Q1[linear regression]. Please follow the video lectures and practice the ideas with the following dataset:

GPA_Dataset.xlsxDownload GPA_Dataset.xlsx (below is the data set)

GPA	High School GPA	SAT	# of Recommendation letter
2.04	2.01	1070	5
2.56	3.4	1254	6
3.75	3.68	1466	6
1.1	1.54	706	4
3	3.32	1160	5
0.05	0.33	756	3
1.38	0.36	1058	2
1.5	1.97	1008	7
1.38	2.03	1104	4
4.01	2.05	1200	7
1.5	2.13	896	7
1.29	1.34	848	3
1.9	1.51	958	5
3.11	3.12	1246	6
1.92	2.14	1106	4
0.81	2.6	790	5
1.01	1.9	954	4
3.66	3.06	1500	6
2	1.6	1046	5
2.05	1.96	1054	4
2.6	1.96	1198	6
2.55	1.56	940	3
0.38	1.6	456	6
2.48	1.92	1150	7
2.74	3.09	636	6
1.77	0.78	744	5
1.61	2.12	644	5
0.99	1.85	842	3
1.62	1.78	852	5
2.03	1.03	1170	3
3.5	3.44	1034	10
3.18	2.42	1202	5
2.39	1.74	1018	5
1.48	1.89	1180	5
1.54	1.43	952	3
1.57	1.64	1038	4
2.46	2.69	1090	6
2.42	1.79	694	5
2.11	2.72	1096	6
2.04	2.15	1114	5
1.68	2.22	1256	6
1.64	1.55	1208	5
2.41	2.34	820	6
2.1	2.92	1222	4
1.4	2.1	1120	5
2.03	1.64	886	4
1.99	2.83	1126	7
2.24	1.76	1158	4
0.45	1.81	676	6
2.31	2.68	1214	7
2.41	2.55	1136	6
2.56	2.7	1264	6
2.5	1.66	1116	3
2.92	2.23	1292	4
2.35	2.01	604	5
2.82	1.24	854	6
1.8	1.95	814	6
1.29	1.73	778	3
1.68	1.08	800	2
3.44	3.46	1424	7
1.9	3.01	950	6
2.06	0.54	1056	3
3.3	3.2	956	8
1.8	1.5	1352	5
2	1.71	852	5
1.68	1.99	1168	5
1.94	2.76	970	6
0.97	1.56	776	4
1.12	1.78	854	6
1.31	1.32	1232	5
1.68	0.87	1140	6
3.09	1.75	1084	4
1.87	1.41	954	2
2	2.77	1000	4
2.39	1.78	1084	4
1.5	1.34	1058	4
1.82	1.52	816	5
1.8	2.97	1146	7
2.01	1.75	1000	6
1.88	1.64	856	4
1.64	1.8	798	4
2.42	3.37	1324	6
0.22	1.15	704	6
2.31	1.72	1222	5
0.95	2.27	948	6
1.99	2.85	1182	8
1.86	2.21	1000	6
1.79	1.94	910	6
3.02	4.25	1374	9
1.85	1.83	1014	6
1.98	2.75	1420	7
2.15	1.71	400	6
1.46	2.2	998	7
2.29	2.13	776	6
2.39	2.38	1134	7
1.8	1.64	772	4
2.64	1.87	1304	6
2.08	2.53	1212	4
0.7	1.78	818	6
0.89	1.2	864	2

1. Please apply a multiple linear regression model, use the high school GPA, SAT and # of recommendation to predict the students' GPA.

2. Explain the model. (Eg: What is the model formula? the coefficient? R square? P-value? which variable/variables is/are statistics significant, which one/ones is/are not? What is the meaning of the coefficient? )