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 (data117.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 =

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

Data:

worker wages los size 1 52.9346 183 Large 2 46.5457 69 Small 3 60.2976 104 Small 4 72.0801 27 Small 5 54.6028 105 Large 6 53.2802 86 Small 7 53.4939 36 Large 8 40.4958 20 Large 9 54.626 52 Large 10 42.3821 37 Small 11 42.844 72 Large 12 41.143 60 Small 13 77.8717 65 Small 14 65.834 29 Large 15 62.1566 23 Large 16 67.713 122 Large 17 59.7909 124 Large 18 62.4005 106 Small 19 40.0718 18 Large 20 46.2152 20 Large 21 45.1799 22 Large 22 42.2771 97 Small 23 52.4645 79 Large 24 48.0469 23 Small 25 44.4731 35 Large 26 40.7649 36 Small 27 50.6375 88 Small 28 45.4043 74 Large 29 52.9125 22 Large 30 60.0693 24 Large 31 49.3684 22 Small 32 54.527 56 Large 33 45.8271 60 Large 34 57.5896 23 Small 35 41.7001 15 Large 36 38.4826 84 Large 37 46.8481 70 Large 38 58.7057 99 Small 39 65.4643 72 Large 40 45.1564 116 Small 41 65.2734 177 Small 42 69.5617 100 Small 43 54.1896 87 Large 44 54.3447 27 Small 45 37.6578 20 Large 46 39.3685 179 Small 47 66.917 76 Large 48 73.1906 48 Large 49 67.2132 52 Small 50 38.3865 69 Large 51 75.0269 167 Large 52 91.1291 122 Large 53 44.4168 28 Large 54 83.2958 36 Small 55 45.1767 114 Small 56 46.5962 81 Large 57 70.87 34 Small 58 56.6501 167 Large 59 57.2335 147 Small 60 61.7817 125 Large

Answer 1

a)

Plot wages versus LOS

Let independent variable LOS size = 0 for "Small" and 1 for "Large."

The scatter plot is obtained in excel. The screenshot is shown below,

Since the LOS is a binary variable, the linear regression is not appropriate here.

b)

The regression equation is defined as,

The least square estimate of intercept and slope are,

From the data points,

worker	wages, Y	los size, X	X^2	Y^2	XY
1	52.9346	1	1	2802	53	53	-0.4961	0
2	46.5457	0	0	2167	0	56	-9.4938	90
3	60.2976	0	0	3636	0	56	4.2581	18
4	72.0801	0	0	5196	0	56	16.0406	257
5	54.6028	1	1	2981	55	53	1.1721	1
6	53.2802	0	0	2839	0	56	-2.7593	8
7	53.4939	1	1	2862	53	53	0.0632	0
8	40.4958	1	1	1640	40	53	-12.9349	167
9	54.626	1	1	2984	55	53	1.1953	1
10	42.3821	0	0	1796	0	56	-13.6574	187
11	42.844	1	1	1836	43	53	-10.5867	112
12	41.143	0	0	1693	0	56	-14.8965	222
13	77.8717	0	0	6064	0	56	21.8322	477
14	65.834	1	1	4334	66	53	12.4033	154
15	52.1566	1	1	2720	52	53	-1.2741	2
16	67.713	1	1	4585	68	53	14.2823	204
17	59.7909	1	1	3575	60	53	6.3602	40
18	62.4005	0	0	3894	0	56	6.3610	40
19	40.0718	1	1	1606	40	53	-13.3589	178
20	46.2152	1	1	2136	46	53	-7.2155	52
21	45.1799	1	1	2041	45	53	-8.2508	68
22	42.2771	0	0	1787	0	56	-13.7624	189
23	52.4645	1	1	2753	52	53	-0.9662	1
24	48.0469	0	0	2309	0	56	-7.9926	64
25	44.4731	1	1	1978	44	53	-8.9576	80
26	40.7649	0	0	1662	0	56	-15.2746	233
27	50.6375	0	0	2564	0	56	-5.4020	29
28	45.4043	1	1	2062	45	53	-8.0264	64
29	52.9125	1	1	2800	53	53	-0.5182	0
30	60.0693	1	1	3608	60	53	6.6386	44
31	49.3684	0	0	2437	0	56	-6.6711	45
32	54.527	1	1	2973	55	53	1.0963	1
33	45.8271	1	1	2100	46	53	-7.6036	58
34	57.5896	0	0	3317	0	56	1.5501	2
35	41.7001	1	1	1739	42	53	-11.7306	138
36	38.4826	1	1	1481	38	53	-14.9481	223
37	46.8481	1	1	2195	47	53	-6.5826	43
38	58.7057	0	0	3446	0	56	2.6662	7
39	65.4643	1	1	4286	65	53	12.0336	145
40	45.1564	0	0	2039	0	56	-10.8831	118
41	65.2734	0	0	4261	0	56	9.2339	85
42	69.4617	0	0	4825	0	56	13.4222	180
43	54.1896	1	1	2937	54	53	0.7589	1
44	54.3447	0	0	2953	0	56	-1.6948	3
45	37.6578	1	1	1418	38	53	-15.7729	249
46	39.3685	0	0	1550	0	56	-16.6710	278
47	66.917	1	1	4478	67	53	13.4863	182
48	73.1906	1	1	5357	73	53	19.7599	390
49	67.4168	0	0	4545	0	56	11.3773	129
50	38.3865	1	1	1474	38	53	-15.0442	226
51	75.0269	1	1	5629	75	53	21.5962	466
52	91.1291	1	1	8305	91	53	37.6984	1421
53	44.4168	1	1	1973	44	53	-9.0139	81
54	83.2958	0	0	6938	0	56	27.2563	743
55	45.1767	0	0	2041	0	56	-10.8628	118
56	46.5962	1	1	2171	47	53	-6.8345	47
57	70.87	0	0	5023	0	56	14.8305	220
58	56.6501	1	1	3209	57	53	3.2194	10
59	57.2335	0	0	3276	0	56	1.1940	1
60	61.7817	1	1	3817	62	53	8.3510	70
SUM	3271.0622	35	35	187097.6792	1870.0737			8667.624

The regression equation is,