An economist is studying the link between the total value of a country’s exports and that country’s gross domestic product, or GDP. The economist recorded the GDP and Export value (in millions of $’s) for 30 nations for the same fiscal year. This sample data is provided below.

GDP Exports

225274 214010

297106 205300

1470543 189700

511685 188300

930808 184300

261974 180500

542857 152000

331360 151100

703318 148400

269115 142900

154027 128970

101848 125927

271392 104968

97980 88546

181876 93763

266641 82414

139535 77731

76381 74824

212411 62118

169385 61143

594857 65205

144020 57241

353487 55861

99688 55691

155857 53762

137955 55400

164110 46322

422231 45940

149899 43284

257349 37922
Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

Ans: r = 0.49

The table below shows data on annual expenditure, x (in dollars), on recreation and annual income, y (in dollars), of 20 families. Use Excel to find the best fit linear regression equation. Round the slope and intercept to the nearest integer.

x y

2400 41200

2650 50100

2350 52000

4950 66000

3100 44500

2500 37700

5106 73500

3100 37500

2900 56700

1750 35600

1450 37500

2020 36900

3750 48200

1675 34400

2400 29900

2550 44750

3880 60550

3330 52000

4050 67700

1150 20600

Jorge is an economist trying to understand whether there is a strong link between CEO compensation and corporate revenue. He gathered data including the CEO compensation for 30 randomly selected corporations for a particular year as well as the corporate revenue of those corporations for the same year. The data Jorge gathered are provided in the accompanying data table. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

CEO Compensation ($) Corporate Revenue (million $)

14215830 20101

14499807 28266

15268679 18524

14476928 28738

15083546 52884

15237297 117162

13881835 23704

13771160 33749

14269205 62478

13025536 44150

12793113 18347

12981100 31891

12682976 20980

13475291 17324

12433901 220088

12972799 29532

12580828 62901

12099198 21757

11965940 20469

11945915 20012

12393340 18356

11860228 22915

11109548 21577

11606923 21132

10978619 19258

11457940 21204

10774262 127285

10357350 18836

10621145 35626

10238177 155104

In the following table, the age (in years) of the respondents is given as the x value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places.

x y

21 42.136

22 24.900

22 13.884

24 29.597

24 30.306

25 42.000

25 40.257

27 38.081

27 29.434

30 50.188

31 38.000

32 22.776

32 45.000

33 52.000

34 39.500

38 60.000

40 51.844

40 39.575

42 57.824

42 42.346

43 35.214

43 42.388

43 41.962

44 42.388

45 45.000

45 40.500

46 46.193

47 48.853

48 52.000

48 52.884

49 36.480

49 40.069

50 46.630

50 40.308

51 20.103

53 42.384

54 30.995

55 56.657

56 42.374

56 52.368

57 69.000

57 64.748

57 52.884

58 42.398

59 40.000

The heights (in inches) and weights (in pounds) of 25 baseball players are given below. Use Excel to find the best fit linear regression equation, where height is the explanatory variable. Round the slope and intercept to two decimal places.

Height Weight

71 186

72 211

73 220

70 165

72 180

72 195

70 175

74 202

78 240

71 170

74 180

73 185

76 257

77 215

76 287

77 220

73 200

76 223

76 200

70 220

75 215

71 195

77 194

75 195

75 225

The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x y

0 0.1

5 0.1

10 0.1

15 0.2

20 0.2

25 0.3

30 0.4

35 0.5

40 0.6

45 1.1

50 1.5

55 3.0

60 4.5

65 5.5

70 6.1

75 6.8

80 7.0

85 8.0

90 9.3

95 10.7

100 12.4

105 14.1

110 16.6

115 17.5

120 19.7

125 19.4

130 32.7

135 40.9

140 47.6

145 57.8

150 57.0

155 61.7

160 63.2

165 75.0

170 76.5

175 96.0

180 92.0

185 100.0

190 100.0

The table below contains the geographic latitudes, x, and average January temperatures, y, of 20 cities. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x y

46 23

32 60

39 40

33 59

38 57

40 33

42 33

30 64

34 56

41 39

36 49

39 54

47 20

26 76

45 25

31 62

39 42

43 31

37 55

41 31

The table below represents the number of young people in a certain city enrolled in the academic support and enrichment program of youth services. Here, x represents the number of months from January 2011, and y represents the number of young people enrolled. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x y

0 3199

1 3282

2 3432

3 3245

4 3076

5 3485

6 1524

7 1880

8 2715

9 2963

10 2917

11 3064

12 2730

13 3002

14 3115

15 3148

16 3372

17 3070

18 1813

19 1820

20 2720

21 3297

22 3157

23 2932

24 2839

25 2738

26 2721

27 2999

28 807

29 221

30 1537

31 1922

32 2532

33 3070

34 3091

35 2965

36 2956

37 3116

38 3294

39 3271

40 3211

41 3383

42 2243

43 2035

44 2625

45 2970

46 3046

47 2785

48 2650

49 1121

50 204

51 2796

52 2692

53 2830

54 2068

55 1802

56 2181

57 2675

58 2625

59 2632

60 2354

61 2501

62 2476

63 2458

64 2391

65 2375

An economist is trying to understand whether there is a strong link between CEO pay ratio and corporate revenue. The economist gathered data including the CEO pay ratio and corporate revenue for 30 companies for a particular year. The pay ratio data is reported by the companies and represents the ratio of CEO compensation to the median employee salary. The data are provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

CEO Pay Ratio Corporate Revenue (million $)

275 151007

293 20612

980 29498

336 39286

255 20338

181 25991

315 98334

131 36196

279 63827

224 60328

256 26675

90 25175

356 53525

1407 20764

220 17494

177 64190

316 45760

335 17476

126 33467

288 20142

267 63580

276 22302

137 20094

2433 20430

223 20867

1292 19183

164 22079

145 20478

226 34635

141 27072

Q10

An energy economist studying the growth and decay of both the coal and natural gas industries wanted to leverage data collected by environmental scientists. Particularly, the economist wanted to study the link between the total yearly carbon emissions from both energy sources. They looked at 30 years of total yearly carbon emissions for a particular nation (measured in million metric tons of carbon dioxide) for both forms of energy. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

MMTons CO2 Natural Gas MMTons CO2 from Coal

144.975 1552.524

173.578 1519.755

168.448 1517.232

183.205 1537.343

178.596 1528.600

190.391 1658.477

212.140 1708.757

222.428 1626.367

210.728 1810.590

219.543 1733.430

257.485 1773.156

256.113 1828.702

274.249 1991.943

292.051 1807.748

316.249 1849.436

272.586 1948.157

310.474 1874.673

313.879 1923.322

340.916 1999.025

356.621 2057.241

368.335 1959.583

362.115 1805.112

399.512 1809.525

392.326 1745.279

468.730 1570.326

434.550 1513.523

456.864 1512.334

503.702 1369.385

561.474 1245.502

490.599 1258.338

Solution