A researcher wanted to know what factors determine a state public employee’s annual salary; especially, whether there was a gender pay gap in the state government. The data file “State Employee Salaries.xslx” includes data on state employees’ annual salaries, gender (coded 0 if male; coded 1 if female), years of service, and years of educationUse the regression coefficient of Gender (b1) to explain the gender pay gap in the state government. The regression coefficient of Gender (b1) are different in the estimated simple regression equation and estimated multiple regression equation. Explain why. SalaryGenderYears Of ServiceYears Of Education52,100051355,0150201355,5200231243,430071243,813051251,903061254,5800241454,9130181252,1000291250,6930141247,8780101246,555061447,878071647,878091254,9130161350,123041350,6930201248,9330291258,2700121250,538051348,9330121245,078051247,878051453,5080241242,250011653,508181542,250131547,808111350,1801111344,163191041,718131047,878181237,635111649,285171250,6931141243,655031243,910191343,9101111268,3030191485,128031253,488031266,4300221259,7080101271,5550151253,5650141673,4900151269,0450131663,0250131256,7150121366,7280161259,3480291268,0680141469,5400201247,268021270,2530191264,3900131267,2350111374,1550291364,1800231265,5680141250,4150121365,113071261,463011259,8650221254,158091264,3650161272,2050221264,4000141276,9480291261,4400211253,488021371,0300151276,4900181256,215021359,7080101274,1550321270,1950101557,918031277,8150161260,498041280,1250201274,9750261272,3380151263,9100191356,818071262,450041368,3030231277,8150261256,7150131256,618031261,463051655,1400151268,6100191263,218091283,0400351263,6350171259,708071252,335051253,265071269,058051367,4600321256,6500161661,4400281258,2900241272,2050181364,825091359,5630141669,513071278,0030201261,463091252,335071459,8650191358,2900191264,400081259,5980121253,565071268,3030111275,4150161262,3900101251,990071356,7150121664,9730241372,2050311261,4630131282,1400231261,4630151451,125081264,400061664,400061460,498021468,3030151256,118091253,9980111266,3530131470,2530221361,4400181265,423061461,4630171270,2530201258,548041664,7280221253,5650101269,0350261458,2900171251,990081253,565091451,125051263,2180161467,003081260,1530141271,328081255,1400141072,2050261355,1400151251,990091257,953071259,853061357,953051364,9730281250,415031282,1400181356,7150151256,7150141269,835091255,348071261,4400231457,953081382,3080201268,4830221262,3150141247,630041271,0300141273,8701211462,6531121251,990191362,8581131256,1181101256,198171388,3181231351,990161271,933171265,113171683,288191273,6001241258,290111267,085131665,708131674,1551181269,0581111271,3281181248,933191261,4401341060,368191258,385191265,213161270,3831211558,548151670,820151257,953191282,1401101262,7801261372,205151375,653161664,9731221482,1401341247,268111372,2051271548,843171253,565191355,1401131377,580141261,0651191251,990131456,198151579,2551101261,4401131288,3251191851,168191255,1401101351,9901101471,3281111471,3281101366,3531121451,990151277,155191684,303131645,850171352,688131248,843131253,565181284,3031201656,818151264,180061358,2900161261,4400381050,415061361,4630181551,9900101347,268121558,548131268,148071464,8400111475,7180221257,953051456,198081256,543041257,035051269,5130161282,140081647,268011655,015111455,1401191258,548171274,1551271682,140131463,2181151271,018151279,9781281478,155031686,655021897,523091486,6550516112,6600316112,005081690,7830616107,3200121889,5450101679,383061698,21301613121,1650191283,55302114103,99002514112,4300191288,13502212119,68301216126,9350201885,0680512103,99001716123,36302612128,5480131486,88802212105,008051677,2380912115,50501116133,00302216112,0050418115,50501112136,5030281290,535021682,06302312119,00501312115,505091672,4100118112,65802214115,505061693,4550151278,7800101674,005031696,37803414119,6830918119,6830221296,3780181292,43301712115,5050221698,39302013103,9900181374,00502012125,55801616121,16503912103,99001718122,07001914108,505041898,21302612114,24301216103,9900171595,32302716118,0430316104,99801712114,2430201287,6130516110,78002914121,1650101876,3930312114,2430211283,363031690,0580251287,6130312108,505071676,418061299,8780516109,2800271385,93801016129,5030161888,32502914107,32001512117,70301213103,9900281386,6550211671,6200216115,16302114101,91501514114,24301418112,083051499,86302313108,0600241695,3230151295,32301616100,8730414106,478051672,03501518101,1000281686,655031685,9380201483,5530211483,55302312128,5480171374,103071298,21302912119,0050615108,9430416118,0230351485,9380151683,7550818135,01001514119,85801416122,4800211283,5530241285,93801912124,6250101895,3230111677,2380812117,70302112120,890091692,43302012102,5300281489,3880201298,07002713102,19801016122,86802814105,4530181488,32502612112,6580161895,5530716138,12512316128,08813816124,62511618115,2581191694,5681514117,5331916122,50511816112,6581311876,3931101897,53311915103,8581416117,703171696,8351416131,54811816120,760161590,3081216129,50312816

1. Use the data to predict the employee's annual salary based on the variable Gender. To perform the…

Answered: Use the regression coefficient of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Question

A researcher wanted to know what factors determine a state public employee’s annual salary; especially, whether there was a gender pay gap in the state government. The data file “State Employee Salaries.xslx” includes data on state employees’ annual salaries, gender (coded 0 if male; coded 1 if female), years of service, and years of education

Use the regression coefficient of Gender (b₁) to explain the gender pay gap in the state government.
The regression coefficient of Gender (b₁) are different in the estimated simple regression equation and estimated multiple regression equation. Explain why.

Salary	Gender	Years Of Service	Years Of Education
52,100	0	5	13
55,015	0	20	13
55,520	0	23	12
43,430	0	7	12
43,813	0	5	12
51,903	0	6	12
54,580	0	24	14
54,913	0	18	12
52,100	0	29	12
50,693	0	14	12
47,878	0	10	12
46,555	0	6	14
47,878	0	7	16
47,878	0	9	12
54,913	0	16	13
50,123	0	4	13
50,693	0	20	12
48,933	0	29	12
58,270	0	12	12
50,538	0	5	13
48,933	0	12	12
45,078	0	5	12
47,878	0	5	14
53,508	0	24	12
42,250	0	1	16
53,508	1	8	15
42,250	1	3	15
47,808	1	1	13
50,180	1	11	13
44,163	1	9	10
41,718	1	3	10
47,878	1	8	12
37,635	1	1	16
49,285	1	7	12
50,693	1	14	12
43,655	0	3	12
43,910	1	9	13
43,910	1	11	12
68,303	0	19	14
85,128	0	3	12
53,488	0	3	12
66,430	0	22	12
59,708	0	10	12
71,555	0	15	12
53,565	0	14	16
73,490	0	15	12
69,045	0	13	16
63,025	0	13	12
56,715	0	12	13
66,728	0	16	12
59,348	0	29	12
68,068	0	14	14
69,540	0	20	12
47,268	0	2	12
70,253	0	19	12
64,390	0	13	12
67,235	0	11	13
74,155	0	29	13
64,180	0	23	12
65,568	0	14	12
50,415	0	12	13
65,113	0	7	12
61,463	0	1	12
59,865	0	22	12
54,158	0	9	12
64,365	0	16	12
72,205	0	22	12
64,400	0	14	12
76,948	0	29	12
61,440	0	21	12
53,488	0	2	13
71,030	0	15	12
76,490	0	18	12
56,215	0	2	13
59,708	0	10	12
74,155	0	32	12
70,195	0	10	15
57,918	0	3	12
77,815	0	16	12
60,498	0	4	12
80,125	0	20	12
74,975	0	26	12
72,338	0	15	12
63,910	0	19	13
56,818	0	7	12
62,450	0	4	13
68,303	0	23	12
77,815	0	26	12
56,715	0	13	12
56,618	0	3	12
61,463	0	5	16
55,140	0	15	12
68,610	0	19	12
63,218	0	9	12
83,040	0	35	12
63,635	0	17	12
59,708	0	7	12
52,335	0	5	12
53,265	0	7	12
69,058	0	5	13
67,460	0	32	12
56,650	0	16	16
61,440	0	28	12
58,290	0	24	12
72,205	0	18	13
64,825	0	9	13
59,563	0	14	16
69,513	0	7	12
78,003	0	20	12
61,463	0	9	12
52,335	0	7	14
59,865	0	19	13
58,290	0	19	12
64,400	0	8	12
59,598	0	12	12
53,565	0	7	12
68,303	0	11	12
75,415	0	16	12
62,390	0	10	12
51,990	0	7	13
56,715	0	12	16
64,973	0	24	13
72,205	0	31	12
61,463	0	13	12
82,140	0	23	12
61,463	0	15	14
51,125	0	8	12
64,400	0	6	16
64,400	0	6	14
60,498	0	2	14
68,303	0	15	12
56,118	0	9	12
53,998	0	11	12
66,353	0	13	14
70,253	0	22	13
61,440	0	18	12
65,423	0	6	14
61,463	0	17	12
70,253	0	20	12
58,548	0	4	16
64,728	0	22	12
53,565	0	10	12
69,035	0	26	14
58,290	0	17	12
51,990	0	8	12
53,565	0	9	14
51,125	0	5	12
63,218	0	16	14
67,003	0	8	12
60,153	0	14	12
71,328	0	8	12
55,140	0	14	10
72,205	0	26	13
55,140	0	15	12
51,990	0	9	12
57,953	0	7	12
59,853	0	6	13
57,953	0	5	13
64,973	0	28	12
50,415	0	3	12
82,140	0	18	13
56,715	0	15	12
56,715	0	14	12
69,835	0	9	12
55,348	0	7	12
61,440	0	23	14
57,953	0	8	13
82,308	0	20	12
68,483	0	22	12
62,315	0	14	12
47,630	0	4	12
71,030	0	14	12
73,870	1	21	14
62,653	1	12	12
51,990	1	9	13
62,858	1	13	12
56,118	1	10	12
56,198	1	7	13
88,318	1	23	13
51,990	1	6	12
71,933	1	7	12
65,113	1	7	16
83,288	1	9	12
73,600	1	24	12
58,290	1	1	12
67,085	1	3	16
65,708	1	3	16
74,155	1	18	12
69,058	1	11	12
71,328	1	18	12
48,933	1	9	12
61,440	1	34	10
60,368	1	9	12
58,385	1	9	12
65,213	1	6	12
70,383	1	21	15
58,548	1	5	16
70,820	1	5	12
57,953	1	9	12
82,140	1	10	12
62,780	1	26	13
72,205	1	5	13
75,653	1	6	16
64,973	1	22	14
82,140	1	34	12
47,268	1	1	13
72,205	1	27	15
48,843	1	7	12
53,565	1	9	13
55,140	1	13	13
77,580	1	4	12
61,065	1	19	12
51,990	1	3	14
56,198	1	5	15
79,255	1	10	12
61,440	1	13	12
88,325	1	19	18
51,168	1	9	12
55,140	1	10	13
51,990	1	10	14
71,328	1	11	14
71,328	1	10	13
66,353	1	12	14
51,990	1	5	12
77,155	1	9	16
84,303	1	3	16
45,850	1	7	13
52,688	1	3	12
48,843	1	3	12
53,565	1	8	12
84,303	1	20	16
56,818	1	5	12
64,180	0	6	13
58,290	0	16	12
61,440	0	38	10
50,415	0	6	13
61,463	0	18	15
51,990	0	10	13
47,268	1	2	15
58,548	1	3	12
68,148	0	7	14
64,840	0	11	14
75,718	0	22	12
57,953	0	5	14
56,198	0	8	12
56,543	0	4	12
57,035	0	5	12
69,513	0	16	12
82,140	0	8	16
47,268	0	1	16
55,015	1	1	14
55,140	1	19	12
58,548	1	7	12
74,155	1	27	16
82,140	1	3	14
63,218	1	15	12
71,018	1	5	12
79,978	1	28	14
78,155	0	3	16
86,655	0	2	18
97,523	0	9	14
86,655	0	5	16
112,660	0	3	16
112,005	0	8	16
90,783	0	6	16
107,320	0	12	18
89,545	0	10	16
79,383	0	6	16
98,213	0	16	13
121,165	0	19	12
83,553	0	21	14
103,990	0	25	14
112,430	0	19	12
88,135	0	22	12
119,683	0	12	16
126,935	0	20	18
85,068	0	5	12
103,990	0	17	16
123,363	0	26	12
128,548	0	13	14
86,888	0	22	12
105,008	0	5	16
77,238	0	9	12
115,505	0	11	16
133,003	0	22	16
112,005	0	4	18
115,505	0	11	12
136,503	0	28	12
90,535	0	2	16
82,063	0	23	12
119,005	0	13	12
115,505	0	9	16
72,410	0	1	18
112,658	0	22	14
115,505	0	6	16
93,455	0	15	12
78,780	0	10	16
74,005	0	3	16
96,378	0	34	14
119,683	0	9	18
119,683	0	22	12
96,378	0	18	12
92,433	0	17	12
115,505	0	22	16
98,393	0	20	13
103,990	0	18	13
74,005	0	20	12
125,558	0	16	16
121,165	0	39	12
103,990	0	17	18
122,070	0	19	14
108,505	0	4	18
98,213	0	26	12
114,243	0	12	16
103,990	0	17	15
95,323	0	27	16
118,043	0	3	16
104,998	0	17	12
114,243	0	20	12
87,613	0	5	16
110,780	0	29	14
121,165	0	10	18
76,393	0	3	12
114,243	0	21	12
83,363	0	3	16
90,058	0	25	12
87,613	0	3	12
108,505	0	7	16
76,418	0	6	12
99,878	0	5	16
109,280	0	27	13
85,938	0	10	16
129,503	0	16	18
88,325	0	29	14
107,320	0	15	12
117,703	0	12	13
103,990	0	28	13
86,655	0	21	16
71,620	0	2	16
115,163	0	21	14
101,915	0	15	14
114,243	0	14	18
112,083	0	5	14
99,863	0	23	13
108,060	0	24	16
95,323	0	15	12
95,323	0	16	16
100,873	0	4	14
106,478	0	5	16
72,035	0	15	18
101,100	0	28	16
86,655	0	3	16
85,938	0	20	14
83,553	0	21	14
83,553	0	23	12
128,548	0	17	13
74,103	0	7	12
98,213	0	29	12
119,005	0	6	15
108,943	0	4	16
118,023	0	35	14
85,938	0	15	16
83,755	0	8	18
135,010	0	15	14
119,858	0	14	16
122,480	0	21	12
83,553	0	24	12
85,938	0	19	12
124,625	0	10	18
95,323	0	11	16
77,238	0	8	12
117,703	0	21	12
120,890	0	9	16
92,433	0	20	12
102,530	0	28	14
89,388	0	20	12
98,070	0	27	13
102,198	0	10	16
122,868	0	28	14
105,453	0	18	14
88,325	0	26	12
112,658	0	16	18
95,553	0	7	16
138,125	1	23	16
128,088	1	38	16
124,625	1	16	18
115,258	1	19	16
94,568	1	5	14
117,533	1	9	16
122,505	1	18	16
112,658	1	31	18
76,393	1	10	18
97,533	1	19	15
103,858	1	4	16
117,703	1	7	16
96,835	1	4	16
131,548	1	18	16
120,760	1	6	15
90,308	1	2	16
129,503	1	28	16