Q1
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 $’s) for 30 nations for the same fiscal year. This sample data is provided below.
GDP Exports
225274 214010
297106 205300
1470543 189700
511685 188300
930808 184300
261974 180500
542857 152000
331360 151100
703318 148400
269115 142900
154027 128970
101848 125927
271392 104968
97980 88546
181876 93763
266641 82414
139535 77731
76381 74824
212411 62118
169385 61143
594857 65205
144020 57241
353487 55861
99688 55691
155857 53762
137955 55400
164110 46322
422231 45940
149899 43284
257349 37922
Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
Ans: r = 0.49
Q2
The table below shows data on annual expenditure, x (in dollars), on recreation and annual income, y (in dollars), of 20 families. Use Excel to find the best fit linear regression equation. Round the slope and intercept to the nearest integer.
x y
2400 41200
2650 50100
2350 52000
4950 66000
3100 44500
2500 37700
5106 73500
3100 37500
2900 56700
1750 35600
1450 37500
2020 36900
3750 48200
1675 34400
2400 29900
2550 44750
3880 60550
3330 52000
4050 67700
1150 20600
Q3
Jorge is an economist trying to understand whether there is a strong link between CEO compensation and corporate revenue. He gathered data including the CEO compensation for 30 randomly selected corporations for a particular year as well as the corporate revenue of those corporations for the same year. The data Jorge gathered are provided in the accompanying data table. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
CEO Compensation ($) 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
Q4
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
Q5
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
Q6
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
Q7
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
Q8
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
Q9
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
Q1
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
Q2
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
Ans:
yˆ=11x+14,949…………….please follow the link below to purchase all the solutions at $5