy Bachelor Officers’ Quarters which are used to estimate manpower needs (Hours)
for manning Bachelors Officers’ Quarters. The following table summarizes the variables along with a
description for each variable contained in the data set.
Source: Procedures and Analyses for Staffing Standards Development: Data/Regression Analysis Handbook (1979),
Navy Manpower and Materials Analysis Center, San Diego.
Variable
Occupancy
CheckIns
ServiceDesk
CommonArea
Wings
Berthing
Rooms
Hours
Description
Average daily occupancy
Monthly average number of check-ins
Weekly hours of service desk operation
Square feet of common area use
Number of building wings
Operational berthing capacity
Number of rooms
Monthly man hours
a. Using backward elimination, find the best model for predicting manpower needs. Make sure to
give a detailed description of each step in the process. Also, provide a detailed sketch of or
paste the JMP output used to answer this question below. (10 points)
Step 1: Fit model with Occupancy, CheckIns, ServiceDesk, CommonArea, Wings,
Berthing, Rooms
Service Desk has largest p-value = 0.7215 > 0.10 so it should be removed
1
Step 2: Fit model with Occupancy, CheckIns, CommonArea, Wings, Berthing, Rooms
Wings has the largest p-value = 0.6964 > 0.10 so it should be removed
Step 3: Fit model with Occupancy, CheckIns, CommonArea, Berthing, Rooms
Occupancy has the largest p-value = 0.0963 < 0.10 so the process should stop
The best model includes Occupancy, CheckIns, CommonArea, Berthing, Rooms
b. Give the estimated regression equation for the model identified in part a. Provide a detailed
sketch of or paste the JMP output used to answer this question. (3 points)
Ê (Hours | Occupancy, CheckIns, CommonArea, Berthing, Rooms) = 201.36 – 1.32O + 1.77CI – 20.34CA –
15.20B + 30.76R
2
c. Create a scatterplot matrix of the variables identified in part a. Provide a detailed sketch of or
paste the JMP output below. (2 points)
d. Looking at the scatterplot matrix created in part c, which variable has the strongest linear
relationship with manpower needs? (1 point)
Rooms
e. Give the estimated correlation between Berthing and Rooms. (1 point)
r̂ (Berthing, Rooms) = 0.9782
3
2. Experience with a certain type of plastic indicates that a relationship exists between the Hardness
(measured in Brinell units) of items molded from the plastic (Y) and the elapsed Time since termination
of the molding process (X). The data can be found on the course website in the file Plastic.jmp.
a. Create a scatterplot of the data. Provide a detailed sketch of or paste your plot below. (2 points)
b. Looking at the plot created in part a, does it seem reasonable to perform simple linear
regression on these data? Explain your reasoning. (2 points)
Yes, there seems to be a linear pattern in the data. Therefore, simple linear regression
seems appropriate.
Regardless of your answer to part b, use the data to answer the remaining questions.
c. Test whether regression is useful for these data. Make sure to include the appropriate
hypotheses, test statistic, p-value, and conclusion. Provide a detailed sketch of or paste the JMP
output below. (8 points)
H0: The regression is NOT useful
Ha: The regression IS useful
Test statistic = 506.51
p-value = 0.0001
Evidence regression is useful in this scenario.
4
d. Give the estimated regression equation. Provide a detailed sketch of or paste the JMP output
used to answer this question. (3 points)
Ê (Hardness | Time) = 168.6 + 2.03Time
e. Interpret the regression coefficients, i.e. the slope and the intercept. (4 points)
Intercept: When Time = 0 the best guess for Hardness is 168.6 Brinell units
Slope: For every 1 minute increase in Time, the Hardness increase by 2.03 Brinell units
f.
Check the assumptions behind the regression model. Provide a detailed sketch of or paste the
appropriate JMP graphs below as part of your answer. (10 points)
Linearity - The horizontal bands seems like it is present, therefore the assumption of
linearity is OK.
Constant Variance – there does not seem to be a fan/wedge shape, therefore the
assumption of constant variance is OK.
Normality – the points follow the reference line fairly well, even though the curves
don’t match exact. The assumption of normality seems OK.
5
Outliers – RMSE = 3.23  2RMSE = 6.46 so we need to look to see if there are points
outside 6.46 or -6.46. There are no points outside this band, therefore
there are no outliers.
g. Using the estimated regression equation identified in part d, predict the hardness of a piece of
molded plastic whose termination time is 38 minutes. (2 points)
Ê (Hardness | Time) = 168.6 + 2.03(38) = 245.74 Brinell units
3. In an experiment conducted at the National Institute of Environmental Health Sciences, the absorption
(or uptake) of a chemical by a rat on one of two different diets, I (Diet = 0) or II (Diet = 1), was known to
be affected by the weight (or size) of the rat. A completely randomized design using four rats on each
diet was employed in the experiment, and the initial weight of each rat was recorded so that the diets
could be compared after the researchers adjusted for the effect of initial weight. The data can be found
in the file Absorption.jmp on the course website.
a. Test whether the unequal slopes model is appropriate. That is, determine whether the model
which includes an interaction is appropriate for these data. Make sure to include the
appropriate hypotheses, test statistic, p-value, and conclusion. Provide a detailed sketch of or
paste the appropriate JMP output below. (8 points)
H0: β3 = 0
Ha: β3 ≠ 0
Test statistic = 0
p-value = 1
No evidence that β3 ≠ 0, so there is no evidence that an unequal slopes model should
be used.
b. Based on your answer to part a, should an equal slopes model be considered instead? Explain.
(2 points)
Yes, an equal slopes model should be used instead since there is no evidence of
unequal slopes.
6
c. Test whether the equal slopes model is appropriate. That is, determine whether diet has a
significant impact on absorption. Make sure to include the appropriate hypotheses, test
statistic, p-value, and conclusion. Provide a detailed sketch of or paste the appropriate JMP
output below. (8 points)
H0: β2 = 0
Ha: β2 ≠ 0
Test statistic = 10
p-value = 0.0250
There is evidence that β2 = ≠ 0, so there is evidence that an equal slopes model is
appropriate.
d. Based on your answer to part c, give the “best” regression model for these data. This should
look something like this: E(Y | X) = β0 + β1X. (2 points)
E(Absorption | Initial Weight, Diet) = β0 + β1Initial Weight + β2Diet
e. Using JMP, find the estimated regression equation for the model identified in part d. Make sure
to provide a detailed sketch of or paste your JMP output below. (3 points)
Ê (Absorption | Initial Weight, Diet) = 12.5 + 0.50Initial Weight + 1Diet
f.
Using the equation from part e, give the estimated regression equation for Diet I. (1 point)
Ê (Absorption | Initial Weight, Diet) = 12.5 + 0.50Initial Weight + 1(0)
= 12.5 + 0.50Initial Weight
g. Using the equation from part e, give the estimated regression equation for Diet II. (1 point)
Ê (Absorption | Initial Weight, Diet) = 12.5 + 0.50Initial Weight + 1(1)
= 13.5 + 0.50Initial Weight
h. Predict the absorption for a rat on Diet II with an initial weight of 2. (2 points)
Ê (Absorption | Initial Weight, Diet) = 13.5 + 0.50(2) = 14.5
7