The Following data is given for the period 1999-2003 Interest rateInflation iπ 19994.74.4 20004.65.4 20016.35.7 20024.84.6 20032.92.4 According to Fisher Equation “a rise in inflation also rises the nominal interest rate by the same amount”. Construct a regression model by determining dependent and independent variables according to this theory. Obtain residuals of the regression. Calculate variance of the residuals and the standard errors of the parameters. (note: use the table above for calculations, just write down the final results here). Test significance of the slope parameter (the parameter of the independent variable) at 5% significance level. Is it in line with the proposition? Evaluate the overall significance of the model with R2 and F test. TABLE D.2Percentage Points ofthe DistributionExamplePr(t > 2.086) = 0.025Pr (t > 1.725) = 0.05 for df = 200.05Soure FmES Pane andHO Herey, e Pr (14| > 1.725) = 0.10Tles for S vlI.Mel. e 12. CambridgeUnivenity P, Now York196. Repradcedbypermin of he ad andtrustos of tnka.1.725Pr0.250.100.050.100.0250.010.0050.001df0.500.200.050.020.0100.00231.8216.9654.5413.747318.3122.32710.2147.1731.00012.7064.3033.1822.77663.6579.9255.84110.8160.7650.7413.0781.8861.6381.5336.3142.9202.3532.13234.4.6040.7270.7180.7111.4761.4401.4151.3972.0151.9431.8952.5712.4472.3652.3063.3653.1432.9982.8964.0323.7073.4993.3555.8935.2084.7854.5014.2976.0.7060.7031.8601.83381.3832.2622.8213.25010110.7000.6971.3721.3631.8121.7962.2282.2012.7642.7183.1694.1443.1064.0251213142.1792.1602.1450.6951.3561.7820.6940.6921.3501.3452.6812.6502.6243.0553.0122.9773.9303.8523.7871.7711.76115162.1312.6022.9472.9212.8982.8783.7333.6863.6463.6103.5790.6911.3411.7531.7460.6900.6890.6880.6881.3371.3331.3301.3282.1202.1102.1012.5832.5672.5522.539171.740181.734191.7292.0932.86120210.6870.6861.3251.3231.7251.7211.7172.0862.0802.0742.5282.5182.8452.8313.5523.5271.3211.3192.8192.8072.7973.5053.4853.467220.6862.50823240.6851.7142.0692.5000.6851.3181.7112.0642.492250.6841.3161.7081.7062.0602.4852.7873.4502.0562.0522.0482.0452.7792.7712.7632.756260.6840.6840.6830.6831.3152728291.3141.3131.3111.7031.7011.6992.4792.4732.4672.4623.4353.4213.4083.3963040601200.6830.6810.6790.6771.3101.3031.2961.6971.6841.6712.0422.0212.0002.4572.4232.3902.7502.7042.6602.6173.3853.3073.2323.1603.0901.2891.2821.6581.6451.9802.3580.6741.9602.3262.576Note: The maller probubility shown at the head of cach column is the area in one tail; the larger probubility is the area inbeth tails.

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MATLAB: An Introduction with Applications

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The Following data is given for the period 1999-2003

	Interest rate	Inflation
	i	π
1999	4.7	4.4
2000	4.6	5.4
2001	6.3	5.7
2002	4.8	4.6
2003	2.9	2.4

According to Fisher Equation “a rise in inflation also rises the nominal interest rate by the same amount”. Construct a regression model by determining dependent and independent variables according to this theory.

Obtain residuals of the regression. Calculate variance of the residuals and the standard errors of the parameters. (note: use the table above for calculations, just write down the final results here).

Test significance of the slope parameter (the parameter of the independent variable) at 5% significance level. Is it in line with the proposition?

Evaluate the overall significance of the model with R² and F test.

TABLE D.2
Percentage Points of
the Distribution
Example
Pr(t > 2.086) = 0.025
Pr (t > 1.725) = 0.05 for df = 20
0.05
Soure FmES Pane and
HO Herey, e Pr (14| > 1.725) = 0.10
Tles for S vlI.
Mel. e 12. Cambridge
Univenity P, Now York
196. Repradcedby
permin of he ad and
trustos of tnka.
1.725
Pr
0.25
0.10
0.05
0.10
0.025
0.01
0.005
0.001
df
0.50
0.20
0.05
0.02
0.010
0.002
31.821
6.965
4.541
3.747
318.31
22.327
10.214
7.173
1.000
12.706
4.303
3.182
2.776
63.657
9.925
5.841
1
0.816
0.765
0.741
3.078
1.886
1.638
1.533
6.314
2.920
2.353
2.132
3
4.
4.604
0.727
0.718
0.711
1.476
1.440
1.415
1.397
2.015
1.943
1.895
2.571
2.447
2.365
2.306
3.365
3.143
2.998
2.896
4.032
3.707
3.499
3.355
5.893
5.208
4.785
4.501
4.297
6.
0.706
0.703
1.860
1.833
8
1.383
2.262
2.821
3.250
10
11
0.700
0.697
1.372
1.363
1.812
1.796
2.228
2.201
2.764
2.718
3.169
4.144
3.106
4.025
12
13
14
2.179
2.160
2.145
0.695
1.356
1.782
0.694
0.692
1.350
1.345
2.681
2.650
2.624
3.055
3.012
2.977
3.930
3.852
3.787
1.771
1.761
15
16
2.131
2.602
2.947
2.921
2.898
2.878
3.733
3.686
3.646
3.610
3.579
0.691
1.341
1.753
1.746
0.690
0.689
0.688
0.688
1.337
1.333
1.330
1.328
2.120
2.110
2.101
2.583
2.567
2.552
2.539
17
1.740
18
1.734
19
1.729
2.093
2.861
20
21
0.687
0.686
1.325
1.323
1.725
1.721
1.717
2.086
2.080
2.074
2.528
2.518
2.845
2.831
3.552
3.527
1.321
1.319
2.819
2.807
2.797
3.505
3.485
3.467
22
0.686
2.508
23
24
0.685
1.714
2.069
2.500
0.685
1.318
1.711
2.064
2.492
25
0.684
1.316
1.708
1.706
2.060
2.485
2.787
3.450
2.056
2.052
2.048
2.045
2.779
2.771
2.763
2.756
26
0.684
0.684
0.683
0.683
1.315
27
28
29
1.314
1.313
1.311
1.703
1.701
1.699
2.479
2.473
2.467
2.462
3.435
3.421
3.408
3.396
30
40
60
120
0.683
0.681
0.679
0.677
1.310
1.303
1.296
1.697
1.684
1.671
2.042
2.021
2.000
2.457
2.423
2.390
2.750
2.704
2.660
2.617
3.385
3.307
3.232
3.160
3.090
1.289
1.282
1.658
1.645
1.980
2.358
0.674
1.960
2.326
2.576
Note: The maller probubility shown at the head of cach column is the area in one tail; the larger probubility is the area in
beth tails.

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