CAS MA 416 Lecture Notes - Lecture 2: Generalized Inverse, The Xx

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violetfly908

9 Nov 2017

School

Boston University

Department

Mathematics & Statistics

Course

CAS MA 416

Professor

Joe Massaro

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Document Summary

Input design store casessold @@; class design; var casessold; options nodate nonumber nocenter; data one; cards; 4 1 27 4 2 33 4 3 22 4 4 26 4 5 28 run; proc means data=one; run; proc glm data=one; run; proc glm data=one; run; Proc means output: class design; model casessold=design/solution; class design; model casessold=design/noint solution; contrast "design effect" design 1 0 0 -1, design 0 1 0 -1, design 0 0 1 -1; Df contrast ss mean square f value pr > f. Squares mean square f value pr > f. Source df type i ss mean square f value pr > f design. Source df type iii ss mean square f value pr > f design. Note: the x"x matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter "b" are not uniquely estimable.

Related Questions

Please explain answers

pleasee helpp

Let the mortgage rate be the dependent variable and use the unemployment rate, unemployment duration, real GDP, housing starts, and the CPI as explanatory variables. Conduct a multiple regression estimation and discuss your results. Is this a good model? What do the coefficients on the explanatory variables mean and which explanatory variables are important in explaining mortgage rates? Use any level of significance you believe is appropriate in your discussion. What is the multiple regression equation and the goodness of fit measure?
From your work in question 1, eliminate all the explanatory variables that are not statistically important. What is the equation of your new regression model? Discuss the coefficients and the goodness of fit for the new model.




Year	Quarter	MORTRATE	FFUNDS	EMPLOY	URATE	UDUR	RGDP	HOUSING	CPI	TREND
1972	1	7.413	4.563	71179.000	5.900	11.233	5097.179	2020.333	40.300	1
1972	2	7.658	5.473	71434.000	6.033	11.633	5139.128	2094.000	40.700	2
1972	3	7.553	4.750	71866.000	5.933	12.033	5151.245	2201.667	41.000	3
1972	4	7.349	3.540	72677.667	5.767	12.267	5245.974	2406.000	41.333	4
1973	1	7.347	4.300	73463.000	5.700	12.367	5365.045	2241.333	41.600	5
1973	2	7.406	4.740	74038.000	5.567	11.900	5415.712	2371.667	41.933	6
1973	3	7.431	5.143	74971.667	5.367	11.500	5506.396	2424.000	42.367	7
1973	4	7.446	6.537	75971.667	4.933	10.700	5642.669	2378.333	43.033	8
1974	1	7.650	7.817	76663.333	4.933	9.900	5704.098	2139.000	43.933	9
1974	2	8.457	10.560	77119.000	4.800	9.600	5674.100	2016.000	44.800	10
1974	3	8.626	9.997	77852.667	4.767	9.867	5727.960	1642.333	45.933	11
1974	4	8.462	9.323	78216.667	5.133	9.600	5678.713	1586.000	47.300	12
1975	1	8.887	11.250	78511.667	5.200	9.700	5692.210	1515.333	48.567	13
1975	2	9.606	12.090	78621.667	5.633	9.767	5638.411	1202.667	49.933	14
1975	3	9.793	9.347	78182.333	6.600	9.867	5616.526	1023.667	51.467	15
1975	4	9.168	6.303	76953.000	8.267	11.400	5548.156	976.333	52.567	16
1976	1	8.875	5.420	76535.000	8.867	13.867	5587.800	1071.000	53.200	17
1976	2	8.984	6.160	77050.333	8.467	15.567	5683.444	1250.000	54.267	18
1976	3	9.161	5.413	77747.333	8.300	16.167	5759.972	1341.667	55.267	19
1976	4	8.873	4.827	78789.000	7.733	16.467	5889.500	1442.000	55.900	20
1977	1	8.777	5.197	79326.667	7.567	15.933	5932.711	1449.667	56.400	21
1977	2	8.968	5.283	79714.333	7.733	15.500	5965.265	1557.000	57.300	22
1977	3	8.847	4.873	80199.667	7.767	15.200	6008.504	1691.333	58.133	23
1977	4	8.693	4.660	81023.000	7.500	14.800	6079.494	1844.333	59.200	24
1978	1	8.808	5.157	82101.333	7.133	14.567	6197.686	1918.667	60.233	25
1978	2	8.925	5.820	83147.000	6.900	14.067	6309.514	2009.000	61.067	26
1978	3	8.937	6.513	84127.667	6.667	13.633	6309.652	2075.333	61.967	27
1978	4	9.127	6.757	85000.667	6.333	12.600	6329.791	1829.333	63.033	28
1979	1	9.558	7.283	86540.333	6.000	12.167	6574.390	2114.000	64.467	29
1979	2	9.760	8.100	87436.000	6.033	11.600	6640.497	2019.333	65.967	30
1979	3	10.122	9.583	88339.333	5.900	11.133	6729.755	2039.667	67.500	31
1979	4	10.409	10.073	89114.000	5.867	11.333	6741.854	1665.667	69.200	32
1980	1	10.764	10.180	89771.333	5.700	10.833	6749.063	1845.667	71.400	33
1980	2	11.157	10.947	90281.333	5.867	10.467	6799.200	1790.000	73.700	34
1980	3	12.485	13.577	90575.333	5.967	10.633	6816.203	1567.667	76.033	35
1980	4	13.680	15.047	90892.333	6.300	10.667	6837.641	1246.000	79.033	36
1981	1	14.419	12.687	90456.667	7.333	11.200	6696.753	1058.000	81.700	37
1981	2	12.643	9.837	90050.667	7.667	12.367	6688.794	1392.000	83.233	38
1981	3	14.226	15.853	90726.667	7.400	13.467	6813.535	1505.000	85.567	39
1981	4	15.127	16.570	91116.000	7.433	14.133	6947.042	1366.333	87.933	40
1982	1	16.239	17.780	91356.333	7.400	13.733	6895.559	1181.667	89.767	41
1982	2	17.380	17.577	91547.667	7.400	13.933	6978.135	964.000	92.267	42
1982	3	17.736	13.587	91148.667	8.233	13.233	6902.105	873.333	93.767	43
1982	4	17.414	14.227	90520.667	8.833	13.867	6794.878	880.000	94.600	44
1983	1	16.766	14.513	90040.667	9.433	15.033	6825.876	948.000	95.967	45
1983	2	16.222	11.007	89355.667	9.900	16.067	6799.781	1118.667	97.633	46
1983	3	14.033	9.287	88821.333	10.667	17.467	6802.497	1282.667	97.933	47
1983	4	13.030	8.653	88999.000	10.367	19.333	6892.144	1630.333	98.000	48
1984	1	12.763	8.803	89676.333	10.133	20.267	7048.982	1660.333	99.133	49
1984	2	13.641	9.460	90604.333	9.367	20.467	7189.896	1801.667	100.100	50
1984	3	13.460	9.430	91875.000	8.533	19.700	7339.893	1729.333	101.100	51
1984	4	13.333	9.687	93086.333	7.867	19.500	7483.371	1940.000	102.533	52
1985	1	14.035	10.557	94123.000	7.433	18.600	7612.668	1822.667	103.500	53
1985	2	14.494	11.390	95055.000	7.433	17.433	7686.059	1672.000	104.400	54
1985	3	13.648	9.267	95906.000	7.300	16.833	7749.151	1630.333	105.300	55
1985	4	13.064	8.477	96572.333	7.233	15.967	7824.247	1714.333	106.267	56
1986	1	12.785	7.923	97269.667	7.300	15.733	7893.136	1725.667	107.233	57
1986	2	12.141	7.900	97844.333	7.200	15.367	8013.674	1701.000	107.900	58
1986	3	11.731	8.103	98428.333	7.033	15.367	8073.239	1824.667	109.000	59
1986	4	10.584	7.827	98837.667	7.033	14.867	8148.603	1898.667	109.567	60
1987	1	10.246	6.920	99174.667	7.167	14.867	8185.303	1878.000	109.033	61
1987	2	10.235	6.207	99665.000	6.967	15.367	8263.639	1758.667	109.700	62
1987	3	9.684	6.267	100312.667	6.833	15.067	8308.021	1712.333	110.467	63
1987	4	9.115	6.220	100920.333	6.600	14.833	8369.930	1761.333	111.800	64
1988	1	10.343	6.650	101709.000	6.267	14.867	8460.233	1612.000	113.067	65
1988	2	10.482	6.843	102438.000	6.000	14.267	8533.635	1625.000	114.267	66
1988	3	10.864	6.917	103390.333	5.833	14.067	8680.162	1523.667	115.333	67
1988	4	10.068	6.663	104152.000	5.700	14.100	8725.006	1425.333	116.233	68
1989	1	10.359	7.157	105006.667	5.467	13.400	8839.641	1490.667	117.567	69
1989	2	10.496	7.983	105745.667	5.467	13.533	8891.435	1484.000	119.000	70
1989	3	10.410	8.470	106597.000	5.333	12.967	9009.913	1551.333	120.300	71
1989	4	10.820	9.443	107403.000	5.200	12.433	9101.508	1489.333	121.667	72
1990	1	10.636	9.727	107910.333	5.233	11.867	9170.977	1355.667	123.633	73
1990	2	10.008	9.083	108186.000	5.233	11.567	9238.923	1346.000	124.600	74
1990	3	9.814	8.613	108688.000	5.367	11.733	9257.128	1337.333	125.867	75
1990	4	10.132	8.250	109425.333	5.300	11.700	9358.289	1425.667	128.033	76
1991	1	10.324	8.243	109794.667	5.333	11.700	9392.251	1212.333	129.300	77
1991	2	10.103	8.160	109653.667	5.700	12.167	9398.499	1132.000	131.533	78
1991	3	9.959	7.743	109249.000	6.133	12.367	9312.937	1042.667	133.767	79
1991	4	9.501	6.427	108789.000	6.600	12.600	9269.367	894.667	134.767	80
1992	1	9.522	5.863	108318.333	6.833	13.367	9341.642	1011.000	135.567	81
1992	2	9.273	5.643	108314.333	6.867	13.900	9388.845	1042.333	136.600	82
1992	3	8.690	4.817	108328.000	7.100	14.867	9421.565	1087.000	137.733	83
1992	4	8.688	4.023	108351.000	7.367	16.633	9534.346	1241.000	138.667	84
1993	1	8.678	3.770	108631.333	7.600	17.800	9637.732	1152.667	139.733	85
1993	2	8.018	3.257	108895.333	7.633	18.067	9732.979	1183.667	140.800	86
1993	3	8.192	3.037	109306.667	7.367	18.600	9834.510	1228.333	142.033	87
1993	4	7.723	3.040	109948.333	7.133	18.033	9850.973	1167.667	143.067	88
1994	1	7.453	3.000	110542.333	7.067	17.633	9908.347	1266.000	144.100	89
1994	2	7.088	3.060	111240.000	6.800	17.933	9955.641	1299.000	144.767	90
1994	3	7.046	2.990	112015.333	6.633	18.333	10091.049	1433.667	145.967	91
1994	4	7.296	3.213	112878.000	6.567	18.867	10188.954	1391.000	146.700	92
1995	1	8.428	3.940	113920.667	6.200	19.100	10327.019	1466.667	147.533	93
1995	2	8.594	4.487	114922.000	6.000	18.833	10387.382	1454.333	148.900	94
1995	3	9.105	5.167	115837.000	5.633	18.367	10506.372	1472.000	149.767	95
1995	4	8.785	5.810	116707.667	5.467	17.133	10543.644	1324.000	150.867	96
1996	1	7.918	6.020	117141.667	5.667	16.833	10575.100	1287.333	152.100	97
1996	2	7.696	5.797	117636.333	5.667	16.300	10665.060	1415.333	152.867	98
1996	3	7.339	5.720	118182.667	5.567	16.233	10737.478	1417.333	153.700	99
1996	4	7.272	5.363	118689.333	5.533	16.600	10817.896	1460.667	155.067	100
1997	1	8.102	5.243	119480.667	5.500	17.400	10998.322	1495.667	156.400	101
1997	2	8.147	5.307	120215.000	5.267	16.933	11096.976	1501.333	157.300	102
1997	3	7.703	5.280	120931.667	5.333	15.933	11212.205	1417.000	158.667	103
1997	4	7.793	5.277	121684.333	5.233	15.767	11284.587	1432.667	159.633	104
1998	1	7.927	5.523	122559.333	5.000	15.500	11472.137	1476.000	160.000	105
1998	2	7.470	5.533	123270.667	4.867	16.100	11615.636	1457.667	160.800	106
1998	3	7.205	5.507	124248.333	4.667	15.800	11715.393	1532.000	161.667	107
1998	4	7.050	5.520	125007.000	4.633	15.167	11832.486	1558.667	162.000	108
1999	1	7.098	5.500	125798.333	4.400	14.500	11942.032	1572.333	162.533	109
1999	2	6.872	5.533	126509.333	4.533	14.067	12091.614	1631.333	163.367	110
1999	3	6.764	4.860	127272.667	4.433	14.200	12287.000	1722.333	164.133	111
1999	4	6.878	4.733	128027.667	4.300	13.533	12403.293	1709.333	164.733	112
2000	1	7.182	4.747	128843.667	4.267	13.667	12498.694	1574.333	165.967	113
2000	2	7.786	5.093	129592.333	4.233	13.267	12662.385	1650.667	167.200	114
2000	3	7.841	5.307	130485.000	4.067	13.033	12877.593	1654.667	168.433	115
2000	4	8.257	5.677	131255.000	4.033	12.800	12924.179	1659.000	170.100	116
2001	1	8.316	6.273	132032.333	3.933	12.433	13160.842	1586.667	171.433	117
2001	2	8.020	6.520	132283.667	4.000	12.833	13178.419	1503.667	173.000	118
2001	3	7.621	6.473	132552.333	3.900	12.533	13260.506	1544.000	174.233	119
2001	4	7.007	5.593	132759.000	4.233	12.767	13222.690	1605.000	175.900	120
2002	1	7.130	4.327	132404.333	4.400	12.400	13299.984	1630.000	177.133	121
2002	2	6.964	3.497	132007.000	4.833	13.133	13244.784	1599.667	177.633	122
2002	3	6.771	2.133	131207.667	5.500	14.033	13280.859	1570.000	177.500	123
2002	4	6.972	1.733	130784.000	5.700	15.033	13397.002	1723.000	178.067	124
2003	1	6.813	1.750	130659.333	5.833	16.667	13478.152	1691.000	179.467	125
2003	2	6.289	1.740	130577.000	5.733	17.000	13538.072	1697.333	180.433	126
2003	3	6.075	1.443	130587.667	5.867	17.967	13559.032	1729.667	181.500	127
2003	4	5.841	1.250	130434.333	5.867	18.367	13634.253	1736.000	183.367	128
2004	1	5.507	1.247	130204.333	6.133	19.433	13751.543	1753.667	183.067	129
2004	2	6.034	1.017	130217.667	6.133	19.467	13985.073	1889.667	184.433	130
2004	3	5.919	0.997	130522.667	5.833	19.667	14145.645	2035.667	185.133	131
2004	4	5.598	1.003	130929.000	5.700	19.933	14221.147	1918.333	186.700	132
2005	1	6.106	1.010	131647.667	5.600	19.967	14329.523	1937.333	188.167	133
2005	2	5.894	1.433	131977.000	5.433	19.000	14464.984	1977.000	189.367	134
2005	3	5.736	1.950	132543.667	5.433	19.533	14609.876	1965.333	191.400	135
2005	4	5.768	2.470	133004.333	5.300	19.367	14771.602	2071.667	192.367	136
2006	1	5.708	2.943	133733.000	5.100	18.700	14839.782	2051.333	193.667	137
2006	2	5.764	3.460	134471.333	4.967	17.967	14972.054	2100.000	196.600	138
2006	3	6.226	3.980	134951.000	4.967	17.633	15066.597	2068.667	198.433	139
2006	4	6.247	4.457	135754.000	4.733	17.267	15267.026	2120.333	199.467	140
2007	1	6.602	4.907	136274.667	4.633	16.800	15302.705	1855.000	201.267	141
2007	2	6.560	5.247	136703.667	4.633	17.100	15326.368	1702.333	203.167	142
2007	3	6.244	5.247	137073.333	4.433	16.200	15456.928	1570.000	202.333	143
2007	4	6.215	5.257	137625.333	4.500	16.933	15493.328	1461.333	204.317	144
2008	1	6.358	5.250	137986.667	4.500	16.667	15582.085	1451.000	206.631	145
2008	2	6.552	5.073	138067.000	4.667	16.833	15666.738	1289.000	207.939	146
2008	3	6.225	4.497	138299.333	4.800	16.967	15761.967	1166.000	210.490	147
2008	4	5.872	3.177	138351.333	5.000	16.967	15671.383	1064.000	212.770	148
2009	1	6.087	2.087	137878.000	5.333	16.867	15752.308	1010.667	215.538	149
2009	2	6.322	1.940	137168.667	6.000	17.767	15667.032	862.333	218.861	150
2009	3	5.841	0.507	135568.667	6.867	19.567	15328.027	663.000	213.849	151
2009	4	5.060	0.183	133311.667	8.267	20.300	15155.940	525.667	212.378	152
2010	1	5.012	0.180	131450.667	9.300	22.667	15134.117	534.333	213.507	153
2010	2	5.162	0.157	130481.667	9.633	25.667	15189.222	588.333	215.344	154
2010	3	4.922	0.120	129979.333	9.933	28.700	15356.058	567.667	217.030	155
2010	4	4.996	0.133	129805.667	9.833	30.567	15415.145	618.000	217.374	156
2011	1	4.922	0.193	130442.667	9.633	33.933	15557.277	602.000	217.297	157
2011	2	4.447	0.187	130417.333	9.467	33.667	15671.967	579.667	217.934	158
2011	3	4.436	0.187	130748.667	9.500	34.200	15750.625	542.333	219.699	159
2011	4	4.847	0.157	131078.333	9.033	37.900	15712.754	582.333	222.044	160
2012	1	4.651	0.093	131766.667	9.067	39.400	15825.096	574.333	224.568	161
2012	2	4.292	0.083	132176.000	9.000	40.533	15820.700	619.333	226.033	162
2012	3	4.002	0.073	132734.000	8.633	39.767	16004.107	671.667	227.047	163
2012	4	3.922	0.103	133523.000	8.267	39.733	16129.418	707.333	228.326	164
2013	1	3.795	0.153	133942.000	8.200	39.700	16198.807	739.333	228.808	165
2013	2	3.554	0.143	134352.333	8.033	39.567	16220.667	780.333	229.841	166
2013	3	3.359	0.160	134877.333	7.800	38.733	16239.138	908.000	231.369	167
2013	4	3.497	0.143	135514.333	7.733	36.333	16382.964	953.333	232.299	168
2014	1	3.672	0.117	136099.667	7.533	36.567	16403.180	868.000	232.045	169
2014	2	4.440	0.083	136624.333	7.233	37.433	16531.685	882.333	233.300	170
2014	3	4.293	0.087	137256.333	6.933	36.067	16663.649	1009.000	234.163	171
2014	4	4.365	0.073	137762.333	6.667	35.633	16621.696	934.000	235.621	172
2015	1	4.228	0.093	138567.333	6.200	34.400	16830.111	987.000	236.872	173
2015	2	4.135	0.090	139313.000	6.067	32.200	17033.572	1030.667	237.478	174
2015	3	3.964	0.100	140121.333	5.700	32.567	17113.945	1049.333	236.888	175
2015	4	3.717	0.110	140800.000	5.533	31.200	17254.744	980.667	235.320	176
2016	1	3.819	0.123	141503.333	5.433	30.000	17397.029	1157.000	236.938	177
2016	2	3.955	0.137	142141.667	5.100	27.467	17438.802	1161.667	237.862	178
2016	3	3.898	0.160	142860.000	5.033	27.733	17456.225	1129.333	237.871	179
2016	4	3.738	0.360	143447.667	4.933	28.867	17523.374	1145.667	237.780	180
2017	1	3.589	0.373	143996.000	4.900	27.733	17622.486	1160.667	239.486	181
2017	2	3.446	0.397	144705.000	4.900	27.333	17706.705	1151.333	240.601	182
2017	3	3.842	0.450	145243.000	4.767	26.100	17784.185	1254.000	242.164	183
2017	4	4.173	0.700	145831.333	4.600	25.233	17863.023	1230.667	243.830	184
2018	1	3.980	0.950	146337.667	4.367	24.833	17995.150	1169.333	244.065	185
2018	2	3.884	1.153	146867.667	4.300	25.200	18120.843	1175.333	245.368	186
2018	3	3.922	1.203	147406.667	4.133	24.800	18223.758	1259.667	247.273	187
2018	4	4.282	1.447	148047.667	4.067	23.667	18323.963	1320.667	249.250	188
2019	1	4.545	1.737	148742.333	3.900	21.833	18511.576	1259.667	250.579	189
2019	2	4.567	1.923	149409.000	3.800	23.267	18664.973	1233.000	251.829	190
2019	3	4.785	2.220	150058.333	3.800	21.967	18765.256	1185.000	252.759	191
2019	4	4.374	2.403	150675.333	3.867	21.467	18910.332	1213.000	253.311	192



MORTRATE	30-Year Fixed Mortgage Rate
FFUNDS	Federal Funds Rate
EMPLOY	Non-Farm Employment (Thousands)
URATE	Unemployment Rate
UDUR	Average Unemployment Duration (Weeks)
RGDP	Real GDP (Billions of dollars)
HOUSING	Housing Starts (Thousands)
CPI	Consumer Price Index
TREND	Linear trend

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