Table 4 Critical Values of the Durbin-Watson Test Statistics dL and dy: 5-Percent One-Sided Level of Significance (10-Percent Two-Sided Level of Significance) • K = 1 K = 2 K = 3 K = = 4 K = - 5 K = = 6 K = = 7 Sl dL dL du dL du dL du dL du dL du 15 1 08 1 36 0.95 1 54 0.81 1 75 0.69 1 97 0.56 2.21 0.45 2.47 0.34 2.73 16 1 11 1 37 0.98 1 54 0.86 1 73 0.73 1 93 0.62 2.15 0.50 2.39 0.40 2.62 17 1 13 1 38 1 02 1 54 0.90 1 71 0.78 1 90 0.66 2.10 0.55 2.32 0.45 2.54 18 1 16 1 39 1 05 1 53 0.93 1 69 0.82 1 87 0.71 2.06 0.60 2.26 0.50 2.46 19 1 18 1 40 1 07 1 53 0.97 1 68 0.86 1 85 0.75 2.02 0.65 2.21 0.55 2.40 20 1 20 1 41 1 10 1 54 1 00 1 68 0.89 1 83 0.79 1 99 0.69 2.16 0.60 2.34 21 1 22 1 42 1 13 1 54 1 03 1 67 0.93 1 81 0.83 1 96 0.73 2.12 0.64 2.29 22 1 24 1 43 1 15 1 54 1 05 1 66 0.96 1 80 0.86 1 94 0.77 2.09 0.68 2.25 23 1 26 1 44 1 17 1 54 1 08 1 66 0.99 1 79 0.90 1 92 0.80 2.06 0.72 2.21 24 1 27 1 45 1 19 1 55 1 10 1 66 1.01 1 78 0.93 1 90 0.84 2.04 0.75 2.17 25 1 29 1 45 1 21 1 55 1 12 1 66 1.04 1 77 0.95 1 89 0.87 2.01 0.78 2.14 26 1 30 1 46 1 22 1 55 1 14 1 65 1.06 1 76 0.98 1 88 0.90 1.99 0.82 2.12 27 1 32 1 47 1 24 1 56 1 16 1 65 1.08 1 76 1.00 1 86 0.93 1.97 0.85 2.09 28 1 33 1 48 1 26 1 56 1 18 1 65 1.10 1 75 1.03 1 85 0.95 1.96 0.87 2.07 29 1 34 1 48 1 27 1 56 1 20 1 65 1.12 1 74 1.05 1 84 0.98 1.94 0.90 2.05 30 1 35 1 49 1 28 1 57 1 21 1 65 1.14 1 74 1.07 1 83 1.00 1.93 0.93 2.03 31 1 36 1 50 1 30 1 57 1 23 1 65 1.16 1 74 1.09 1 83 1.02 1.92 0.95 2.02 32 1 37 1 50 1 31 1 57 1 24 1 65 1.18 1 73 1.11 1 82 1.04 1.91 0.97 2.00 33 1 38 1 51 1 32 1 58 1 26 1 65 1.19 1 73 1.13 1 81 1.06 1.90 0.99 1.99 34 1 39 1 51 1 33 1 58 1 27 1 65 1.21 1 73 1.14 1 81 1.08 1.89 1.02 1.98 35 1 40 1 52 1 34 1 58 1 28 1 65 1.22 1 73 1.16 1 80 1.10 1.88 1.03 1.97 36 1 41 1 52 1 35 1 59 1 30 1 65 1.24 1 73 1.18 1 80 1.11 1.88 1.05 1.96 37 1 42 1 53 1 36 1 59 1 31 1 66 1.25 1 72 1.19 1 80 1.13 1.87 1.07 1.95 38 1 43 1 54 1 37 1 59 1 32 1 66 1.26 1 72 1.20 1 79 1.15 1.86 1.09 1.94 39 1 43 1 54 1 38 1 60 1 33 1 66 1.27 1 72 1.22 1 79 1.16 1.86 1.10 1.93 40 1 44 1 54 1 39 1 60 1 34 1 66 1.29 1 72 1.23 1 79 1.18 1.85 1.12 1.93 45 1 48 1 57 1 43 1 62 1 38 1 67 1.34 1 72 1.29 1 78 1.24 1.84 1.19 1.90 50 1 50 1 59 1 46 1 63 1 42 1 67 1.38 1 72 1.34 1 77 1.29 1.82 1.25 1.88 55 1 53 1 60 1 49 1 64 1 45 1 68 1.41 1 72 1.37 1 77 1.33 1.81 1.29 1.86 60 1 55 1 62 1 51 1 65 1 48 1 69 1.44 1 73 1.41 1 77 1.37 1.81 1.34 1.85 65 1 57 1 63 1 54 1 66 1 50 1 70 1.47 1 73 1.44 1 77 1.40 1.81 1.37 1.84 70 1 58 1 64 1 55 1 67 1 53 1 70 1.49 1 74 1.46 1 77 1.43 1.80 1.40 1.84 75 1 60 1 65 1 57 1 68 1 54 1 71 1.52 1 74 1.49 1 77 1.46 1.80 1.43 1.83 80 1 61 1 66 1 59 1 69 1 56 1 72 1.53 1 74 1.51 1 77 1.48 1.80 1.45 1.83 85 1 62 1 67 1 60 1 70 1 58 1 72 1.55 1 75 1.53 1 77 1.50 1.80 1.47 1.83 90 1 63 1 68 1 61 1 70 1 59 1 73 1.57 1 75 1.54 1 78 1.52 1.80 1.49 1.83 95 1 64 1 69 1 62 1 71 1 60 1 73 1.58 1 75 1.56 1 78 1.54 1.80 1.51 1.83 100 1 65 1 69 1 63 1 72 1 61 1 74 1.59 1 76 1.57 1 78 1.55 1.80 1.53 1.83 Source: N. E. Savin and Kenneth J. White, "The Durbin-Watson Test for Serial Correlation with Extreme Sample Sizes or Many Regressors," Econometrica, November 1977, p. 1994. Reprinted with permission. Note: N = number of observations, K = number of explanatory variables excluding the constant term. We assume that the equation contains a constant term and no lagged dependent variables. Table 5 Critical Values of the Durbin-Watson Test Statistics of dL and dy: 2.5-Percent One-Sided Level of Significance (5-Percent Two-Sided Level of Significance) • K = 1 K = 2 K = 3 K = 4 K = 5 dL du dL du dL du dL du dL du 15 0.95 1 .23 0.83 1 40 0.71 1 .61 0.59 1 .84 0.48 2.09 16 0.98 1 .24 0.86 1 40 0.75 1 .59 0.64 1 .80 0.53 2.03 17 1 .01 1 .25 0.90 1 40 0.79 1 .58 0.68 1 .77 0.57 1.98 18 1 .03 1 .26 0.93 1 40 0.82 1 .56 0.72 1 .74 0.62 1.93 19 1 .06 1 .28 0.96 1 41 0.86 1 .55 0.76 1 .72 0.66 1.90 20 1 .08 1 .28 0.99 1 41 0.89 1 .55 0.79 1 .70 0.70 1.87 21 1 .10 1 .30 1.01 1 41 0.92 1 .54 0.83 1 .69 0.73 1.84 22 1 .12 1 .31 1.04 1 42 0.95 1 .54 0.86 1 .68 0.77 1.82 23 1 .14 1 .32 1.06 1 42 0.97 1 .54 0.89 1 .67 0.80 1.80 24 1 .16 1 .33 1.08 1 43 1.00 1 .54 0.91 1 .66 0.83 1.79 25 1 .18 1 .34 1.10 1 43 1.02 1 .54 0.94 1 .65 0.86 1.77 26 1 .19 1 .35 1.12 1 44 1.04 1 .54 0.96 1 .65 0.88 1.76 27 1 .21 1 .36 1.13 1 44 1.06 1 .54 0.99 1 .64 0.91 1.75 28 1 .22 1 .37 1.15 1 45 1.08 1 .54 1.01 1 .64 0.93 1.74 29 1 .24 1 .38 1.17 1 45 1.10 1 .54 1.03 1 .63 0.96 1.73 30 1 .25 1 .38 1.18 1 46 1.12 1 .54 1.05 1 .63 0.98 1.73 31 1 .26 1 .39 1.20 1 47 1.13 1 .55 1.07 1 .63 1.00 1.72 32 1 .27 1 .40 1.21 1 47 1.15 1 .55 1.08 1 .63 1.02 1.71 33 1 .28 1 .41 1.22 1 48 1.16 1 .55 1.10 1 .63 1.04 1.71 34 1 .29 1 .41 1.24 1 48 1.17 1 .55 1.12 1 .63 1.06 1.70 35 1 .30 1 .42 1.25 1 48 1.19 1 .55 1.13 1 .63 1.07 1.70 36 1 .31 1 .43 1.26 1 49 1.20 1 .56 1.15 1 .63 1.09 1.70 37 1 .32 1 .43 1.27 1 49 1.21 1 .56 1.16 1 .62 1.10 1.70 38 1 .33 1 .44 1.28 1 50 1.23 1 .56 1.17 1 .62 1.12 1.70 39 1 .34 1 .44 1.29 1 50 1.24 1 .56 1.19 1 .63 1.13 1.69 40 1 .35 1 .45 1.30 1 51 1.25 1 .57 1.20 1 .63 1.15 1.69 45 1 .39 1 .48 1.34 1 53 1.30 1 .58 1.25 1 .63 1.21 1.69 50 1 .42 1 .50 1.38 1 54 1.34 1 .59 1.30 1 .64 1.26 1.69 55 1 .45 1 .52 1.41 1 56 1.37 1 .60 1.33 1 .64 1.30 1.69 60 1 .47 1 .54 1.44 1 57 1.40 1 .61 1.37 1 .65 1.33 1.69 65 1 .49 1 .55 1.46 1 59 1.43 1 .62 1.40 1 .66 1.36 1.69 70 1 .51 1 .57 1.48 1 60 1.45 1 .63 1.42 1 .66 1.39 1.70 75 1 .53 1 .58 1.50 1 61 1.47 1 .64 1.45 1 .67 1.42 1.70 80 1 .54 1 .59 1.52 1 62 1.49 1 .65 1.47 1 .67 1.44 1.70 85 1 .56 1 .60 1.53 1 63 1.51 1 .65 1.49 1 .68 1.46 1.71 90 1 .57 1 .61 1.55 1 64 1.53 1 .66 1.50 1 .69 1.48 1.71 95 1 .58 1 .62 1.56 1 65 1.54 1 .67 1.52 1 .69 1.50 1.71 100 1 .59 1 .63 1.57 1 65 1.55 1 .67 1.53 1 .70 1.51 1.72 Source: J. Durbin and G. S. Watson, "Testing for Serial Correlation in Least Squares Regression," Biometrika, Vol. 38, 1951, pp. 159-171. Reprinted with permission of the Biometrika trustees. Note: N = number of observations, K= number of explanatory variables excluding the constant term. It is assumed that the equation contains a constant term and no lagged dependent variables. Table 6 Critical Values of the Durbin-Watson Test Statistics dL and dy: 1-Percent One-Sided Level of Significance (2-Percent Two-Sided Level of Significance) ■ K = 1 K = 2 K = 3 K = 4 K = 5 dL du dL du dL du dL du dL < *u 15 0.81 1 .07 0.70 1 25 0.59 1 .46 0.49 1 .70 0.39 1 96 16 0.84 1 .09 0.74 1 25 0.63 1 .44 0.53 1 .66 0.44 1 90 17 0.87 1 .10 0.77 1 25 0.67 1 .43 0.57 1 .63 0.48 1 85 18 0.90 1 .12 0.80 1 26 0.71 1 .42 0.61 1 .60 0.52 1 80 19 0.93 1 .13 0.83 1 26 0.74 1 .41 0.65 1 .58 0.56 1 77 20 0.95 1 .15 0.86 1 27 0.77 1 .41 0.68 1 .57 0.60 1 74 21 0.97 1 .16 0.89 1 27 0.80 1 .41 0.72 1 .55 0.63 1 71 22 1.00 1 .17 0.91 1 28 0.83 1 .40 0.75 1 .54 0.66 1 69 23 1.02 1 .19 0.94 1 29 0.86 1 .40 0.77 1 .53 0.70 1 67 24 1.04 1 .20 0.96 1 30 0.88 1 .41 0.80 1 .53 0.72 1 66 25 1.05 1 .21 0.98 1 30 0.90 1 .41 0.83 1 .52 0.75 1 65 26 1.07 1 .22 1.00 1 31 0.93 1 .41 0.85 1 .52 0.78 1 64 27 1.09 1 .23 1.02 1 32 0.95 1 .41 0.88 1 .51 0.81 1 63 28 1.10 1 .24 1.04 1 32 0.97 1 .41 0.90 1 .51 0.83 1 62 29 1.12 1 .25 1.05 1 33 0.99 1 .42 0.92 1 .51 0.85 1 61 30 1.13 1 .26 1.07 1 34 1.01 1 .42 0.94 1 .51 0.88 1 61 31 1.15 1 .27 1.08 1 34 1.02 1 .42 0.96 1 .51 0.90 1 60 32 1.16 1 .28 1.10 1 35 1.04 1 .43 0.98 1 .51 0.92 1 60 33 1.17 1 .29 1.11 1 36 1.05 1 .43 1.00 1 .51 0.94 1 59 34 1.18 1 .30 1.13 1 36 1.07 1 .43 1.01 1 .51 0.95 1 59 35 1.19 1 .31 1.14 1 37 1.08 1 .44 1.03 1 .51 0.97 1 59 36 1.21 1 .32 1.15 1 38 1.10 1 .44 1.04 1 .51 0.99 1 59 37 1.22 1 .32 1.16 1 38 1.11 1 .45 1.06 1 .51 1.00 1 59 38 1.23 1 .33 1.18 1 39 1.12 1 .45 1.07 1 .52 1.02 1 58 39 1.24 1 .34 1.19 1 39 1.14 1 .45 1.09 1 .52 1.03 1 58 40 1.25 1 .34 1.20 1 40 1.15 1 .46 1.10 1 .52 1.05 1 58 45 1.29 1 .38 1.24 1 42 1.20 1 .48 1.16 1 .53 1.11 1 58 50 1.32 1 .40 1.28 1 45 1.24 1 .49 1.20 1 .54 1.16 1 59 55 1.36 1 .43 1.32 1 47 1.28 1 .51 1.25 1 .55 1.21 1 59 60 1.38 1 .45 1.35 1 48 1.32 1 .52 1.28 1 .56 1.25 1 60 65 1.41 1 .47 1.38 1 50 1.35 1 .53 1.31 1 .57 1.28 1 61 70 1.43 1 .49 1.40 1 52 1.37 1 .55 1.34 1 .58 1.31 1 61 75 1.45 1 .50 1.42 1 53 1.39 1 .56 1.37 1 .59 1.34 1 62 80 1.47 1 .52 1.44 1 54 1.42 1 .57 1.39 1 .60 1.36 1 62 85 1.48 1 .53 1.46 1 55 1.43 1 .58 1.41 1 .60 1.39 1 63 90 1.50 1 .54 1.47 1 56 1.45 1 .59 1.43 1 .61 1.41 1 64 95 1.51 1 .55 1.49 1 57 1.47 1 .60 1.45 1 .62 1.42 1 64 100 1.52 1 .56 1.50 1 58 1.48 1 .60 1.46 1 .63 1.44 1 65 Source: J. Durbin and G. S. Watson, "Testing for Serial Correlation in Least Squares Regression," Biometrika, Vol. 38, 1951, pp. 159-171. Reprinted with permission of the Biometrika trustees. Note: N = number of observations, K= number of explanatory variables excluding the constant term. It is assumed that the equation contains a constant term and no lagged dependent variables. 549