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The Excel file hills.xlsx provided in the Assessments tab on moodle gives the record times for 35 hill races in Scotland. The data consists of the name of each race, the distance covered in miles, the elevation climbed in feet, and the record time in minutes.

a) Create (and include with your answer) scatterplots for each pair of quantitative variables (climb vs distance, time vs distance, time vs climb).Also do this after taking logs (ln) of all quantities. Would it be better to perform linear regression analysis using the raw data, or the logs? Justify your answer.

b) Are there any outliers? Justify your answer, and remove any outliers from subsequent analyses.

c) What is the best choice of predictors for predicting record time: 1) distance only, 2) climb only, or 3) distance and climb? Your answer should includeAIC calculations.

d) Give a formula for predicting record time, based on the model chosen in c).


Race

 

Greenmantle

 

Carnethy

 

CraigDunain

 

BenRha

 

BenLomond

 

Goatfell

 

BensofJura

 

Cairnpapple

 

Scolty

 

Traprain

 

LairigGhru

 

Dollar

 

Lomonds

 

CairnTable

 

EildonTwo

 

Cairngorm

 

SevenHills

 

KnockHill

 

BlackHill

 

CreagBeag

 

KildconHill

 

MeallAnt­Suidhe

 

HalfBenNevis

 

CowHill

 

NBerwickLaw

 

CreagDubh

 

Burnswark

 

LargoLaw

 

Criffel

 

Acmony

 

BenNevis

 

Knockfarrel

 

TwoBreweries

 

Cockleroi

 

MoffatChase

 


 

Distance

 


 

Climb

 

2.5

 

6

 

6

 

7.5

 

8

 

8

 

16

 

6

 

5

 

6

 

28

 

5

 

9.5

 

6

 

4.5

 

10

 

14

 

3

 

4.5

 

5.5

 

3

 

3.5

 

6

 

2

 

3

 

4

 

6

 

5

 

6.5

 

5

 

10

 

6

 

18

 

4.5

 

20

 


 

Time

 

650

 

2500

 

900

 

800

 

3070

 

2866

 

7500

 

800

 

800

 

650

 

2100

 

2000

 

2200

 

500

 

1500

 

3000

 

2200

 

350

 

1000

 

600

 

300

 

1500

 

2200

 

900

 

600

 

2000

 

800

 

950

 

1750

 

500

 

4400

 

600

 

5200

 

850

 

5000

 


 

16.083

 

48.35

 

33.65

 

45.6

 

62.267

 

73.217

 

204.617

 

36.367

 

29.75

 

39.75

 

192.667

 

43.05

 

65

 

44.133

 

26.933

 

72.25

 

98.417

 

78.65

 

17.417

 

32.567

 

15.95

 

27.9

 

47.633

 

17.933

 

18.683

 

26.217

 

34.433

 

28.567

 

50.5

 

20.95

 

85.583

 

32.383

 

170.25

 

28.1

 

159.833

 


 

 







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