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

Table D.1Areas under the Standardized Normal Distribution Table D.2Percentage Points of the t DistributionTable D.3Upper Percentage Points of the F DistributionTable D.4Upper Percentage

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 χ2Distribution

Table D.5ADurbin–Watson d Statistic: Significance Points of dLand dUat 0.05 Level of Significance

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

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

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,

880 Appendix D Statistical Tables

TABLE D.3 Upper Percentage Points of the Distribution

TABLE D.3 Upper Percentage Points of the Distribution()

TABLE D.3 Upper Percentage Points of the Distribution()

= Z follows the standardized normal distribution, where k represents

the degrees of freedom.

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.

TABLE D.5A Durbin–WatsonStatistic: Significance Points of andat 0.05 Level of Significance

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.

TABLE D.5B Durbin–Watson Statistic: Significance Points of and at 0.01 Level of Significance

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.

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

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.