Stat 301
Lab 6: Due March 10
Spring 2014
Data from the Scottish Hill Runners Association gives the name of the race, the distance in
miles, the amount of climb in feet and the record time in minutes. Data on a random sample of
30 races are given below.
Race
Greenmantle
Carnethy
Craig Dunain
Ben Rha
Ben Lomond
Goatfell
Cairnpapple
Scolty
Traprain
Dollar
Lomonds
Cairn Table
Eildon Two
Cairngorm
Seven Hills
Distance
2.5
6
6
7.5
8
8
6
5
6
5
9.5
6
4.5
10
14
Climb
650
2500
900
800
3070
2866
800
800
650
2000
2200
500
1500
3000
2200
Time
16.08
48.35
33.65
45.60
62.27
73.22
36.37
29.75
39.75
43.05
65.00
44.13
26.93
72.25
98.42
Race
Creag Beag
Kildcon Hill
Half Ben Nevis
Cow Hill
New Berwick Law
Creag Dubh
Burnswark
Largo Law
Criffel
Acmony
Ben Nevis
Knockfarrel
Two Breweries
Cockleroi
Moffat Chase
Distance
5.5
3
6
2
3
4
6
5
6.5
5
10
6
18
4.5
20
Climb
600
300
2200
900
600
2000
800
950
1750
500
4400
600
5200
850
5000
Time
32.57
15.95
47.63
17.93
18.68
26.22
34.43
28.57
50.50
20.95
85.58
32.38
170.25
28.10
159.83
1) Fit a simple linear model with Time as your response variable and Distance as your
explanatory variable. Use the JMP output to answer the following questions. Be sure to
attach the JMP to your assignment.
a)
b)
c)
d)
e)
f)
g)
What is the least squares regression equation for this model?
Predict the record time for the Cairn Table race.
Give the residual for the Cairn Table race.
Give an interpretation of the estimated slope within the context of the problem.
Give and interpretation of the estimated intercept within the context of the problem.
How much of the variation in Time is explained by the linear relationship with Distance?
Is Distance a statistically significant variable for predicting Time? Support your answer
statistically.
2) Fit a multiple regression model with Time as your response variable and Distance and Climb
as explanatory variables. Use the JMP output to answer the following questions. Be sure to
attach the JMP to your assignment.
a)
b)
c)
d)
What is the least squares regression equation for this model?
Predict the record time for the Cairn Table race.
Give the residual for the Cairn Table race.
Give an interpretation of the estimated slope for Distance within the context of the
problem.
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e) Give an interpretation of the estimated slope for Climb within the context of the
problem.
f) Does Climb add significantly to the model with Distance? Support your answer
statistically.
3) Fit a multiple regression model with Time as your response variable and Distance, Climb,
and Distance*Climb as explanatory variables. Be careful! Remember to turn off the
Center Polynomial option before you fit the model. Use the JMP output to answer the
following questions. Be sure to attach the JMP to your assignment.
a)
b)
c)
d)
What is the least squares regression equation for this model?
Predict the record time for the Cairn Table race.
Give the residual for the Cairn Table race.
Does Distance*Climb add significantly to the model with Distance and Climb? Support
your answer statistically.
e) What does the result in d) tell you about interaction between Distance and Climb?
f) What does the result in d) tell you about the relationship between Time and Distance as
you change the amount of climb?
4) Fit a multiple regression model with Time as your response variable and Distance, Climb,
and (Distance – Mean Distance)*(Climb – Mean Climb) i.e. leave the Center Polynomial
option turned on. Use the JMP output to answer the following questions. Be sure to attach
the JMP to your assignment.
a)
b)
c)
d)
What is the least squares regression equation for this model?
Predict the record time for the Cairn Table race.
Give the residual for the Cairn Table race.
Does (Distance – Mean Distance)*(Climb – Mean Climb) add significantly to the model
with Distance and climb?
e) Compare your results in 3) d) to your results in 4) d)?
5) Save the residuals for the interaction model in 4). Plot the residuals versus Distance. Plot
the residuals versus Climb. Analyze the distribution of the residuals. Use the JMP output to
answer the following questions. Be sure to attach the JMP to your assignment.
a) What do the plots of residuals versus the explanatory variables tell you about the
adequacy of the interaction model? What do they tell you about the equal standard
deviation condition? Be sure to support your answers by referring to the plots.
b) What does the analysis of the distribution of residuals tell you about the conditions of
identically and normally distributed residuals? Be sure to support your answers by
referring to the analysis.
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