(Tiểu luận) môn dự báo trong kinh doanh và kinh tế appendixd statistical tables

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Table D.1Areas under the Standardized Normal Distribution Table D.2Percentage Points of the t Distribution

Table D.3Upper Percentage Points of the F Distribution

Table D.4Upper Percentage Points of the χ

Distribution

Table D.5ADurbin–Watson d Statistic: Significance Points of d

L

and d

U

at 0.05 Level of Significance

Table D.5BDurbin–Watson d Statistic: Significance Points of d

L

and d

U

at 0.01 Levels of Significance

Table D.6Critical Values of Runs in the Runs Test

Table D.71% and 5% Critical Dickey–Fuller t (= τ ) and F Values for Unit Root Tests

Statistical Tables

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Note: This table gives the area in the right-hand tail of the distribution (i.e., Z ≥ 0). But since the normal distribution is symmetrical about Z = 0, the area in the left-hand tail is the same as the area in the corresponding right-hand tail. For example,

P(−1.96 ≤ ≤ Z 0) = 0.4750. Therefore, (−1.96 P ≤ ≤ Z 1.96) = 2(0.4750) =0.95.

Z

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Percentage Points ofthe Distribution

Source: From E. S. Pearson and

H. O. Hartley, eds., BiometrikaTables for Statisticians, vol. 1,

3d ed., table 12, Cambridge University Press, New York,

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880 Appendix D Statistical Tables

TABLE D.3

Upper Percentage Points of the Distribution

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TABLE D.3

Upper Percentage Points of the Distribution()

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TABLE D.3

Upper Percentage Points of the Distribution()

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= Z follows the standardized normal distribution, where k represents

the degrees of freedom.

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Source: Abridged from E. S. Pearson and H. O. Hartley, eds., Biometrika Tables for Statisticians, vol. 1, 3d ed., table 8, Cambridge University Press, New York, 1966.Reproduced by permission of the editors and trustees of Biometrika.

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TABLE D.5A

Durbin–WatsonStatistic: Significance Points of andat 0.05 Level of Significance

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Note: n = number of observations, k= number of explanatory variables excluding the constant term.

Source: This table is an extension of the original Durbin–Watson table and is reproduced from N. E. Savin and K. J. White, “The Durbin-Watson Test for Serial Correlation

with Extreme Small Samples or Many Regressors,” Econometrica, vol. 45, November 1977, pp. 1989–96 and as corrected by R. W. Farebrother, Econometrica,vol. 48, September 1980, p. 1554. Reprinted by permission of the Econometric Society.

If n = 40 and k= 4, dL= 1.285 and dU= 1 721. . If a computed value is less than 1.285,d

there is evidence of positive first-order serial correlation; if it is greater than 1.721, there is no evidence of positive first-order serial correlation; but if lies between the lower and thed

upper limit, there is inconclusive evidence regarding the presence or absence of positive first-order serial correlation.

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TABLE D.5B

Durbin–Watson Statistic: Significance Points of and at 0.01 Level of Significance

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Note: n = number of observations.

k= number of explanatory variables excluding the constant term. Source: Savin and White, op. cit., by permission of the Econometric Society.

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TABLE D.6A

Critical Values of Runs in the Runs Test

Note: Tables D.6A and D.6B give the critical values of runs n for various values of N1(+symbol) and N2(− symbol). For the one-sample runs test, any value

of n that is equal to or smaller than that shown in Table D.6A or equal to or larger than that shown in Table D.6B is significant at the 0.05 level.Source: Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill Book Company, New York, 1956, table F, pp. 252–253. The tables have beenadapted by Siegel from the original source: Frieda S. Swed and C. Eisenhart, “Tables for Testing Randomness of Grouping in a Sequence of Alternatives,” Annals ofMathematical Statistics, vol. 14, 1943. Used by permission of McGraw-Hill Book Company and Annals of Mathematical Statistics.

TABLE D.6B

Critical Values of Runs in the Runs Test

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In a sequence of 30 observations consisting of 20 + signs ( = N1) and 10 − signs ( = N ),2

the critical values of runs at the 0.05 level of significance are 9 and 20, as shown by Tables D.6A and D.6B, respectively. Therefore, if in an application it is found that the number of runs is equal to or less than 9 or equal to or greater than 20, one can reject (at the 0.05 level of significance) the hypothesis that the observed sequence is random.

TABLE D.7

1% and 5% Critical Dickey–Fuller () and Values for Unit Root Tests

*Subscripts nc, , and ct denote, respectively, that there is no constant, a constant, and a constant and trend term in the regression Eq. (21.9.5).c

†The critical F values are for the joint hypothesis that the constant and terms in Eq. (21.9.5) are simultaneously equal to zero.δ ‡The critical F values are for the joint hypothesis that the constant, trend, and δterms in Eq. (21.9.5) are simultaneously equal to zero.

Source: Adapted from W. A. Fuller, Introduction to Statistical Time Series, John Wiley & Sons, New York, 1976, p. 373 (for the τtest), and D. A. Dickey and W. A. Fuller,

“Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, vol. 49, 1981, p. 1063.

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