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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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This question was answered on: Feb 21, 2020

Solution~000471006.zip (18.37 KB)