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: S 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: S 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% Carry out the two hypothesis tests for the net regression coefficients using the information above. State the hypothesis you are testing. State your decision and the reason you are making the decision. Finally, explain what the decision means.
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:
S 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:
S 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%
Carry out the two hypothesis tests for the net regression coefficients using the information above.
State the hypothesis you are testing. State your decision and the reason you are making the decision. Finally, explain what the decision means.
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