Stat 301 Lab 6
Group Activity on Multiple Regression
Names of Group Members: _______________, _______________, _______________
_______________, _______________, _______________
1. On the first exam you looked at the relationship between carcass weight and belly weight for
of pigs randomly selected from a pork processing facility. There were actually two sets of
data representing two pork processing facilities. In this group exercise you will look at the
analysis of the combined samples (117 pigs). In addition to the carcass and belly weight,
each carcass is probed between the 3rd and 4th ribs using a Fat-O-Meat’er (FOM) that
measures fat depth and muscle depth. Use the JMP output provided to you to answer the
following questions about the relationship between carcass weight, fat depth and muscle
depth and belly weight.
a) Give the prediction equation for the line relating carcass weight to belly weight.
b) Give an interpretation, within the context of the problem, of the estimated slope β̂ 1 .
c) Is there a statistically significant linear relationship between carcass weight and belly
weight? Support your answer with a test of hypothesis.
d) What proportion of the variation in belly weight can be explained by the linear
relationship with carcass weight?
e) Give the prediction equation for the line relating belly weight to carcass weight and fat
depth.
f) Give an interpretation, within the context of the problem, of the estimated slope for fat
depth β̂ 2|1 .
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g) What is the additional proportion of the variation in belly weight that can be explained by
the addition of fat depth to the model with carcass weight?
h) Does fat depth add significantly to the model that already contains carcass weight?
Support your answer with a test of hypothesis.
i)
Complete the analysis of variance table for the simple linear regression of belly weight on
fat depth.
Source
Model
df
Sum of Squares
Mean Square
F
Prob > F
< 0.0001
Error
C. Total
j)
Give the prediction equation for the line relating belly weight to carcass weight, fat depth
and muscle depth.
k) What is the additional proportion of the variation in belly weight that can be explained by
the addition of muscle depth to the model with carcass weight and fat depth?
l)
Does muscle depth add significantly to the model that already contains carcass weight
and fat depth? Support your answer with a test of hypothesis.
m) Does carcass weight add significantly to the model that already contains fat depth and
muscle depth? Support your answer with a test of hypothesis.
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n) Complete the analysis of variance table for the multiple regression of belly weight on fat
depth and muscle depth.
Source
df
Sum of Squares
Mean Square
F
Model
Prob > F
< 0.0001*
Error
C. Total
Extra Credit: Complete the Effect Tests below for the multiple regression of belly weight on fat
depth and muscle depth.
Source
FatDepth FOM
MuscleDepth FOM
df
Sum of Squares
F
Prob > F
< 0.0001*
0.0046*
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