Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
1
Probability Distribution Function of the Standard Normal Distribution
Z:
(
)
0
x
Z
P
<
(six significant digits)
x
0
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09
0,0
0,500000 0,503989 0,507978 0,511966 0,515953 0,519939 0,523922 0,527903 0,531881 0,535856
0,1
0,539828 0,543795 0,547758 0,551717 0,555670 0,559618 0,563559 0,567495 0,571424 0,575345
0,2
0,579260 0,583166 0,587064 0,590954 0,594835 0,598706 0,602568 0,606420 0,610261 0,614092
0,3
0,617911 0,621720 0,625516 0,629300 0,633072 0,636831 0,640576 0,644309 0,648027 0,651732
0,4
0,655422 0,659097 0,662757 0,666402 0,670031 0,673645 0,677242 0,680822 0,684386 0,687933
0,5
0,691462 0,694974 0,698468 0,701944 0,705401 0,708840 0,712260 0,715661 0,719043 0,722405
0,6
0,725747 0,729069 0,732371 0,735653 0,738914 0,742154 0,745373 0,748571 0,751748 0,754903
0,7
0,758036 0,761148 0,764238 0,767305 0,770350 0,773373 0,776373 0,779350 0,782305 0,785236
0,8
0,788145 0,791030 0,793892 0,796731 0,799546 0,802337 0,805105 0,807850 0,810570 0,813267
0,9
0,815940 0,818589 0,821214 0,823814 0,826391 0,828944 0,831472 0,833977 0,836457 0,838913
1,0
0,841345 0,843752 0,846136 0,848495 0,850830 0,853141 0,855428 0,857690 0,859929 0,862143
1,1
0,864334 0,866500 0,868643 0,870762 0,872857 0,874928 0,876976 0,879000 0,881000 0,882977
1,2
0,884930 0,886861 0,888768 0,890651 0,892512 0,894350 0,896165 0,897958 0,899727 0,901475
1,3
0,903200 0,904902 0,906582 0,908241 0,909877 0,911492 0,913085 0,914657 0,916207 0,917736
1,4
0,919243 0,920730 0,922196 0,923641 0,925066 0,926471 0,927855 0,929219 0,930563 0,931888
1,5
0,933193 0,934478 0,935745 0,936992 0,938220 0,939429 0,940620 0,941792 0,942947 0,944083
1,6
0,945201 0,946301 0,947384 0,948449 0,949497 0,950529 0,951543 0,952540 0,953521 0,954486
1,7
0,955435 0,956367 0,957284 0,958185 0,959070 0,959941 0,960796 0,961636 0,962462 0,963273
1,8
0,964070 0,964852 0,965620 0,966375 0,967116 0,967843 0,968557 0,969258 0,969946 0,970621
1,9
0,971283 0,971933 0,972571 0,973197 0,973810 0,974412 0,975002 0,975581 0,976148 0,976705
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
2
Probability Distribution Function of the Standard Normal Distribution
Z:
(
)
0
x
Z
P
<
(six significant digits)
x
0
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09
2,0
0,977250 0,977784 0,978308 0,978822 0,979325 0,979818 0,980301 0,980774 0,981237 0,981691
2,1
0,982136 0,982571 0,982997 0,983414 0,983823 0,984222 0,984614 0,984997 0,985371 0,985738
2,2
0,986097 0,986447 0,986791 0,987126 0,987455 0,987776 0,988089 0,988396 0,988696 0,988989
2,3
0,989276 0,989556 0,989830 0,990097 0,990358 0,990613 0,990863 0,991106 0,991344 0,991576
2,4
0,991802 0,992024 0,992240 0,992451 0,992656 0,992857 0,993053 0,993244 0,993431 0,993613
2,5
0,993790 0,993963 0,994132 0,994297 0,994457 0,994614 0,994766 0,994915 0,995060 0,995201
2,6
0,995339 0,995473 0,995604 0,995731 0,995855 0,995975 0,996093 0,996207 0,996319 0,996427
2,7
0,996533 0,996636 0,996736 0,996833 0,996928 0,997020 0,997110 0,997197 0,997282 0,997365
2,8
0,997445 0,997523 0,997599 0,997673 0,997744 0,997814 0,997882 0,997948 0,998012 0,998074
2,9
0,998134 0,998193 0,998250 0,998305 0,998359 0,998411 0,998462 0,998511 0,998559 0,998605
3,0
0,998650 0,998694 0,998736 0,998777 0,998817 0,998856 0,998893 0,998930 0,998965 0,998999
3,1
0,999032 0,999065 0,999096 0,999126 0,999155 0,999184 0,999211 0,999238 0,999264 0,999289
3,2
0,999313 0,999336 0,999359 0,999381 0,999402 0,999423 0,999443 0,999462 0,999481 0,999499
3,3
0,999517 0,999534 0,999550 0,999566 0,999581 0,999596 0,999610 0,999624 0,999638 0,999651
3,4
0,999663 0,999675 0,999687 0,999698 0,999709 0,999720 0,999730 0,999740 0,999749 0,999758
3,5
0,999767 0,999776 0,999784 0,999792 0,999800 0,999807 0,999815 0,999822 0,999828 0,999835
3,6
0,999841 0,999847 0,999853 0,999858 0,999864 0,999869 0,999874 0,999879 0,999883 0,999888
3,7
0,999892 0,999896 0,999900 0,999904 0,999908 0,999912 0,999915 0,999918 0,999922 0,999925
3,8
0,999928 0,999931 0,999933 0,999936 0,999938 0,999941 0,999943 0,999946 0,999948 0,999950
3,9
0,999952 0,999954 0,999956 0,999958 0,999959 0,999961 0,999963 0,999964 0,999966 0,999967
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
3
Two-Sided Critical Values
α
t of the Student's t Distribution:
(
)
α
α
=
> t
T
P
,
where
α is the significance level
(six significant digits)
DF
α =
0,9
α =
0,7
α =
0,5
α =
0,3
α =
0,1
α =
0,05
α =
0,02
α =
0,01
α =
0,002
α =
0,001
1
0,158384 0,509525 1,00000 1,96261 6,31375 12,7062 31,8205 63,6567 318,309 636,619
2
0,142134 0,444750 0,816497 1,38621 2,91999 4,30265 6,96456 9,92484 22,3271 31,5991
3
0,136598 0,424202 0,764892 1,24978 2,35336 3,18245 4,54070 5,84091 10,2145 12,9240
4
0,133830 0,414163 0,740697 1,18957 2,13185 2,77645 3,74695 4,60409 7,17318 8,61030
5
0,132175 0,408229 0,726687 1,15577 2,01505 2,57058 3,36493 4,03214 5,89343 6,86883
6
0,131076 0,404313 0,717558 1,13416 1,94318 2,44691 3,14267 3,70743 5,20763 5,95882
7
0,130293 0,401538 0,711142 1,11916 1,89458 2,36462 2,99795 3,49948 4,78529 5,40788
8
0,129707 0,399469 0,706387 1,10815 1,85955 2,30600 2,89646 3,35539 4,50079 5,04131
9
0,129253 0,397868 0,702722 1,09972 1,83311 2,26216 2,82144 3,24984 4,29681 4,78091
10
0,128890 0,396591 0,699812 1,09306 1,81246 2,22814 2,76377 3,16927 4,14370 4,58689
11
0,128594 0,395551 0,697445 1,08767 1,79588 2,20099 2,71808 3,10581 4,02470 4,43698
12
0,128347 0,394686 0,695483 1,08321 1,78229 2,17881 2,68100 3,05454 3,92963 4,31779
13
0,128139 0,393955 0,693829 1,07947 1,77093 2,16037 2,65031 3,01228 3,85198 4,22083
14
0,127961 0,393331 0,692417 1,07628 1,76131 2,14479 2,62449 2,97684 3,78739 4,14045
15
0,127806 0,392790 0,691197 1,07353 1,75305 2,13145 2,60248 2,94671 3,73283 4,07277
16
0,127671 0,392318 0,690132 1,07114 1,74588 2,11991 2,58349 2,92078 3,68615 4,01500
17
0,127552 0,391902 0,689195 1,06903 1,73961 2,10982 2,56693 2,89823 3,64577 3,96513
18
0,127447 0,391533 0,688364 1,06717 1,73406 2,10092 2,55238 2,87844 3,61048 3,92165
19
0,127352 0,391202 0,687621 1,06551 1,72913 2,09302 2,53948 2,86093 3,57940 3,88341
20
0,127267 0,390906 0,686954 1,06402 1,72472 2,08596 2,52798 2,84534 3,55181 3,84952
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
4
Two-Sided Critical Values
α
t of the Student's t Distribution:
(
)
α
α
=
> t
T
P
,
where
α is the significance level
(six significant digits)
DF
α =
0,9
α =
0,7
α =
0,5
α =
0,3
α =
0,1
α =
0,05
α =
0,02
α =
0,01
α =
0,002
α =
0,001
21
0,127190 0,390637 0,686352 1,06267 1,72074 2,07961 2,51765 2,83136 3,52715 3,81928
22
0,127120 0,390394 0,685805 1,06145 1,71714 2,07387 2,50832 2,81876 3,50499 3,79213
23
0,127056 0,390171 0,685306 1,06034 1,71387 2,06866 2,49987 2,80734 3,48496 3,76763
24
0,126998 0,389967 0,684850 1,05932 1,71088 2,06390 2,49216 2,79694 3,46678 3,74540
25
0,126944 0,389780 0,684430 1,05838 1,70814 2,05954 2,48511 2,78744 3,45019 3,72514
26
0,126895 0,389607 0,684043 1,05752 1,70562 2,05553 2,47863 2,77871 3,43500 3,70661
27
0,126849 0,389448 0,683685 1,05673 1,70329 2,05183 2,47266 2,77068 3,42103 3,68959
28
0,126806 0,389299 0,683353 1,05599 1,70113 2,04841 2,46714 2,76326 3,40816 3,67391
29
0,126767 0,389161 0,683044 1,05530 1,69913 2,04523 2,46202 2,75639 3,39624 3,65941
30
0,126730 0,389032 0,682756 1,05466 1,69726 2,04227 2,45726 2,75000 3,38518 3,64596
40
0,126462 0,388100 0,680673 1,05005 1,68385 2,02108 2,42326 2,70446 3,30688 3,55097
50
0,126301 0,387542 0,679428 1,04729 1,67591 2,00856 2,40327 2,67779 3,26141 3,49601
60
0,126194 0,387170 0,678601 1,04547 1,67065 2,00030 2,39012 2,66028 3,23171 3,46020
70
0,126118 0,386905 0,678011 1,04417 1,66691 1,99444 2,38081 2,64790 3,21079 3,43501
80
0,126061 0,386707 0,677569 1,04320 1,66412 1,99006 2,37387 2,63869 3,19526 3,41634
90
0,126016 0,386552 0,677225 1,04244 1,66196 1,98667 2,36850 2,63157 3,18327 3,40194
100
0,125981 0,386429 0,676951 1,04184 1,66023 1,98397 2,36422 2,62589 3,17374 3,39049
110
0,125952 0,386328 0,676727 1,04134 1,65882 1,98177 2,36073 2,62126 3,16598 3,38118
120
0,125928 0,386244 0,676540 1,04093 1,65765 1,97993 2,35782 2,61742 3,15954 3,37345
infinity
0,125661 0,385320 0,674490 1,03643 1,64485 1,95996 2,32635 2,57583 3,09023 3,29053
1
As the number of degrees of freedom approaches infinity, the Student’s t Distribution approaches Standard Normal Distribution.
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
5
Right-Hand-Sided Critical Values
α
F of the F Distribution:
(
)
α
α
=
> F
F
P
,
=
α
0,05
,
where
α is the significance level
(four significant digits)
n
2
n
1
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 30 50 70 90 100
1
161,4 199,5 215,7 224,6 230,2 234,0 236,8 238,9 240,5 241,9 243,9 245,4 246,5 247,3 248,0 250,1 251,8 252,5 252,9 253,0
2
18,51 19,00 19,16 19,25 19,30 19,33 19,35 19,37 19,38 19,40 19,41 19,42 19,43 19,44 19,45 19,46 19,48 19,48 19,48 19,49
3
10,13 9,552 9,277 9,117 9,013 8,941 8,887 8,845 8,812 8,786 8,745 8,715 8,692 8,675 8,660 8,617 8,581 8,566 8,557 8,554
4
7,709 6,944 6,591 6,388 6,256 6,163 6,094 6,041 5,999 5,964 5,912 5,873 5,844 5,821 5,803 5,746 5,699 5,679 5,668 5,664
5
6,608 5,786 5,409 5,192 5,050 4,950 4,876 4,818 4,772 4,735 4,678 4,636 4,604 4,579 4,558 4,496 4,444 4,422 4,409 4,405
6
5,987 5,143 4,757 4,534 4,387 4,284 4,207 4,147 4,099 4,060 4,000 3,956 3,922 3,896 3,874 3,808 3,754 3,730 3,716 3,712
7
5,591 4,737 4,347 4,120 3,972 3,866 3,787 3,726 3,677 3,637 3,575 3,529 3,494 3,467 3,445 3,376 3,319 3,294 3,280 3,275
8
5,318 4,459 4,066 3,838 3,687 3,581 3,500 3,438 3,388 3,347 3,284 3,237 3,202 3,173 3,150 3,079 3,020 2,994 2,980 2,975
9
5,117 4,256 3,863 3,633 3,482 3,374 3,293 3,230 3,179 3,137 3,073 3,025 2,989 2,960 2,936 2,864 2,803 2,776 2,761 2,756
10
4,965 4,103 3,708 3,478 3,326 3,217 3,135 3,072 3,020 2,978 2,913 2,865 2,828 2,798 2,774 2,700 2,637 2,610 2,594 2,588
11
4,844 3,982 3,587 3,357 3,204 3,095 3,012 2,948 2,896 2,854 2,788 2,739 2,701 2,671 2,646 2,570 2,507 2,478 2,462 2,457
12
4,747 3,885 3,490 3,259 3,106 2,996 2,913 2,849 2,796 2,753 2,687 2,637 2,599 2,568 2,544 2,466 2,401 2,372 2,356 2,350
13
4,667 3,806 3,411 3,179 3,025 2,915 2,832 2,767 2,714 2,671 2,604 2,554 2,515 2,484 2,459 2,380 2,314 2,284 2,267 2,261
14
4,600 3,739 3,344 3,112 2,958 2,848 2,764 2,699 2,646 2,602 2,534 2,484 2,445 2,413 2,388 2,308 2,241 2,210 2,193 2,187
15
4,543 3,682 3,287 3,056 2,901 2,790 2,707 2,641 2,588 2,544 2,475 2,424 2,385 2,353 2,328 2,247 2,178 2,147 2,130 2,123
16
4,494 3,634 3,239 3,007 2,852 2,741 2,657 2,591 2,538 2,494 2,425 2,373 2,333 2,302 2,276 2,194 2,124 2,093 2,075 2,068
17
4,451 3,592 3,197 2,965 2,810 2,699 2,614 2,548 2,494 2,450 2,381 2,329 2,289 2,257 2,230 2,148 2,077 2,045 2,027 2,020
18
4,414 3,555 3,160 2,928 2,773 2,661 2,577 2,510 2,456 2,412 2,342 2,290 2,250 2,217 2,191 2,107 2,035 2,003 1,985 1,978
19
4,381 3,522 3,127 2,895 2,740 2,628 2,544 2,477 2,423 2,378 2,308 2,256 2,215 2,182 2,155 2,071 1,999 1,966 1,947 1,940
20
4,351 3,493 3,098 2,866 2,711 2,599 2,514 2,447 2,393 2,348 2,278 2,225 2,184 2,151 2,124 2,039 1,966 1,932 1,913 1,907
21
4,325 3,467 3,072 2,840 2,685 2,573 2,488 2,420 2,366 2,321 2,250 2,197 2,156 2,123 2,096 2,010 1,936 1,902 1,883 1,876
22
4,301 3,443 3,049 2,817 2,661 2,549 2,464 2,397 2,342 2,297 2,226 2,173 2,131 2,098 2,071 1,984 1,909 1,875 1,856 1,849
23
4,279 3,422 3,028 2,796 2,640 2,528 2,442 2,375 2,320 2,275 2,204 2,150 2,109 2,075 2,048 1,961 1,885 1,850 1,830 1,823
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
6
Right-Hand-Sided Critical Values
α
F of the F Distribution:
(
)
α
α
=
> F
F
P
,
=
α
0,05
,
where
α is the significance level
(four significant digits)
n
2
n
1
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 30 50 70 90 100
24
4,260 3,403 3,009 2,776 2,621 2,508 2,423 2,355 2,300 2,255 2,183 2,130 2,088 2,054 2,027 1,939 1,863 1,828 1,808 1,800
25
4,242 3,385 2,991 2,759 2,603 2,490 2,405 2,337 2,282 2,236 2,165 2,111 2,069 2,035 2,007 1,919 1,842 1,807 1,787 1,779
26
4,225 3,369 2,975 2,743 2,587 2,474 2,388 2,321 2,265 2,220 2,148 2,094 2,052 2,018 1,990 1,901 1,823 1,788 1,767 1,760
27
4,210 3,354 2,960 2,728 2,572 2,459 2,373 2,305 2,250 2,204 2,132 2,078 2,036 2,002 1,974 1,884 1,806 1,770 1,749 1,742
28
4,196 3,340 2,947 2,714 2,558 2,445 2,359 2,291 2,236 2,190 2,118 2,064 2,021 1,987 1,959 1,869 1,790 1,754 1,733 1,725
29
4,183 3,328 2,934 2,701 2,545 2,432 2,346 2,278 2,223 2,177 2,104 2,050 2,007 1,973 1,945 1,854 1,775 1,738 1,717 1,710
30
4,171 3,316 2,922 2,690 2,534 2,421 2,334 2,266 2,211 2,165 2,092 2,037 1,995 1,960 1,932 1,841 1,761 1,724 1,703 1,695
31
4,160 3,305 2,911 2,679 2,523 2,409 2,323 2,255 2,199 2,153 2,080 2,026 1,983 1,948 1,920 1,828 1,748 1,711 1,689 1,681
32
4,149 3,295 2,901 2,668 2,512 2,399 2,313 2,244 2,189 2,142 2,070 2,015 1,972 1,937 1,908 1,817 1,736 1,698 1,676 1,669
33
4,139 3,285 2,892 2,659 2,503 2,389 2,303 2,235 2,179 2,133 2,060 2,004 1,961 1,926 1,898 1,806 1,724 1,686 1,665 1,657
34
4,130 3,276 2,883 2,650 2,494 2,380 2,294 2,225 2,170 2,123 2,050 1,995 1,952 1,917 1,888 1,795 1,713 1,675 1,653 1,645
35
4,121 3,267 2,874 2,641 2,485 2,372 2,285 2,217 2,161 2,114 2,041 1,986 1,942 1,907 1,878 1,786 1,703 1,665 1,643 1,635
36
4,113 3,259 2,866 2,634 2,477 2,364 2,277 2,209 2,153 2,106 2,033 1,977 1,934 1,899 1,870 1,776 1,694 1,655 1,633 1,625
37
4,105 3,252 2,859 2,626 2,470 2,356 2,270 2,201 2,145 2,098 2,025 1,969 1,926 1,890 1,861 1,768 1,685 1,646 1,623 1,615
38
4,098 3,245 2,852 2,619 2,463 2,349 2,262 2,194 2,138 2,091 2,017 1,962 1,918 1,883 1,853 1,760 1,676 1,637 1,614 1,606
39
4,091 3,238 2,845 2,612 2,456 2,342 2,255 2,187 2,131 2,084 2,010 1,954 1,911 1,875 1,846 1,752 1,668 1,628 1,606 1,597
40
4,085 3,232 2,839 2,606 2,449 2,336 2,249 2,180 2,124 2,077 2,003 1,948 1,904 1,868 1,839 1,744 1,660 1,621 1,597 1,589
50
4,034 3,183 2,790 2,557 2,400 2,286 2,199 2,130 2,073 2,026 1,952 1,895 1,850 1,814 1,784 1,687 1,599 1,558 1,534 1,525
60
4,001 3,150 2,758 2,525 2,368 2,254 2,167 2,097 2,040 1,993 1,917 1,860 1,815 1,778 1,748 1,649 1,559 1,516 1,491 1,481
70
3,978 3,128 2,736 2,503 2,346 2,231 2,143 2,074 2,017 1,969 1,893 1,836 1,790 1,753 1,722 1,622 1,530 1,486 1,459 1,450
80
3,960 3,111 2,719 2,486 2,329 2,214 2,126 2,056 1,999 1,951 1,875 1,817 1,772 1,734 1,703 1,602 1,508 1,463 1,436 1,426
90
3,947 3,098 2,706 2,473 2,316 2,201 2,113 2,043 1,986 1,938 1,861 1,803 1,757 1,720 1,688 1,586 1,491 1,445 1,417 1,407
100
3,936 3,087 2,696 2,463 2,305 2,191 2,103 2,032 1,975 1,927 1,850 1,792 1,746 1,708 1,676 1,573 1,477 1,430 1,402 1,392
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
7
Right-Hand-Sided Critical Values
α
F of the F Distribution:
(
)
α
α
=
> F
F
P
,
=
α
0,01
,
where
α is the significance level
(four significant digits)
n
2
n
1
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 30 50 70 90 100
1
4052 4999 5403 5625 5764 5859 5928 5981 6022 6056 6106 6143 6170 6192 6209 6261 6303 6321 6331 6334
2
98,50 99,00 99,17 99,25 99,30 99,33 99,36 99,37 99,39 99,40 99,42 99,43 99,44 99,44 99,45 99,47 99,48 99,48 99,49 99,49
3
34,12 30,82 29,46 28,71 28,24 27,91 27,67 27,49 27,35 27,23 27,05 26,92 26,83 26,75 26,69 26,50 26,35 26,29 26,25 26,24
4
21,20 18,00 16,69 15,98 15,52 15,21 14,98 14,80 14,66 14,55 14,37 14,25 14,15 14,08 14,02 13,84 13,69 13,63 13,59 13,58
5
16,26 13,27 12,06 11,39 10,97 10,67 10,46 10,29 10,16 10,05 9,888 9,770 9,680 9,610 9,553 9,379 9,238 9,176 9,142 9,130
6
13,75 10,92 9,780 9,148 8,746 8,466 8,260 8,102 7,976 7,874 7,718 7,605 7,519 7,451 7,396 7,229 7,091 7,032 6,998 6,987
7
12,25 9,547 8,451 7,847 7,460 7,191 6,993 6,840 6,719 6,620 6,469 6,359 6,275 6,209 6,155 5,992 5,858 5,799 5,766 5,755
8
11,26 8,649 7,591 7,006 6,632 6,371 6,178 6,029 5,911 5,814 5,667 5,559 5,477 5,412 5,359 5,198 5,065 5,007 4,975 4,963
9
10,56 8,022 6,992 6,422 6,057 5,802 5,613 5,467 5,351 5,257 5,111 5,005 4,924 4,860 4,808 4,649 4,517 4,459 4,426 4,415
10
10,04 7,559 6,552 5,994 5,636 5,386 5,200 5,057 4,942 4,849 4,706 4,601 4,520 4,457 4,405 4,247 4,115 4,058 4,025 4,014
11
9,646 7,206 6,217 5,668 5,316 5,069 4,886 4,744 4,632 4,539 4,397 4,293 4,213 4,150 4,099 3,941 3,810 3,752 3,719 3,708
12
9,330 6,927 5,953 5,412 5,064 4,821 4,640 4,499 4,388 4,296 4,155 4,052 3,972 3,909 3,858 3,701 3,569 3,511 3,478 3,467
13
9,074 6,701 5,739 5,205 4,862 4,620 4,441 4,302 4,191 4,100 3,960 3,857 3,778 3,716 3,665 3,507 3,375 3,317 3,284 3,272
14
8,862 6,515 5,564 5,035 4,695 4,456 4,278 4,140 4,030 3,939 3,800 3,698 3,619 3,556 3,505 3,348 3,215 3,157 3,124 3,112
15
8,683 6,359 5,417 4,893 4,556 4,318 4,142 4,004 3,895 3,805 3,666 3,564 3,485 3,423 3,372 3,214 3,081 3,022 2,989 2,977
16
8,531 6,226 5,292 4,773 4,437 4,202 4,026 3,890 3,780 3,691 3,553 3,451 3,372 3,310 3,259 3,101 2,967 2,908 2,875 2,863
17
8,400 6,112 5,185 4,669 4,336 4,102 3,927 3,791 3,682 3,593 3,455 3,353 3,275 3,212 3,162 3,003 2,869 2,810 2,776 2,764
18
8,285 6,013 5,092 4,579 4,248 4,015 3,841 3,705 3,597 3,508 3,371 3,269 3,190 3,128 3,077 2,919 2,784 2,724 2,690 2,678
19
8,185 5,926 5,010 4,500 4,171 3,939 3,765 3,631 3,523 3,434 3,297 3,195 3,116 3,054 3,003 2,844 2,709 2,649 2,614 2,602
20
8,096 5,849 4,938 4,431 4,103 3,871 3,699 3,564 3,457 3,368 3,231 3,130 3,051 2,989 2,938 2,778 2,643 2,582 2,548 2,535
21
8,017 5,780 4,874 4,369 4,042 3,812 3,640 3,506 3,398 3,310 3,173 3,072 2,993 2,931 2,880 2,720 2,584 2,523 2,488 2,475
22
7,945 5,719 4,817 4,313 3,988 3,758 3,587 3,453 3,346 3,258 3,121 3,019 2,941 2,879 2,827 2,667 2,531 2,469 2,434 2,422
23
7,881 5,664 4,765 4,264 3,939 3,710 3,539 3,406 3,299 3,211 3,074 2,973 2,894 2,832 2,781 2,620 2,483 2,421 2,386 2,373
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
8
Right-Hand-Sided Critical Values
α
F of the F Distribution:
(
)
α
α
=
> F
F
P
,
=
α
0,01
,
where
α is the significance level
(four significant digits)
n
2
n
1
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 30 50 70 90 100
24
7,823 5,614 4,718 4,218 3,895 3,667 3,496 3,363 3,256 3,168 3,032 2,930 2,852 2,789 2,738 2,577 2,440 2,377 2,342 2,329
25
7,770 5,568 4,675 4,177 3,855 3,627 3,457 3,324 3,217 3,129 2,993 2,892 2,813 2,751 2,699 2,538 2,400 2,337 2,302 2,289
26
7,721 5,526 4,637 4,140 3,818 3,591 3,421 3,288 3,182 3,094 2,958 2,857 2,778 2,715 2,664 2,503 2,364 2,301 2,265 2,252
27
7,677 5,488 4,601 4,106 3,785 3,558 3,388 3,256 3,149 3,062 2,926 2,824 2,746 2,683 2,632 2,470 2,330 2,267 2,231 2,218
28
7,636 5,453 4,568 4,074 3,754 3,528 3,358 3,226 3,120 3,032 2,896 2,795 2,716 2,653 2,602 2,440 2,300 2,236 2,200 2,187
29
7,598 5,420 4,538 4,045 3,725 3,499 3,330 3,198 3,092 3,005 2,868 2,767 2,689 2,626 2,574 2,412 2,271 2,207 2,171 2,158
30
7,562 5,390 4,510 4,018 3,699 3,473 3,304 3,173 3,067 2,979 2,843 2,742 2,663 2,600 2,549 2,386 2,245 2,181 2,144 2,131
31
7,530 5,362 4,484 3,993 3,675 3,449 3,281 3,149 3,043 2,955 2,820 2,718 2,640 2,577 2,525 2,362 2,220 2,156 2,119 2,106
32
7,499 5,336 4,459 3,969 3,652 3,427 3,258 3,127 3,021 2,934 2,798 2,696 2,618 2,555 2,503 2,340 2,198 2,133 2,095 2,082
33
7,471 5,312 4,437 3,948 3,630 3,406 3,238 3,106 3,000 2,913 2,777 2,676 2,597 2,534 2,482 2,319 2,176 2,111 2,074 2,060
34
7,444 5,289 4,416 3,927 3,611 3,386 3,218 3,087 2,981 2,894 2,758 2,657 2,578 2,515 2,463 2,299 2,156 2,091 2,053 2,040
35
7,419 5,268 4,396 3,908 3,592 3,368 3,200 3,069 2,963 2,876 2,740 2,639 2,560 2,497 2,445 2,281 2,137 2,072 2,034 2,020
36
7,396 5,248 4,377 3,890 3,574 3,351 3,183 3,052 2,946 2,859 2,723 2,622 2,543 2,480 2,428 2,263 2,120 2,054 2,016 2,002
37
7,373 5,229 4,360 3,873 3,558 3,334 3,167 3,036 2,930 2,843 2,707 2,606 2,527 2,464 2,412 2,247 2,103 2,037 1,998 1,985
38
7,353 5,211 4,343 3,858 3,542 3,319 3,152 3,021 2,915 2,828 2,692 2,591 2,512 2,449 2,397 2,232 2,087 2,021 1,982 1,968
39
7,333 5,194 4,327 3,843 3,528 3,305 3,137 3,006 2,901 2,814 2,678 2,577 2,498 2,434 2,382 2,217 2,072 2,005 1,967 1,953
40
7,314 5,179 4,313 3,828 3,514 3,291 3,124 2,993 2,888 2,801 2,665 2,563 2,484 2,421 2,369 2,203 2,058 1,991 1,952 1,938
50
7,171 5,057 4,199 3,720 3,408 3,186 3,020 2,890 2,785 2,698 2,562 2,461 2,382 2,318 2,265 2,098 1,949 1,880 1,839 1,825
60
7,077 4,977 4,126 3,649 3,339 3,119 2,953 2,823 2,718 2,632 2,496 2,394 2,315 2,251 2,198 2,028 1,877 1,806 1,764 1,749
70
7,011 4,922 4,074 3,600 3,291 3,071 2,906 2,777 2,672 2,585 2,450 2,348 2,268 2,204 2,150 1,980 1,826 1,754 1,711 1,695
80
6,963 4,881 4,036 3,563 3,255 3,036 2,871 2,742 2,637 2,551 2,415 2,313 2,233 2,169 2,115 1,944 1,788 1,714 1,671 1,655
90
6,925 4,849 4,007 3,535 3,228 3,009 2,845 2,715 2,611 2,524 2,389 2,286 2,206 2,142 2,088 1,916 1,759 1,684 1,639 1,623
100
6,895 4,824 3,984 3,513 3,206 2,988 2,823 2,694 2,590 2,503 2,368 2,265 2,185 2,120 2,067 1,893 1,735 1,659 1,614 1,598
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
9
Right-Hand-Sided Critical Values
2
α
χ
of the
2
χ
(Chi-Squared) Distribution:
(
)
α
χ
χ
α
=
>
2
2
P
,
where
α is the significance level
(five significant digits)
DF
α =
0,9
α =
0,8
α =
0,7
α =
0,6
α =
0,5
α =
0,4
α =
0,3
α =
0,2
α =
0,1
α =
0,05
α =
0,01
α =
0,001
1
0,015791 0,064185 0,14847 0,27500 0,45494 0,70833 1,0742 1,6424 2,7055 3,8415 6,6349 10,828
2
0,21072 0,44629 0,71335 1,0217 1,3863 1,8326 2,4079 3,2189 4,6052 5,9915 9,2103 13,816
3
0,58437 1,0052 1,4237 1,8692 2,3660 2,9462 3,6649 4,6416 6,2514 7,8147 11,345 16,266
4
1,0636 1,6488 2,1947 2,7528 3,3567 4,0446 4,8784 5,9886 7,7794 9,4877 13,277 18,467
5
1,6103 2,3425 2,9999 3,6555 4,3515 5,1319 6,0644 7,2893 9,2364 11,070 15,086 20,515
6
2,2041 3,0701 3,8276 4,5702 5,3481 6,2108 7,2311 8,5581 10,645 12,592 16,812 22,458
7
2,8331 3,8223 4,6713 5,4932 6,3458 7,2832 8,3834 9,8032 12,017 14,067 18,475 24,322
8
3,4895 4,5936 5,5274 6,4226 7,3441 8,3505 9,5245 11,030 13,362 15,507 20,090 26,124
9
4,1682 5,3801 6,3933 7,3570 8,3428 9,4136 10,656 12,242 14,684 16,919 21,666 27,877
10
4,8652 6,1791 7,2672 8,2955 9,3418 10,473 11,781 13,442 15,987 18,307 23,209 29,588
11
5,5778 6,9887 8,1479 9,2373 10,341 11,530 12,899 14,631 17,275 19,675 24,725 31,264
12
6,3038 7,8073 9,0343 10,182 11,340 12,584 14,011 15,812 18,549 21,026 26,217 32,909
13
7,0415 8,6339 9,9257 11,129 12,340 13,636 15,119 16,985 19,812 22,362 27,688 34,528
14
7,7895 9,4673 10,821 12,078 13,339 14,685 16,222 18,151 21,064 23,685 29,141 36,123
15
8,5468 10,307 11,721 13,030 14,339 15,733 17,322 19,311 22,307 24,996 30,578 37,697
16
9,3122 11,152 12,624 13,983 15,338 16,780 18,418 20,465 23,542 26,296 32,000 39,252
17
10,085 12,002 13,531 14,937 16,338 17,824 19,511 21,615 24,769 27,587 33,409 40,790
18
10,865 12,857 14,440 15,893 17,338 18,868 20,601 22,760 25,989 28,869 34,805 42,312
19
11,651 13,716 15,352 16,850 18,338 19,910 21,689 23,900 27,204 30,144 36,191 43,820
20
12,443 14,578 16,266 17,809 19,337 20,951 22,775 25,038 28,412 31,410 37,566 45,315
21
13,240 15,445 17,182 18,768 20,337 21,991 23,858 26,171 29,615 32,671 38,932 46,797
22
14,041 16,314 18,101 19,729 21,337 23,031 24,939 27,301 30,813 33,924 40,289 48,268
23
14,848 17,187 19,021 20,690 22,337 24,069 26,018 28,429 32,007 35,172 41,638 49,728
Statistical Tables
Course: Econometrics
Bachelor Studies in Finance Year II
Author: dr Bartłomiej Bartoszewicz
10
Right-Hand-Sided Critical Values
2
α
χ
of the
2
χ
(Chi-Squared) Distribution:
(
)
α
χ
χ
α
=
>
2
2
P
,
where
α is the significance level
(five significant digits)
DF
α =
0,9
α =
0,8
α =
0,7
α =
0,6
α =
0,5
α =
0,4
α =
0,3
α =
0,2
α =
0,1
α =
0,05
α =
0,01
α =
0,001
24
15,659 18,062 19,943 21,652 23,337 25,106 27,096 29,553 33,196 36,415 42,980 51,179
25
16,473 18,940 20,867 22,616 24,337 26,143 28,172 30,675 34,382 37,652 44,314 52,620
26
17,292 19,820 21,792 23,579 25,336 27,179 29,246 31,795 35,563 38,885 45,642 54,052
27
18,114 20,703 22,719 24,544 26,336 28,214 30,319 32,912 36,741 40,113 46,963 55,476
28
18,939 21,588 23,647 25,509 27,336 29,249 31,391 34,027 37,916 41,337 48,278 56,892
29
19,768 22,475 24,577 26,475 28,336 30,283 32,461 35,139 39,087 42,557 49,588 58,301
30
20,599 23,364 25,508 27,442 29,336 31,316 33,530 36,250 40,256 43,773 50,892 59,703
31
21,434 24,255 26,440 28,409 30,336 32,349 34,598 37,359 41,422 44,985 52,191 61,098
32
22,271 25,148 27,373 29,376 31,336 33,381 35,665 38,466 42,585 46,194 53,486 62,487
33
23,110 26,042 28,307 30,344 32,336 34,413 36,731 39,572 43,745 47,400 54,776 63,870
34
23,952 26,938 29,242 31,313 33,336 35,444 37,795 40,676 44,903 48,602 56,061 65,247
35
24,797 27,836 30,178 32,282 34,336 36,475 38,859 41,778 46,059 49,802 57,342 66,619
36
25,643 28,735 31,115 33,252 35,336 37,505 39,922 42,879 47,212 50,998 58,619 67,985
37
26,492 29,635 32,053 34,222 36,336 38,535 40,984 43,978 48,363 52,192 59,893 69,346
38
27,343 30,537 32,992 35,192 37,335 39,564 42,045 45,076 49,513 53,384 61,162 70,703
39
28,196 31,441 33,932 36,163 38,335 40,593 43,105 46,173 50,660 54,572 62,428 72,055
40
29,051 32,345 34,872 37,134 39,335 41,622 44,165 47,269 51,805 55,758 63,691 73,402
41
29,907 33,251 35,813 38,105 40,335 42,651 45,224 48,363 52,949 56,942 64,950 74,745
42
30,765 34,157 36,755 39,077 41,335 43,679 46,282 49,456 54,090 58,124 66,206 76,084
43
31,625 35,065 37,698 40,050 42,335 44,706 47,339 50,548 55,230 59,304 67,459 77,419
44
32,487 35,974 38,641 41,022 43,335 45,734 48,396 51,639 56,369 60,481 68,710 78,750
45
33,350 36,884 39,585 41,995 44,335 46,761 49,452 52,729 57,505 61,656 69,957 80,077
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