Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 5.8031512605042 -0.412605042016806X[t] -0.000630252100846359M1[t] -0.100630252100840M2[t] -0.100630252100840M3[t] + 0.159369747899159M4[t] + 0.60189075630252M5[t] + 0.741890756302521M6[t] + 0.721890756302521M7[t] + 0.581890756302521M8[t] + 0.441890756302521M9[t] + 0.241890756302521M10[t] + 0.15M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	5.8031512605042	0.234228	24.7756	0	0
X	-0.412605042016806	0.134394	-3.0701	0.003621	0.001811
M1	-0.000630252100846359	0.311073	-0.002	0.998392	0.499196
M2	-0.100630252100840	0.311073	-0.3235	0.74782	0.37391
M3	-0.100630252100840	0.311073	-0.3235	0.74782	0.37391
M4	0.159369747899159	0.311073	0.5123	0.61093	0.305465
M5	0.60189075630252	0.311653	1.9313	0.059761	0.02988
M6	0.741890756302521	0.311653	2.3805	0.021584	0.010792
M7	0.721890756302521	0.311653	2.3163	0.025152	0.012576
M8	0.581890756302521	0.311653	1.8671	0.068408	0.034204
M9	0.441890756302521	0.311653	1.4179	0.16311	0.081555
M10	0.241890756302521	0.311653	0.7762	0.441718	0.220859
M11	0.15	0.327823	0.4576	0.649467	0.324734

Multiple Linear Regression - Regression Statistics
Multiple R	0.629006732730117
R-squared	0.395649469819817
Adjusted R-squared	0.234489328438435
F-TEST (value)	2.45500820754135
F-TEST (DF numerator)	12
F-TEST (DF denominator)	45
p-value	0.0147483021027165
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.463611648873337
Sum Squared Residuals	9.67210924369745

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	6.3	5.80252100840339	0.497478991596615
2	6.2	5.70252100840336	0.497478991596639
3	6.1	5.70252100840336	0.397478991596638
4	6.3	5.96252100840336	0.337478991596638
5	6.5	6.40504201680672	0.0949579831932773
6	6.6	6.54504201680672	0.0549579831932784
7	6.5	6.52504201680672	-0.0250420168067217
8	6.2	6.38504201680672	-0.185042016806723
9	6.2	6.24504201680672	-0.0450420168067223
10	5.9	6.04504201680672	-0.145042016806723
11	6.1	5.9531512605042	0.146848739495799
12	6.1	5.8031512605042	0.296848739495798
13	6.1	5.80252100840335	0.297478991596645
14	6.1	5.70252100840336	0.397478991596639
15	6.1	5.70252100840336	0.397478991596639
16	6.4	5.96252100840336	0.437478991596639
17	6.7	6.40504201680672	0.294957983193278
18	6.9	6.54504201680672	0.354957983193278
19	7	6.52504201680672	0.474957983193277
20	7	6.38504201680672	0.614957983193277
21	6.8	6.24504201680672	0.554957983193277
22	6.4	6.04504201680672	0.354957983193278
23	5.9	5.9531512605042	-0.0531512605042011
24	5.5	5.8031512605042	-0.303151260504202
25	5.5	5.80252100840335	-0.302521008403355
26	5.6	5.70252100840336	-0.102521008403362
27	5.8	5.70252100840336	0.0974789915966388
28	5.9	5.96252100840336	-0.0625210084033609
29	6.1	6.40504201680672	-0.305042016806723
30	6.1	6.54504201680672	-0.445042016806723
31	6	6.52504201680672	-0.525042016806723
32	6	6.38504201680672	-0.385042016806722
33	5.9	6.24504201680672	-0.345042016806722
34	5.5	6.04504201680672	-0.545042016806723
35	5.6	5.9531512605042	-0.353151260504202
36	5.4	5.8031512605042	-0.403151260504201
37	5.2	5.80252100840335	-0.602521008403355
38	5.2	5.70252100840336	-0.502521008403361
39	5.2	5.70252100840336	-0.502521008403361
40	5.5	5.96252100840336	-0.462521008403361
41	5.8	5.99243697478992	-0.192436974789916
42	5.8	6.13243697478992	-0.332436974789916
43	5.5	6.11243697478992	-0.612436974789917
44	5.3	5.97243697478992	-0.672436974789916
45	5.1	5.83243697478992	-0.732436974789917
46	5.2	5.63243697478992	-0.432436974789916
47	5.8	5.5405462184874	0.259453781512605
48	5.8	5.3905462184874	0.409453781512605
49	5.5	5.38991596638655	0.110084033613451
50	5	5.28991596638655	-0.289915966386555
51	4.9	5.28991596638655	-0.389915966386555
52	5.3	5.54991596638656	-0.249915966386555
53	6.1	5.99243697478992	0.107563025210084
54	6.5	6.13243697478992	0.367563025210084
55	6.8	6.11243697478992	0.687563025210083
56	6.6	5.97243697478992	0.627563025210084
57	6.4	5.83243697478992	0.567563025210084
58	6.4	5.63243697478992	0.767563025210084

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0113208333279507	0.0226416666559015	0.98867916667205
17	0.00514789252480899	0.0102957850496180	0.99485210747519
18	0.0048484102494393	0.0096968204988786	0.99515158975056
19	0.0135235781977798	0.0270471563955597	0.98647642180222
20	0.076096461457403	0.152192922914806	0.923903538542597
21	0.113985444267235	0.227970888534471	0.886014555732765
22	0.119010148954997	0.238020297909994	0.880989851045003
23	0.0752108253957213	0.150421650791443	0.924789174604279
24	0.0780240226420835	0.156048045284167	0.921975977357916
25	0.109359207322238	0.218718414644476	0.890640792677762
26	0.115828281216412	0.231656562432825	0.884171718783588
27	0.108578588816481	0.217157177632962	0.89142141118352
28	0.102628231863816	0.205256463727633	0.897371768136184
29	0.0894971269811349	0.178994253962270	0.910502873018865
30	0.0900666210755518	0.180133242151104	0.909933378924448
31	0.0986350239449495	0.197270047889899	0.90136497605505
32	0.0851840540951067	0.170368108190213	0.914815945904893
33	0.0728102313600826	0.145620462720165	0.927189768639917
34	0.0636287028919842	0.127257405783968	0.936371297108016
35	0.0426816668862187	0.0853633337724375	0.957318333113781
36	0.0301515636260804	0.0603031272521607	0.96984843637392
37	0.0304947019525504	0.0609894039051008	0.96950529804745
38	0.0249852828126665	0.0499705656253331	0.975014717187333
39	0.0194985557459480	0.0389971114918959	0.980501444254052
40	0.0124343851147607	0.0248687702295214	0.98756561488524
41	0.00540532709661672	0.0108106541932334	0.994594672903383
42	0.0027555012217546	0.0055110024435092	0.997244498778245

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	2	0.0740740740740741	NOK
5% type I error level	9	0.333333333333333	NOK
10% type I error level	12	0.444444444444444	NOK