Question

We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data238.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

Wages =	+  LOS
t =
P =

(c) State carefully what the slope tells you about the relationship between wages and length of service.


(d) Give a 95% confidence interval for the slope.
(  ,  )

worker  wages   los     size
1       39.7268 99      Large
2       47.9395 108     Small
3       50.0018 36      Small
4       56.5056 37      Small
5       39.9768 99      Large
6       42.1023 51      Small
7       68.3662 149     Large
8       62.1544 118     Large
9       45.573  151     Large
10      50.4117 83      Small
11      38.4135 53      Large
12      62.4993 40      Small
13      60.3019 58      Small
14      37.6291 26      Large
15      38.3317 104     Large
16      44.7494 158     Large
17      72.8137 58      Large
18      52.989  83      Small
19      73.2051 49      Large
20      39.127  113     Large
21      44.2316 59      Large
22      69.7851 40      Small
23      49.472  26      Large
24      38.5196 77      Small
25      46.0804 69      Large
26      59.7664 118     Small
27      55.661  115     Small
28      58.2214 28      Large
29      57.7969 39      Large
30      46.9105 44      Large
31      38.4955 56      Small
32      58.9224 110     Large
33      53.8302 82      Large
34      43.2473 58      Small
35      50.2706 84      Large
36      50.6164 20      Large
37      49.6558 93      Large
38      78.595  66      Small
39      82.6382 92      Large
40      75.3109 40      Small
41      49.842  131     Small
42      50.6961 61      Small
43      72.7987 38      Large
44      45.2429 101     Small
45      67.4423 121     Large
46      53.2089 102     Small
47      55.595  28      Large
48      63.0091 45      Large
49      60.6773 41      Small
50      44.6185 20      Large
51      39.0958 91      Large
52      63.4885 200     Large
53      54.8688 149     Large
54      53.0166 26      Small
55      42.1089 95      Small
56      71.9169 50      Large
57      61.4371 62      Small
58      50.6912 16      Large
59      53.9664 23      Small
60      39.0164 15      Large

Answer 1

X G2 -B2^2 A E H K M N O D O R. S T U 1 Worker Los ei Wages ei 2 Los 2 Wages Ans The scatterplot between wages and length 53.5729 service is given as, 2 99 39.7268 13.8461 191.7145 980: 3. 2 108 47.9395 53.5198 5,5803 31.13975 11664 Scatter Plot 36 129 4 50.0018 53.9446 3.9428 5.54567 2 5669 36 90 5. 4 27 56 5056 53.9387 ,588976 -13.5961 184,8539 y0 157 39.9768 6. 5 99 53.5729 980: 80 R-0.0004 -11.7538 138.1518 7 6 51 42.1023 53.8561 2601 70 15.0883 227.6568 22201 8 149 68.3662 53.2779 60 11 62.1544 53.4608 13924 8.6936 75.57868 10 :50 4.575 10 _ _ 3.2556 10.5e - 15.4308 238.1096 12 53 38.4135 53.8443 2809 12 40 58 26 104 158 58 30 13 62.4993 53.921 8.5783 73.58723 1600 14 13 60.3019 53.8148 6,4871 42.08247 3366 20 14 15 37.6291 54.0036 -16.3745 268.1243 676 -15.2117 231.3958 16 15 38.3317 53.5434 L0816 17 16 44.7494 53.2248 -8.4754 71.83241 24964 150 200 100 18 17 72.8137 53.8148 18.9989 360.9582 3366 Length of service 19 18 83 52.989 53.6673 -0.6783 0.460091 688 19 240 20 49 73.2051 53.8679 19.3372 373.9273 14.3633 206.3044 21 20 11: 39.127 53.4903 12769 -9,5773 The relationship between wages and length of service is not clear from this scatterplot, therefore the linear regression might not be 22 21 59 44.2316 53.8089 72468 3481 15.8641 251.6697 23 22 40 69.7851 53.921 1600 appropriate. 24 23 20 49.472 54.0036 -4.5316 20.5354 670 Ans(b). The least square line and t value and p value is given as, 25 7. 53.7027 15.1831 230.5265 5929 24 38.5196 26 s3 4608 6 3056 13924 27 26 118 59.7664 9,76059 Wages 54.157-0.0059* Los 2.1825 4.763306 4.2296 17.88952 13225 variance of wages> 28 27 115 55.661 53.4785 135.5401 Activate Windows Go to Settings to activate Windows. 29 28 58.2214 53.9918 78 Sxx > 102430.4 Standard error of slope coefficient 0.036376 53.9209 c onsol 1510 Sheet Sheet2 Sheet3 + 11:17 PM 6/12/2019

. X G2 B242 A C G J K M N O P O R T 53.8679 19.3372 373.9273 20 19 4: 73.2051 240 113 39.127 21 20 53.4903 14.3633 206.3044 12769 The relationship between wages and length of service is not clear from this scatterplot, therefore the linear regression might not be 22 23 59 44.2316 53.8089 9.5773 1.72468 348 23 22 40 69.7851 53.921 15.8641 251.6697 1600 appropriate. -4.5316 24 23 26 49.472 54.0036 20.5354 676 - 15.183 Ans(b). The least square line and t value and p value 25 24 38.5196 53.7027 230.5265 5929 given as 26 69 46.0804 53.7499 7.6695 8.82123 4761 Wages 54.157- 0.0059 Los 27 2 39.70053 13924 7004 13 of 135.5401 28 7.88952 29 58.2214 53.9918 4.2296 784 102430.4 29 30 39 57.7969 44 46.9105 56 Standard error of slope coefficient > 0.036376 30 53.9269 3.87 14.9769 1521 -6.9869 48.81677 t-value> 31 53.8974 1936 -0.16219 P-value 32 37 38.4955 53.8266 15.3311 235.0426 136 0,43 110 82 33 32 58.9224 53.508 5.4144 29.31573 12100 0.157 0.024649 -10.5675 111.6721 53.6732 6724 Ans c) The value of wages decreases by 0.0059 unit when length of service increase by 1 unit. 34 33 53.8302 53.8148 35 34 58 43.2473 3364 84 20 7056 Ans d) 95% confidence interval given by, 36 35 50.2706 53.6614 3.3908 11.49752 54.039 3.4226 critical value of t-dist > 1.671553 37 36 50.6164 11.71419 401 -t se(b) > -0.06671 38 37 93 49.6558 53.6083 -3.9525 15.62226 8649 Lower limit> 24.8274 616.3998 29.024 842.3926 21.3899 457.5278 3.5421 12.54647 Upper limit=> b+t*se(b) 0.054905 39 38 66 78.595 53.7676 4356 40 39 92 82.6382 53.6142 8464 Therefore, the confidence interval is (-0.0667, 0.0549). 41 40 40 75.3109 53.921 1600 42 133 49.842 53.3841 17161 4. 6. 50.0901 019.616201 .. 45 101 45.2429 53.5611 -8.3182 9.19245 10201 195.9776 46 45 123 7.4423 .9992 14641 53.4431 102 10 53 P819 55 595 Activate Windows Goto Settings to-activate Windows 49 63.0091 53.8915 9.1176 3.13063 2025 41 60 6773 49 53 9151 1681. 6 7622 50. 5.72735 Sheet1 Sheet2 Sheet3 + 4 11:17 PM 6/12/2019

X G2 -82^2 A в C F G J K M N O P Q R S T 33 32 110 58.9224 53.508 5.4144 9.31573 12100 0.024649 82 672- Ans c) The value of wages decreases by 0.0059 unit when length of service increase by 1 unit. 34 33 53.8302 53.6732 0.157 35 58 43.2473 53.8148 10.5675 111.6721 336 8450.2706 20 3.3908 Ans d) 95% confidence interval is given by, 36 35 53.6614 11.49752 705 critical value of t-dist-> 37 36 50.6164 54.039 -3.4226 11.71419 400 1.671553 Lower limit> b-t se(b) b +t*se(b) 38 93 49.6558 53.6083 3.9525 15.62226 8649 -0.06671 3. 24.8274 616.3998 Upper limit> 39 60 78.595 53.7676 0.054905 38 4350 7IQ'Sc 23.024 842.3920 Therefore, the confidence interval is (-0.0667, 0.0549). 1600 3.5421 42 Ат 137 49,842 53.3841 12.54647 17161 43 42 61 50.6961 53.7971 .107 9.616201 3721 38 101 18.8659 355.9222 44 72.7987 53.9328 1дл 45 44 45.2429 53.5611 -8.3182 9.19245 10201 121 102 46 45 67.4423 53.4431 13.9992 195.9776 14642 -0.3463 0.119924 10404 47 46 53.2089 53.5552 2.57025 784 48 42 28 55.595 53.9918 1.6032 49 48 45 63.0091 53.8915 9.1176 3.13063 202 41 168 50 49 60.6773 53.9151 6.7622 5.72735 51 50 20 да 6185 54.039 9.4205 .74582 400 -14.5243 210.9553 91 200 149 52 51 39.0958 53.6201 8281 10.5115 110.4916 53 52 63.4885 52.977 40000 1.5909 2.530963 54 53 54.8688 53.2779 22201 0.987 0.974169 55 20 53.0166 54.0036 67 54 31,965 53. R67 62 16 58 61.4371 53.7912 7.6459 58,45979 3844 58 1.36634 59 50.6912 54.0626 3.3714 256 25 39 0164 15 0521 226 5657 Activate Windows Gote Settings to activate Windews 60 54.0685 425684 62 73.4 7861.329 63 Sheet1 Sheet2 Sheet3 4 11:17 PM 6/12/2019