Climb (m) 0.09717 0.00497 19.55 0.000 Model Summary for Climb: R-sq R-sq(adj) R-sq(pred) 23.9301 81.46% 81.25% 80.54% Here is the information for the 3 dimensional relationship between x1, x2, and Y. Multiple Linear Relationship for the women: Coefficients: Term Coef SE Coef T-Value P-Value Constant -11.70 1.91 -6.11 0.000 Distance(km) 4.432 0.222 20.01 0.000 Climb (m) 0.04526 0.00334 13.56 0.000 Model Summary: S R-sq R-sq(adj) R-sq(pred) 10.1208 96.72% 96.65% 96.09% Does it help to add the second x variable in this case? O Yes O You can't tell from this information O No

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Scottish Hill Climb races
We want to predict the record time for women in a Scottish Hill Climb race. There
are two x variables to choose from, Distance and Climb. Here are the first few rows
from the data table.
Race
Men (mins)
Women(mins) Distance(km) Climb (m)
Alva Games Hill Race
18.650
25.817
2.5
385
Aonach Mor Uphill Race
22.250
26.467
4.0
610
Arrochar Alps
187.650
249.433
25.0
2400
Once you have chosen the best single x variable to predict the record time for
women, does it help to add the 2nd x variable?
Here is the information for the two single x variables.
Coefficients for Distance:
Term
Coef SE Coef
T-Value
P-Value
Constant
-7.15 3.32
-2.16
0.034
Distance(km) 6.765 0.246
27.55
0.000
Model Summary for Distance:
R-sq
R-sq(adj)
R-sq(pred)
17.8222
89.72%
89.60%
88.19%
Coefficients for Climb:
Term
Coef
SE Coef
T-Value P-Value
Constant
2.60
4.20
0.62 0.538
Transcribed Image Text:Scottish Hill Climb races We want to predict the record time for women in a Scottish Hill Climb race. There are two x variables to choose from, Distance and Climb. Here are the first few rows from the data table. Race Men (mins) Women(mins) Distance(km) Climb (m) Alva Games Hill Race 18.650 25.817 2.5 385 Aonach Mor Uphill Race 22.250 26.467 4.0 610 Arrochar Alps 187.650 249.433 25.0 2400 Once you have chosen the best single x variable to predict the record time for women, does it help to add the 2nd x variable? Here is the information for the two single x variables. Coefficients for Distance: Term Coef SE Coef T-Value P-Value Constant -7.15 3.32 -2.16 0.034 Distance(km) 6.765 0.246 27.55 0.000 Model Summary for Distance: R-sq R-sq(adj) R-sq(pred) 17.8222 89.72% 89.60% 88.19% Coefficients for Climb: Term Coef SE Coef T-Value P-Value Constant 2.60 4.20 0.62 0.538
Climb (m)
0.09717
0.00497
19.55 0.000
Model Summary for Climb:
R-sq
R-sq(adj)
R-sq(pred)
23.9301
81.46%
81.25%
80.54%
Here is the information for the 3 dimensional relationship between x1, x2, and Y.
Multiple Linear Relationship for the women:
Coefficients:
Term
Coef
SE Coef
T-Value P-Value
Constant
-11.70
1.91
-6.11
0.000
Distance(km)
4.432
0.222
20.01
0.000
Climb (m)
0.04526
0.00334
13.56
0.000
Model Summary:
S
R-sq
R-sq(adj)
R-sq(pred)
10.1208
96.72%
96.65%
96.09%
Does it help to add the second x variable in this case?
O Yes
O You can't tell from this information
O No
Transcribed Image Text:Climb (m) 0.09717 0.00497 19.55 0.000 Model Summary for Climb: R-sq R-sq(adj) R-sq(pred) 23.9301 81.46% 81.25% 80.54% Here is the information for the 3 dimensional relationship between x1, x2, and Y. Multiple Linear Relationship for the women: Coefficients: Term Coef SE Coef T-Value P-Value Constant -11.70 1.91 -6.11 0.000 Distance(km) 4.432 0.222 20.01 0.000 Climb (m) 0.04526 0.00334 13.56 0.000 Model Summary: S R-sq R-sq(adj) R-sq(pred) 10.1208 96.72% 96.65% 96.09% Does it help to add the second x variable in this case? O Yes O You can't tell from this information O No
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