Labor economists working for the federal government routinely survey workers across the U.S. A random sample of 935 working adults is available in the file "Wages." The file consists of weekly take-home pay (in dollars), length of time with current employer (in years), and the worker's score (in points) on a test of soft skills that emphasizes communication and cooperative traits.

(a) Estimate a simple linear regression model that uses the test score as the independent variable and pay as the dependent variable. Write down the estimated regression equation. Label this Model 1.

(b) Using Model 1, identify the slope coefficient associated with the test score and interpret it within the context of this problem.

(c) Using Model 1, construct a 95% confidence interval for the slope coefficient associated with the test score and interpret it within the context of this problem.

(d) Estimate a simple linear regression model that uses time with employer as the independent variable and pay as the dependent variable. Write down the estimated regression equation. Call this Model 2.

(e) Using Model 2, construct a point estimate for the predicted pay of a worker that has 8 years with his/her current employer.

(f) Compare your regression output for Model 1 and Model 2. Which model offers a better fit to the sample data? Explain your reasoning.

pay	score	time
769	35	2
808	41	16
825	46	9
650	32	7
562	27	5
1400	43	2
600	24	0
1081	50	14
1154	37	1
1000	44	16
930	44	13
921	45	11
900	40	3
1318	24	2
1792	47	9
958	37	2
1360	39	9
850	36	10
830	29	7
471	34	7
1275	37	1
1615	49	4
873	36	3
2137	50	8
1053	35	7
1602	32	9
1188	40	5
800	39	1
1417	41	4
635	35	13
1000	40	2
1424	41	4
2668	41	2
666	40	12
1779	42	9
782	24	10
1572	39	5
1274	35	12
714	37	2
1081	46	7
692	48	11
1318	47	9
1239	44	4
1027	40	15
1748	50	12
981	41	15
770	34	11
1154	37	5
1155	36	5
808	47	12
1100	45	14
1154	46	10
1749	32	9
1000	36	8
462	35	1
769	49	12
875	40	3
1375	34	7
1452	45	7
800	33	12
1748	48	7
1151	34	12
840	34	13
978	47	2
963	43	15
619	20	10
442	32	0
600	45	1
1366	38	15
1643	48	2
1455	44	13
2310	55	7
1682	40	11
1235	45	2
855	45	4
1072	37	8
1040	49	15
1000	45	15
675	27	2
1100	32	1
996	41	14
732	28	5
1200	48	3
1694	30	8
686	38	3
754	37	5
857	39	15
832	30	2
579	36	1
672	38	3
2500	51	9
1076	24	8
750	18	3
1186	41	9
833	37	7
650	37	11
1250	37	16
1122	44	9
865	35	11
808	37	7
1299	44	12
903	39	12
900	28	15
625	32	0
1586	47	1
962	41	16
1539	36	8
1110	42	6
1282	41	6
770	39	2
1000	42	0
895	39	16
1205	32	0
750	27	10
654	51	16
601	30	3
600	32	11
433	28	10
1188	28	7
635	29	15
1225	44	14
1151	38	19
865	34	11
1031	24	5
1049	39	11
1000	41	1
1105	32	11
1924	40	7
1346	44	16
809	32	10
1495	34	3
1346	46	1
1200	35	4
500	35	0
1325	44	5
900	21	5
800	39	3
800	32	7
1034	39	16
980	41	12
884	42	12
480	28	5
923	54	14
513	30	5
1105	36	16
1193	38	10
2771	45	7
779	29	6
950	36	6
1394	41	8
1495	50	9
650	18	3
670	27	5
1126	30	8
450	19	1
1028	28	12
2404	38	0
1899	49	14
757	35	9
1250	36	1
1162	40	11
1025	29	13
1100	51	12
714	34	5
1318	47	17
1411	40	3
2162	51	4
1273	44	16
1140	43	15
578	28	4
942	36	10
1058	50	8
750	32	9
1000	30	6
951	40	7
635	24	2
1250	28	1
675	34	15
400	33	6
577	17	8
590	27	7
923	38	10
1250	26	2
1100	38	8
1130	38	2
652	37	4
618	34	2
962	43	14
529	31	11
817	37	14
962	39	9
840	39	15
866	30	4
2404	42	1
1126	26	2
1160	32	8
723	34	5
1778	43	13
1903	44	5
1010	42	14
971	42	11
525	40	2
525	31	13
670	33	3
500	47	4
1058	45	15
550	44	15
500	43	1
727	40	5
865	26	8
1081	34	2
1304	36	9
575	32	1
623	34	1
515	30	10
1273	42	4
990	42	9
600	32	6
1160	35	2
500	22	9
795	27	18
500	34	3
740	31	13
1250	45	7
1014	42	9
1250	32	3
913	26	13
1346	33	8
445	31	0
265	43	2
1250	31	1
1607	41	9
1452	33	15
1391	38	8
821	39	2
794	36	7
500	46	1
520	30	3
1730	41	12
1924	47	10
1155	46	2
2162	38	4
923	44	7
1115	40	13
449	20	2
1500	29	11
826	40	3
937	36	8
978	36	15
1031	43	12
1272	39	1
1136	36	12
800	36	12
1339	42	9
1063	38	12
935	27	6
808	40	13
375	29	2
537	32	8
1082	40	4
930	44	1
1155	49	4
548	22	0
622	48	1
841	38	1
769	45	15
587	40	5
1924	40	18
1058	28	3
417	39	1
1202	28	6
1154	35	2
1070	41	9
1202	30	11
711	38	3
1202	21	5
850	26	3
1000	46	11
490	33	8
1000	47	4
865	38	4
1375	24	3
1586	48	12
1602	47	14
3078	50	13
898	41	9
906	40	2
952	34	10
571	33	1
445	23	13
289	35	0
1444	50	15
962	45	21
1075	31	10
909	39	5
1250	36	19
620	22	5
1016	18	15
800	29	14
1050	37	18
1079	33	9
654	49	13
781	33	10
1038	36	2
1924	48	14
1202	40	17
666	34	2
905	41	14
890	46	8
817	27	7
812	42	2
577	43	2
756	29	2
1011	43	7
1155	39	1
1025	25	7
1350	37	12
1001	48	22
796	31	15
1230	33	12
754	31	1
714	32	1
1000	29	3
2067	41	13
912	32	5
600	39	5
951	33	1
711	38	5
1151	41	9
1000	31	5
841	40	10
400	43	3
1175	38	14
1202	40	2
1442	38	17
538	45	1
781	24	10
750	23	9
841	37	1
700	29	1
1346	51	4
800	31	12
1250	27	10
1105	29	8
475	33	1
762	37	4
962	33	19
721	38	9
800	28	13
658	34	9
1270	42	16
1313	37	7
824	37	15
1442	33	7
1400	38	3
1038	42	5
668	29	12
1100	41	10
1000	38	7
523	37	2
1111	33	13
962	25	4
729	40	13
690	35	5
1010	37	7
600	22	2
596	36	17
850	37	1
670	27	2
793	43	18
1442	42	7
670	43	8
876	35	8
841	45	2
975	39	0
1223	34	3
910	27	5
533	31	2
750	36	11
1206	37	4
745	40	1
900	38	1
1170	45	14
540	33	3
550	35	1
615	31	4
909	39	2
769	34	12
984	39	18
833	47	12
879	43	10
1027	41	7
1000	41	1
465	33	1
1100	37	12
641	44	0
1035	42	14
1212	33	3
950	40	6
938	41	20
1250	37	8
586	37	10
693	29	6
562	25	12
375	24	5
673	29	11
654	38	13
692	34	7
1111	32	1
1368	31	1
1282	39	13
1250	40	4
1346	42	7
1424	47	12
854	38	5
888	36	5
1161	40	10
583	29	0
1260	37	3
947	41	13
1850	23	15
1575	28	2
758	42	8
1442	42	15
489	47	4
1126	33	0
1000	18	5
500	20	11
1200	13	9
565	30	3
1920	32	2
684	25	7
774	33	4
233	32	4
975	33	10
1366	35	1
2137	48	3
700	38	1
1200	29	11
1161	43	18
729	31	15
750	45	2
1026	46	16
1111	43	3
625	31	8
1200	28	5
1541	39	1
1154	42	9
310	37	0
610	21	4
1749	28	17
1000	34	1
350	48	1
765	38	18
790	34	2
818	41	17
477	32	1
938	39	1
2099	38	4
350	24	3
940	25	0
1202	23	8
450	29	4
1058	44	13
1000	40	15
318	35	5
556	26	9
958	42	9
995	23	13
1600	44	5
606	39	5
511	25	1
1411	40	12
1346	38	11
1522	37	16
1075	28	10
1200	37	11
1377	48	1
874	37	2
625	26	9
1250	40	2
1082	44	12
693	36	3
727	29	11
615	49	15
913	33	7
884	45	10
698	33	4
800	34	18
812	44	3
1000	32	14
549	23	3
1300	38	15
923	30	8
1539	42	15
721	22	9
815	25	14
600	36	2
1100	41	7
1058	48	19
962	46	1
433	40	9
940	20	2
1417	36	10
1000	32	9
500	26	5
800	35	5
766	31	18
750	38	10
550	36	2
795	35	4
723	44	10
1039	49	8
200	38	15
400	36	1
575	31	1
850	35	5
508	35	1
1162	39	4
1199	28	5
1270	34	4
350	36	3
963	32	9
1463	47	11
802	26	12
642	18	7
751	37	2
488	40	3
1400	34	5
940	41	7
866	48	16
675	42	4
375	24	3
325	44	1
346	37	17
1442	39	1
560	37	2
550	42	11
950	26	10
684	45	2
1322	43	1
1634	48	3
417	30	0
472	24	0
666	28	1
1679	45	3
1039	43	9
1250	30	11
760	34	15
1154	32	12
1602	45	1
1442	40	13
865	39	3
705	44	12
1000	36	1
852	36	9
770	25	14
1000	20	9
1329	56	5
1682	48	4
577	47	0
685	27	7
577	37	8
1040	38	9
1250	42	11
600	40	7
480	29	3
1000	26	0
988	39	15
478	35	10
440	23	2
485	43	1
705	32	0
1550	47	1
960	23	9
1000	42	14
625	40	5
1346	39	14
961	17	13
479	45	1
1201	38	16
1346	34	2
1122	45	8
543	31	7
450	26	4
507	36	4
547	38	5
586	41	16
462	24	4
705	32	8
1566	44	1
1634	39	18
1282	48	1
556	44	2
1200	42	8
855	21	6
1053	33	7
1000	39	4
900	27	5
1602	40	10
508	44	2
1500	20	6
1682	41	9
750	45	1
843	32	7
409	26	18
1004	36	15
650	36	10
808	26	9
2137	35	2
761	44	21
769	37	3
345	28	8
495	30	10
987	41	3
2500	41	1
1098	22	1
1212	36	16
577	33	1
390	26	3
1500	43	12
583	24	1
460	22	1
945	41	13
1442	39	3
1333	50	8
1500	41	5
1333	30	1
700	29	4
973	33	5
2162	48	8
797	38	7
400	34	1
1015	31	11
1744	41	9
630	30	2
445	40	4
660	34	9
779	30	7
377	32	1
560	34	11
1122	54	13
453	34	2
1386	38	9
1539	38	9
1154	38	12
962	45	2
722	36	1
480	37	3
808	44	9
1442	36	8
1091	31	4
350	41	0
500	39	11
1026	27	13
577	43	7
1333	38	1
915	36	9
1105	32	10
910	26	5
1000	40	8
1160	18	1
1001	22	3
713	25	12
929	28	5
400	35	9
1241	51	10
1065	40	10
403	37	3
940	30	12
812	20	13
700	27	0
575	20	6
450	23	5
621	24	10
441	24	11
625	25	9
726	32	5
500	18	13
1000	41	2
393	37	16
600	44	3
962	44	12
962	42	4
865	30	7
1154	46	3
1386	43	11
732	36	7
865	44	9
700	26	13
975	12	10
1300	40	3
900	37	3
829	33	15
1000	34	13
827	29	8
500	25	2
1155	25	1
950	30	3
700	35	4
1710	39	6
533	21	1
2004	48	0
890	20	8
3078	23	4
1539	41	13
508	38	1
1354	49	9
1143	40	8
962	34	8
1250	32	20
990	23	3
905	31	4
926	22	0
1559	32	10
1312	39	4
923	36	16
879	41	9
800	37	1
1049	45	10
550	20	1
1190	38	2
583	35	6
1200	27	2
797	36	5
1371	50	13
360	44	1
1270	40	12
1832	38	1
909	34	5
1746	41	10
520	23	1
808	32	7
2137	45	2
692	49	3
931	40	1
812	46	3
866	44	14
1442	47	9
500	31	0
1384	48	2
528	40	9
881	41	14
1026	33	11
1212	26	12
1620	42	5
1843	38	2
1602	36	2
1000	35	1
737	37	4
1699	19	1
1699	40	9
1025	30	5
1107	38	5
625	24	1
720	39	7
855	44	10
1250	23	2
1130	40	13
900	35	1
1924	49	7
962	46	2
1874	37	3
1573	28	3
940	46	7
900	39	9
882	34	13
1710	40	12
1260	39	15
751	42	7
1097	27	12
1001	36	11
1154	42	12
1000	31	16
1250	36	3
857	41	3
1211	33	3
937	23	7
904	29	1
872	30	4
1200	26	0
1261	41	9
950	38	2
115	46	3
673	34	4
1084	38	10
1058	40	14
800	38	12
369	36	1
1924	42	13
855	36	15
864	38	6
1092	34	13
1025	30	4
850	32	2
673	21	10
800	42	12
1049	39	3
884	40	11
800	38	2
1200	32	9
664	30	10
1111	47	18
850	38	8
1000	42	12
875	32	4
1202	32	2
666	32	2
923	39	11
788	20	10
950	31	5
1442	42	16
866	26	12
625	34	5
680	35	9
693	38	19
875	22	2
2308	42	2
1196	45	4
700	36	8
721	32	8
1500	38	2
1050	31	9
801	30	10
640	39	3
1198	39	9
390	38	2
889	37	11
1076	42	20
1127	45	12
750	36	1
855	41	14
525	22	1
1104	39	4
553	22	10
800	27	1
1384	42	7
425	34	0
510	34	4
370	31	2
596	26	14
402	28	4
418	26	2
1133	44	10
681	24	15
950	29	5
600	15	7
661	25	6
925	27	9
550	34	13
606	19	11
425	17	1
340	41	1
692	21	9
575	37	9
571	20	10
817	38	9
987	23	5
616	41	18
1026	34	1
808	34	3
808	34	0
788	42	5
850	34	2
900	40	19
1418	44	20
260	35	0
662	27	2
562	46	1
562	30	5
357	37	2
1009	37	12
1442	40	17
651	30	2
750	28	5
754	23	14
700	23	9
503	14	2
937	37	15
624	40	10
750	27	10
900	36	8
540	25	10
642	26	3
400	38	10
900	34	14
513	40	10
894	35	10
1282	24	5
485	24	9
325	39	5
769	29	5
618	39	8
1040	36	17
751	32	4
380	28	11
300	45	3
753	34	7
1065	39	11
1070	42	1
1573	42	8
650	27	9
700	40	7
494	30	4
890	40	8
520	28	12
891	36	16
570	43	12
1444	33	1
481	26	2
500	40	12
1473	48	15
803	35	1
962	34	2
1000	37	5
600	36	4
450	31	2
629	32	1
492	38	2
1562	28	2
357	34	3
960	25	13
566	46	2
481	27	2
1442	45	10
645	39	3
788	23	6
644	38	5
477	33	3
664	30	9
520	28	1
1202	32	3
538	22	10
873	25	12
1000	32	18