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Bộ mơn Tốn – Thống kê Bài giảng Kinh tế lượng PHỤ LỤC: CÁC BẢNG THỐNG KÊ Bảng phụ lục I: Bảng giá trị tới hạn phân phối t (student): 𝑃(𝑡 > 𝑡𝛼 (𝑘)) = 𝛼 ℎ𝑎𝑦: 𝑃(|𝑡| > 𝑡𝛼 (𝑘)) = 2𝛼 𝛼 0.001 0.002 0.005 0.01 0.02 0.025 0.05 0.1 0.2 318.309 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.375 3.365 3.356 3.348 3.340 3.333 3.326 3.319 3.313 3.307 3.301 3.296 3.291 3.286 3.281 3.277 3.273 3.269 3.265 159.153 15.764 8.053 5.951 5.030 4.524 4.207 3.991 3.835 3.716 3.624 3.550 3.489 3.438 3.395 3.358 3.326 3.298 3.273 3.251 3.231 3.214 3.198 3.183 3.170 3.158 3.147 3.136 3.127 3.118 3.109 3.102 3.094 3.088 3.081 3.075 3.070 3.064 3.059 3.055 3.050 3.046 3.042 3.038 3.034 3.030 3.027 3.024 3.021 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704 2.701 2.698 2.695 2.692 2.690 2.687 2.685 2.682 2.680 31.821 6.965 4.541 3.474 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.453 2.449 2.445 2.441 2.438 2.434 2.431 2.429 2.426 2.423 2.421 2.418 2.416 2.414 2.412 2.410 2.408 2.407 2.405 15.895 4.849 3.482 2.999 2.757 2.612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.205 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.144 2.141 2.138 2.136 2.133 2.131 2.129 2.127 2.125 2.123 2.121 2.120 2.118 2.116 2.115 2.114 2.112 2.211 2.110 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2.024 2.023 2.021 2.020 2.018 2.017 2.015 2.014 2.013 2.012 2.011 2.010 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.696 1.694 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.684 1.683 1.682 1.681 1.680 1.679 1.679 1.678 1.677 1.677 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.309 1.308 1.307 1.306 1.306 1.305 1.304 1.304 1.303 1.303 1.302 1.302 1.301 1.301 1.300 1.300 1.299 1.299 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.853 0.853 0.853 0.852 0.852 0.852 0.851 0.851 0.851 0.851 0.850 0.850 0.850 0.850 0.850 0.850 0.849 0.849 0.849 k 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 < 145 > Bộ môn Toán – Thống kê Bài giảng Kinh tế lượng Bảng giá trị tới hạn 𝒕𝜶 (𝒌) phân phối Student (tiếp theo) 𝛼 0.001 0.002 0.005 0.01 0.02 0.025 0.05 0.1 0.2 50 51 52 53 54 55 56 57 58 59 60 61 3.261 3.258 3.255 3.251 3.248 3.245 3.242 3.239 3.237 3.234 3.232 3.229 3.018 3.015 3.012 3.009 3.007 3.005 3.002 3.000 2.998 2.996 2.994 2.992 2.678 2.676 2.674 2.672 2.670 2.668 2.667 2.665 2.663 2.662 2.660 2.659 2.403 2.402 2.400 2.399 2.397 2.396 2.395 2.394 2.392 2.391 2.390 2.389 2.109 2.108 2.107 2.106 2.105 2.104 2.103 2.102 2.101 2.100 2.099 2.099 2.009 2.008 2.007 2.006 2.005 2.004 2.003 2.002 2.002 2.001 2.000 2.000 1.676 1.675 1.675 1.674 1.674 1.673 1.673 1.672 1.672 1.671 1.671 1.670 1.299 1.298 1.298 1.298 1.297 1.297 1.297 1.297 1.296 1.296 1.296 1.296 0.849 0.849 0.849 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 k Bảng phụ lục II: Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) phân phối F 𝑃(𝐹(𝑘, 𝑚) > 𝐹𝛼 (𝑘, 𝑚)) = 𝛼, với 𝛼 = 0.01 k m 98,503 34,116 21,198 16,258 13,745 99,000 30,817 18,000 13,274 10,925 99,166 29,457 16,694 12,060 9,780 99,249 28,710 15,977 11,392 9,148 99,299 28,237 15,522 10,967 8,746 99,333 27,911 15,207 10,672 8466 99,356 27,672 14,976 10,456 8,260 99,374 27,489 14,799 10,289 8,102 10 11 12,246 11,259 10,561 10,044 9,646 9,547 8,649 8,022 7,559 7,206 8,451 7,591 6,992 6,552 6,217 7,847 7,006 6,422 5,994 5,668 7,460 6,632 6,057 5,636 5,316 7,191 6,371 5,802 5,386 5,069 6,993 6,178 5,613 5,200 4,886 6,840 6,029 5,467 5,057 4,744 12 13 14 15 16 9,330 9,074 8,862 8,683 8,531 6,927 6,701 6,515 6,359 6,226 5,953 5,739 5,564 5,417 5,292 5,412 5,205 5,035 4,893 4,773 5,064 4,862 4,695 4,556 4,437 4,821 4,620 4,456 4,318 4,202 4,640 4,441 4,278 4,142 4,026 4,499 4,302 4,140 4,004 3,890 17 18 19 20 21 8,400 8,285 8,185 8,096 8,017 6,112 6,013 5,926 5,849 5,780 5,185 5,092 5,010 4,938 4,874 4,669 4,579 4,500 4,431 4,369 4,336 4,248 4,171 4,103 4,042 4,102 4,015 3,939 3,871 3,812 3,927 3,841 3,765 3,699 3,640 3,791 3,705 3,631 3,564 3,506 22 23 24 25 26 7,945 7,881 7,823 7,770 7,721 5,719 5,664 5,614 5,568 5,526 4,817 4,765 4,718 4,675 4,637 4,313 4,264 4,218 4,177 4,140 3,988 3,939 3,895 3,855 3,818 3,758 3,710 3,667 3,627 3,591 3,587 3,539 3,496 3,457 3,421 3,453 3,406 3,363 3,324 3,288 27 28 29 30 7,677 7,636 7,598 7,562 5,488 5,453 5,420 5,390 4,601 4,568 4,538 4,510 4,106 4,074 4,045 4,018 3,785 3,754 3,725 3,699 3,558 3,528 3,499 3,473 3,388 3,358 3,330 3,304 3,256 3,226 3,198 3,173 < 146 > Bộ mơn Tốn – Thống kê Bài giảng Kinh tế lượng Bảng giá trị tới hạn 𝐅𝛂 (𝐤, 𝐦) phân phối F, với 𝛂 = 𝟎 𝟎𝟏 (tiếp theo) k m 10 11 12 13 14 15 16 99,388 27,345 99,399 27,229 99,408 27,133 99,416 27,052 99,422 26,983 99,428 26,924 99,433 26,872 99,437 26,827 14,659 10,158 7,976 14,546 10,051 7,874 14,452 9,963 7,790 14,374 9,888 7,718 14,307 9,825 7,657 14,249 9,770 7,605 14,198 9,722 7,559 14,154 9,680 7,519 6,719 5,911 6,620 5,814 6,538 5,734 6,469 5,667 6,410 5,609 6,359 5,559 6,314 5,515 6,275 5,477 10 11 5,351 4,942 4,632 5,257 4,849 4,539 5,178 4,772 4,462 5,111 4,706 4,397 5,055 4,650 4,342 5,005 4,601 4,293 4,962 4,558 4,251 4,924 4,520 4,213 12 13 4,388 4,191 4,296 4,100 4,220 4,025 4,155 3,960 4,100 3,905 4,052 3,857 4,010 3,815 3,972 3,778 14 15 16 4,030 3,895 3,780 3,939 3,805 3,691 3,864 3,730 3,616 3,800 3,666 3,553 3,745 3,612 3,498 3,698 3,564 3,451 3,656 3,522 3,409 3,619 3,485 3,372 17 18 3,682 3,597 3,593 3,508 3,519 3,434 3,455 3,371 3,401 3,316 3,353 3,269 3,312 3,227 3,275 3,190 19 20 21 3,523 3,457 3,398 3,434 3,368 3,310 3,360 3,294 3,236 3,297 3,231 3,173 3,242 3,177 3,119 3,195 3,130 3,072 3,153 3,088 3,030 3,116 3,051 2,993 22 23 3,346 3,299 3,258 3,211 3,184 3,137 3,121 3,074 3,067 3,020 3,019 2,973 2,978 2,931 2,941 2,894 24 25 26 3,256 3,217 3,182 3,168 3,129 3,094 3,094 3,056 3,021 3,032 2,993 2,958 2,977 2,939 2,904 2,930 2,892 2,857 2,889 2,850 2,815 2,852 2,813 2,778 27 28 3,149 3,120 3,062 3,032 2,988 2,959 2,926 2,896 2,871 2,842 2,824 2,795 2,783 2,753 2,746 2,716 29 30 31 3,092 3,067 3,043 3,005 2,979 2,955 2,931 2,906 2,882 2,868 2,843 2,820 2,814 2,789 2,765 2,767 2,742 2,718 2,726 2,700 2,677 2,689 2,663 2,640 32 33 3,021 3,000 2,934 2,913 2,860 2,840 2,798 2,777 2,744 2,723 2,696 2,676 2,655 2,634 2,618 2,597 < 147 > Bộ mơn Tốn – Thống kê Bài giảng Kinh tế lượng Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) phân phối F, với 𝜶 = 𝟎 𝟎𝟓 k m 18,513 19,000 19,164 19,247 19,296 19,330 19,353 19,371 10,128 9,552 9,277 9,117 9,013 8,941 8,887 8,845 7,709 6,944 6,591 6,388 6,256 6,163 6,094 6,041 6,608 5,786 5,409 5,192 5,050 4,950 4,876 4,818 5,987 5,143 4,757 4,534 4,387 4,284 4,207 4,147 5,591 4,737 4,347 4,120 3,972 3,866 3,787 3,726 5,318 4,459 4,066 3,838 3,687 3,581 3,500 3,438 5,117 4,256 3,863 3,633 3,482 3,374 3,293 3,230 10 4,965 4,103 3,708 3,478 3,326 3,217 3,135 3,072 11 4,844 3,982 3,587 3,357 3,204 3,095 3,012 2,948 12 4,747 3,885 3,490 3,259 3,106 2,996 2,913 2,849 13 4,667 3,806 3,411 3,179 3,025 2,915 2,832 2,767 14 4,600 3,739 3,344 3,112 2,958 2,848 2,764 2,699 15 4,543 3,682 3,287 3,056 2,901 2,790 2,707 2,641 16 4,494 3,634 3,239 3,007 2,852 2,741 2,657 2,591 17 4,451 3,592 3,197 2,965 2,810 2,699 2,614 2,548 18 4,414 3,555 3,160 2,928 2,773 2,661 2,577 2,510 19 4,381 3,522 3,127 2,895 2,740 2,628 2,544 2,477 20 4,351 3,493 3,098 2,866 2,711 2,599 2,514 2,447 21 4,325 3,467 3,072 2,840 2,685 2,573 2,488 2,420 22 4,301 3,443 3,049 2,817 2,661 2,549 2,464 2,397 23 4,279 3,422 3,028 2,796 2,640 2,528 2,442 2,375 24 4,260 3,403 3,009 2,776 2,621 2,508 2,423 2,355 25 4,242 3,385 2,991 2,759 2,603 2,490 2,405 2,337 26 4,225 3,369 2,975 2,743 2,587 2,474 2,388 2,321 27 4,210 3,354 2,960 2,728 2,572 2,459 2,373 2,305 28 4,196 3,340 2,947 2,714 2,558 2,445 2,359 2,291 29 4,183 3,328 2,934 2,701 2,545 2,432 2,346 2,278 30 4,171 3,316 2,922 2,690 2,534 2,421 2,334 2,266 < 148 > Bộ môn Toán – Thống kê Bài giảng Kinh tế lượng Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) phân phối F, với 𝜶 = 𝟎 𝟎𝟓 (tiếp theo) k m 10 11 12 13 14 15 16 19,385 19,396 19,405 19,413 19,419 19,424 19,429 19,433 8,812 8,786 8,763 8,745 8,729 8,715 8,703 8,692 5,999 5,964 5,936 5,912 5,891 5,873 5,858 5,844 4,772 4,735 4,704 4,678 4,655 4,636 4,619 4,604 4,099 4,060 4,027 4,000 3,976 3,956 3,938 3,922 3,677 3,637 3,603 3,575 3,550 3,529 3,511 3,494 3,388 3,347 3,313 3,284 3,259 3,237 3,218 3,202 3,179 3,137 3,102 3,073 3,048 3,025 3,006 2,989 10 3,020 2,978 2,943 2,913 2,887 2,865 2,845 2,828 11 2,896 2,854 2,818 2,788 2,761 2,739 2,719 2,701 12 2,796 2,753 2,717 2,687 2,660 2,637 2,617 2,599 13 2,714 2,671 2,635 2,604 2,577 2,554 2,533 2,515 14 2,646 2,602 2,565 2,534 2,507 2,484 2,463 2,445 15 2,588 2,544 2,507 2,475 2,448 2,424 2,403 2,385 16 2,538 2,494 2,456 2,425 2,397 2,373 2,352 2,333 17 2,494 2,450 2,413 2,381 2,353 2,329 2,308 2,289 18 2,456 2,412 2,374 2,342 2,314 2,290 2,269 2,250 19 2,423 2,378 2,340 2,308 2,280 2,256 2,234 2,215 20 2,393 2,348 2,310 2,278 2,250 2,225 2,203 2,184 21 2,366 2,321 2,283 2,250 2,222 2,197 2,176 2,156 22 2,342 2,297 2,259 2,226 2,198 2,173 2,151 2,131 23 2,320 2,275 2,236 2,204 2,175 2,150 2,128 2,109 24 2,300 2,255 2,216 2,183 2,155 2,130 2,108 2,088 25 2,282 2,236 2,198 2,165 2,136 2,111 2,089 2,069 26 2,265 2,220 2,181 2,148 2,119 2,094 2,072 2,052 27 2,250 2,204 2,166 2,132 2,103 2,078 2,056 2,036 28 2,236 2,190 2,151 2,118 2,089 2,064 2,041 2,021 29 2,223 2,177 2,138 2,104 2,075 2,050 2,027 2,007 30 2,211 2,165 2,126 2,092 2,063 2,037 2,015 1,995 31 2,199 2,153 2,114 2,080 2,051 2,026 2,003 1,983 32 2,189 2,142 2,103 2,070 2,040 2,015 1,992 1,972 33 2,179 2,133 2,093 2,060 2,030 2,004 1,982 1,961 < 149 > Bộ mơn Tốn – Thống kê Bài giảng Kinh tế lượng Bảng phụ lục III: Giá trị tới hạn 𝝌𝟐𝜶 (𝒌) phân phối Chi – square: 𝑃(𝜒 (𝑘) > 𝜒𝛼2 (𝑘)) = 𝛼 𝛼 k 0,01 0,99 0,025 0,975 0,05 0,95 6.6349 0.0002 5.0239 0.0010 3.8415 0.0039 9.2103 0.0201 7.3778 0.0506 5.9915 0.1026 11.3449 0.1148 9.3484 0.2158 7.8147 0.3518 13.2767 0.2971 11.1433 0.4844 9.4877 0.7107 15.0863 0.5543 12.8325 0.8312 11.0705 1.1455 16.8119 0.8721 14.4494 1.2373 12.5916 1.6354 18.4753 1.2390 16.0128 1.6899 14.0671 2.1673 20.0902 1.6465 17.5345 2.1797 15.5073 2.7326 21.6660 2.0879 19.0228 2.7004 16.9190 3.3251 10 23.2093 2.5582 20.4832 3.2470 18.3070 3.9403 11 24.7250 3.0535 21.9200 3.8157 19.6751 4.5748 12 26.2170 3.5706 23.3367 4.4038 21.0261 5.2260 13 27.6882 4.1069 24.7356 5.0088 22.3620 5.8919 14 29.1412 4.6604 26.1189 5.6287 23.6848 6.5706 15 30.5779 5.2293 27.4884 6.2621 24.9958 7.2609 16 31.9999 5.8122 28.8454 6.9077 26.2962 7.9616 17 33.4087 6.4078 30.1910 7.5642 27.5871 8.6718 18 34.8053 7.0149 31.5264 8.2307 28.8693 9.3905 19 36.1909 7.6327 32.8523 8.9065 30.1435 10.1170 20 37.5662 8.2604 34.1696 9.5908 31.4104 10.8508 21 38.9322 8.8972 35.4789 10.2829 32.6706 11.5913 22 40.2894 9.5425 36.7807 10.9823 33.9244 12.3380 23 41.6384 10.1957 38.0756 11.6886 35.1725 13.0905 24 42.9798 10.8564 39.3641 12.4012 36.4150 13.8484 25 44.3141 11.5240 40.6465 13.1197 37.6525 14.6114 26 45.6417 12.1981 41.9232 13.8439 38.8851 15.3792 27 46.9629 12.8785 43.1945 14.5734 40.1133 16.1514 28 48.2782 13.5647 44.4608 15.3079 41.3371 16.9279 < 150 > Bộ mơn Tốn – Thống kê Bài giảng Kinh tế lượng Giá trị tới hạn 𝝌𝟐𝜶 (𝒌) phân phối Chi – square (tiếp theo) 𝛼 k 0.01 0.99 0.025 0.975 0.05 0.95 29 49.5879 14.2565 45.7223 16.0471 42.5570 17.7084 30 50.8922 14.9535 46.9792 16.7908 43.7730 18.4927 31 52.1914 15.6555 48.2319 17.5387 44.9853 19.2806 32 53.4858 16.3622 49.4804 18.2908 46.1943 20.0719 33 54.7755 17.0735 50.7251 19.0467 47.3999 20.8665 34 56.0609 17.7891 51.9660 19.8063 48.6024 21.6643 35 57.3421 18.5089 53.2033 20.5694 49.8018 22.4650 36 58.6192 19.2327 54.4373 21.3359 50.9985 23.2686 37 59.8925 19.9602 55.6680 22.1056 52.1923 24.0749 38 61.1621 20.6914 56.8955 22.8785 53.3835 24.8839 39 62.4281 21.4262 58.1201 23.6543 54.5722 25.6954 40 63.6907 22.1643 59.3417 24.4330 55.7585 26.5093 41 64.9501 22.9056 60.5606 25.2145 56.9424 27.3256 42 66.2062 23.6501 61.7768 25.9987 58.1240 28.1440 43 67.4593 24.3976 62.9904 26.7854 59.3035 28.9647 44 68.7095 25.1480 64.2015 27.5746 60.4809 29.7875 45 69.9568 25.9013 65.4102 28.3662 61.6562 30.6123 46 71.2014 26.6572 66.6165 29.1601 62.8296 31.4390 47 72.4433 27.4158 67.8206 29.9562 64.0011 32.2676 48 73.6826 28.1770 69.0226 30.7545 65.1708 33.0981 49 74.9195 28.9406 70.2224 31.5549 66.3386 33.9303 50 76.1539 29.7067 71.4202 32.3574 67.5048 34.7643 51 77.3860 30.4750 72.6160 33.1618 68.6693 35.5999 52 78.6158 31.2457 73.8099 33.9681 69.8322 36.4371 53 79.8433 32.0185 75.0019 34.7763 70.9935 37.2759 54 81.0688 32.7934 76.1920 35.5863 72.1532 38.1162 55 82.2921 33.5705 77.3805 36.3981 73.3115 38.9580 56 83.5134 34.3495 78.5672 37.2116 74.4683 39.0813 57 84.7328 35.1305 79.7522 38.0267 75.6237 40.6459 58 85.9502 35.9135 80.9356 38.8435 76.7778 41.4920 59 87.1657 36.6982 82.1174 39.6619 77.9305 42.3393 60 88.3794 37.4849 83.2977 40.4817 79.0819 43.1880 < 151 >