Stat 301 Lab 4
Group Activity on Regression
Names of Group Members: _______________, _______________, _______________
_______________, _______________, _______________
1. What is the relationship between the temperature or coffee and the time since the
coffee was poured? The data consists of the temperature (oF) of cups of coffee and
the times (minutes) since the coffee was first poured. The data can be considered a
random sample of times/temperatures for cups of coffee.
Time (min)
Temperature (oF)
0
179.5
5
168.7
11
149.2
15
141.7
22
125.4
25
123.5
30
116.3
38
109.1
45
102.2
50
100.5
We wish to be able to predict the temperature of coffee from the time since the coffee
was poured. Use JMP to analyze these data. Use the JMP output that you generate and
your knowledge of regression analysis to answer the following questions. Group
members should discuss the questions and come up with answers that are agreed upon by
all the group members. Turn in this group answer sheet and one copy of your JMP output
at the end of lab today.
a) Give the prediction equation for the line relating temperature to time.
b) Give an interpretation, within the context of the problem, of:
• the estimated slope, β̂ 1 .
•
the estimated Y-intercept, β̂ 0 .
c) Is there a statistically significant linear relationship between the temperature of
the coffee and the time since the coffee was poured? Support your answer with a
test of hypothesis.
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d) Give the value of R2 and an interpretation of this value.
e) The coffee in the pot is supposed to be 180 oF? Based on your prediction
equation, is 180 oF a plausible value for the mean temperature of coffee in the
pot? Support your answer using an appropriate 95% confidence interval.
f) What is the predicted temperature and residual for coffee poured 15 minutes ago?
g) What is the estimated mean temperature for coffee poured 30 minutes ago? Also
give a 95% confidence interval for this mean temperature.
h) How does the 95% prediction interval for coffee poured 30 minutes ago differ
from the confidence interval above? Be sure to indicate differences in
interpretation as well as value.
i) Comment on the plot of residuals versus time. Specifically what does this plot
tell you about the adequacy of the linear model?
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