The accompanying data table contains financial data for 30 random technology companies. One column gives the expenses on research and development (R&D), and another gives the total assets of the 30 companies. Both of these columns are reported in millions of dollars. The data need to be expressed on a log scale; otherwise, two outlying companies dominate the analysis. Use the natural logs of both variables rather than the original variables in the data table. (Note that the variables are recorded in millions, so 1,000 = 1 billion.) Complete parts (a) through (c). Click the icon to view the data table of R&D expenses and total assets. (a) What difference in R&D spending (as a percentage) is associated with a 1% increase in the assets of a firm? Give your answer as a range. A difference between % and % in R&D spending is associated with a 1% increase in the assets of a firm. (Round to three decimal places as needed.) (b) Revise your model to use base 10 logs of assets and R&D expenses. Does using a different base for both log transformations affect your answer to part (a)? Select the correct choice below and, if necessary, fill in the answer boxes in your choice. O A. Yes. The new difference is between % and (Round to three decimal places as needed.) O B. No. The answer to part (a) remains the same. (c) Find a 95% prediction interval for the R&D expenses of a firm with $1 billion in assets. Be sure to express your range on a dollar scale. Do you expect this interval to have 95% coverage? million and $ million. The R&D expenses for a firm with $1 billion in assets would be between (Round to one decimal place as needed.)
The accompanying data table contains financial data for 30 random technology companies. One column gives the expenses on research and development (R&D), and another gives the total assets of the 30 companies. Both of these columns are reported in millions of dollars. The data need to be expressed on a log scale; otherwise, two outlying companies dominate the analysis. Use the natural logs of both variables rather than the original variables in the data table. (Note that the variables are recorded in millions, so 1,000 = 1 billion.) Complete parts (a) through (c). Click the icon to view the data table of R&D expenses and total assets. (a) What difference in R&D spending (as a percentage) is associated with a 1% increase in the assets of a firm? Give your answer as a range. A difference between % and % in R&D spending is associated with a 1% increase in the assets of a firm. (Round to three decimal places as needed.) (b) Revise your model to use base 10 logs of assets and R&D expenses. Does using a different base for both log transformations affect your answer to part (a)? Select the correct choice below and, if necessary, fill in the answer boxes in your choice. O A. Yes. The new difference is between % and (Round to three decimal places as needed.) O B. No. The answer to part (a) remains the same. (c) Find a 95% prediction interval for the R&D expenses of a firm with $1 billion in assets. Be sure to express your range on a dollar scale. Do you expect this interval to have 95% coverage? million and $ million. The R&D expenses for a firm with $1 billion in assets would be between (Round to one decimal place as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The accompanying data table contains financial data for 30 random technology companies. One column gives the expenses on research and development (R&D), and another gives the total assets of the 30 companies. Both of
these columns are reported in millions of dollars. The data need to be expressed on a log scale; otherwise, two outlying companies dominate the analysis. Use the natural logs of both variables rather than the original variables in
the data table. (Note that the variables are recorded in millions, so 1,000 = 1 billion.) Complete parts (a) through (c).
Click the icon to view the data table of R&D expenses and total assets.
(…)
(a) What difference in R&D spending (as a percentage) is associated with a 1% increase in the assets of a firm? Give your answer as a range.
A difference between % and % in R&D spending is associated with a 1% increase in the assets of a firm.
(Round to three decimal places as needed.)
(b) Revise your model to use base 10 logs of assets and R&D expenses. Does using a different base for both log transformations affect your answer to part (a)?
Select the correct choice below and, if necessary, fill in the answer boxes in your choice.
O A. Yes. The new difference is between % and
(Round to three decimal places as needed.)
O B. No. The answer to part (a) remains the same.
(c) Find a 95% prediction interval for the R&D expenses of a firm with $1 billion in assets. Be sure to express your range on a dollar scale. Do you expect this interval to have 95% coverage?
The R&D expenses for a firm with $1 billion in assets would be between S million and $ million.
(Round to one decimal place as needed.)
Transcribed Image Text:Assets
0.27
1.19
9.39
2.04
2.66
4,185.58
96,480.87
8.76
401.34
826.83
42,344.76
77.12
18.61
0.17
10.17
1.68
6.15
9,972.63
11,468.97
2.61
752.80
0.59
435.33
3.46
7,929.14
381.19
1.08
22.92
24.86
1.66
R&D
0.09
0.28
2.39
0.83
0.48
171.25
7,565.09
1.53
39.38
70.63
4,578.38
14.48
2.15
0.10
2.86
0.72
0.99
667.27
376.79
0.94
39.62
0.13
30.78
1.26
305.58
31.59
0.42
3.13
3.91
0.33
Log Assets
-1.3162
0.1704
2.2395
0.7128
0.9794
8.3394
11.4771
2.1707
5.9948
6.7176
10.6536
4.3454
2.9236
-1.7936
2.3191
0.5203
1.8169
9.2076
9.3474
0.9578
6.6238
-0.5245
6.0761
1.2424
8.9783
5.9433
0.0734
3.1321
3.2134
0.5063
Log R&D
-2.4103
-1.2581
0.8709
-0.1808
-0.7382
5.1431
8.9313
0.4233
3.6733
4.2575
8.4291
2.6726
0.7668
-2.3298
1.0523
-0.3287
-0.0115
6.5032
5.9317
-0.0608
3.6793
-2.0621
3.4269
0.2287
5.7222
3.4527
-0.8771
1.1403
1.3633
-1.1151
Log 10 Assets
-0.5716
0.0740
0.9726
0.3096
0.4253
3.6218
4.9844
0.9427
2.6035
2.9174
4.6268
1.8872
1.2697
-0.7790
1.0072
0.2260
0.7891
3.9988
4.0595
0.4160
2.8767
-0.2278
2.6388
0.5396
3.8992
2.5811
0.0319
1.3603
1.3956
0.2199
Log 10 R&D
-1.0468
-0.5464
0.3782
-0.0785
-0.3206
2.2336
3.8788
0.1838
1.5953
1.8490
3.6607
1.1607
0.3330
- 1.0118
0.4570
-0.1428
-0.0050
2.8243
2.5761
-0.0264
1.5979
-0.8956
1.4883
0.0993
2.4851
1.4995
-0.3809
0.4952
0.5921
-0.4843
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