1
00:00:01,080 --> 00:00:02,370
[Instructor] Now I wanted to show you

2
00:00:02,370 --> 00:00:07,370
how to do the Breusch-Pagan,

3
00:00:07,830 --> 00:00:12,720
and the white tests
for heteroscedasticity.

4
00:00:12,720 --> 00:00:15,840
We're gonna test a model to see

5
00:00:15,840 --> 00:00:19,320
if it is heteroscedastic or homoscedastic.

6
00:00:20,670 --> 00:00:25,380
The first thing that we do
is to run the regular model.

7
00:00:25,380 --> 00:00:29,153
It's, again, using the sleep model,

8
00:00:33,030 --> 00:00:36,240
and we're gonna regress
sleep on total work, educ,

9
00:00:36,240 --> 00:00:40,173
age, age squared, young kid,
and male like we did before.

10
00:00:41,580 --> 00:00:46,580
I'm gonna analyze, oh, I
think I have to go back

11
00:00:46,650 --> 00:00:48,970
and unsplit the file.

12
00:00:52,590 --> 00:00:53,790
Okay, good.

13
00:00:53,790 --> 00:00:55,263
This is what we want.

14
00:00:56,790 --> 00:01:00,660
Do it to all groups.

15
00:01:00,660 --> 00:01:05,010
We're gonna just do a linear regression

16
00:01:05,010 --> 00:01:07,533
with sleep as our dependent.

17
00:01:12,630 --> 00:01:15,153
And then our independents are total work,

18
00:01:21,990 --> 00:01:22,823
educ,

19
00:01:25,530 --> 00:01:26,493
age,

20
00:01:27,990 --> 00:01:29,373
age squared,

21
00:01:31,050 --> 00:01:31,953
and male.

22
00:01:34,980 --> 00:01:37,080
And I just wanna make sure
that those are the right ones,

23
00:01:37,080 --> 00:01:41,733
total work, educ, age,
age squared, and male.

24
00:01:43,110 --> 00:01:45,450
Let's go back here and
make sure that's right.

25
00:01:45,450 --> 00:01:49,230
Total work, educ, age, age
squared, oh, and young kid.

26
00:01:49,230 --> 00:01:51,303
Don't forget about young kid.

27
00:01:52,530 --> 00:01:53,400
It's there.

28
00:01:53,400 --> 00:01:55,710
We put that over there.

29
00:01:55,710 --> 00:01:59,550
Now, we've run this before,
but what we wanna do now,

30
00:01:59,550 --> 00:02:02,703
this is where we wanna save things.

31
00:02:04,470 --> 00:02:09,470
We wanna save both of our,
the Y hats and the U hats

32
00:02:11,460 --> 00:02:16,460
because when we do the BP test,

33
00:02:17,400 --> 00:02:20,880
it's on the squared residuals,

34
00:02:20,880 --> 00:02:23,340
and when we do the white test,

35
00:02:23,340 --> 00:02:27,330
it's on the Y hat and the Y hat squared.

36
00:02:27,330 --> 00:02:31,260
Let's run this.

37
00:02:31,260 --> 00:02:33,303
Say okay, boom.

38
00:02:34,320 --> 00:02:39,320
And we see that we have
over here two new variables.

39
00:02:43,290 --> 00:02:46,740
This is Y hat and U hat.

40
00:02:46,740 --> 00:02:48,930
I'm gonna go to variable view

41
00:02:48,930 --> 00:02:53,857
and I'm gonna rename them so
we remember what they are.

42
00:02:54,870 --> 00:02:58,443
This is Y hat and this is U hat.

43
00:03:02,730 --> 00:03:06,570
And we're gonna wanna
then square them both.

44
00:03:06,570 --> 00:03:11,520
We do that by going to transform, compute,

45
00:03:11,520 --> 00:03:14,950
and we're gonna call it U hat squared

46
00:03:19,440 --> 00:03:22,220
as our name, and it is simply...

47
00:03:26,640 --> 00:03:28,410
no, that's wrong.

48
00:03:28,410 --> 00:03:29,440
We actually want

49
00:03:32,130 --> 00:03:36,900
U hat times U hat

50
00:03:36,900 --> 00:03:40,743
so it's taking the U
hats and squaring them.

51
00:03:44,220 --> 00:03:48,720
And we should see now that
there is a new variable

52
00:03:48,720 --> 00:03:53,250
that is called U hat squared.

53
00:03:53,250 --> 00:03:55,680
We're gonna do the same thing

54
00:03:55,680 --> 00:03:59,790
and square the Y hats for the white test.

55
00:03:59,790 --> 00:04:04,790
Now, we're gonna reset
this and we're gonna go to,

56
00:04:05,910 --> 00:04:08,913
we're gonna call it Y hat squared.

57
00:04:14,250 --> 00:04:18,550
Make this a function of Y hat times Y hat

58
00:04:20,550 --> 00:04:21,693
and say okay.

59
00:04:24,270 --> 00:04:29,270
For the BP test, we regress U hat squared

60
00:04:30,360 --> 00:04:35,130
on the regressors from the original model.

61
00:04:35,130 --> 00:04:38,740
We analyze with a regression

62
00:04:39,690 --> 00:04:44,690
and we just take out sleep now
and we put in U hat squared.

63
00:04:46,140 --> 00:04:48,691
Now what this is saying is

64
00:04:48,691 --> 00:04:53,691
once we get the residuals and square them,

65
00:04:54,960 --> 00:04:59,960
do these regressors still
have an effect on that?

66
00:05:00,330 --> 00:05:05,330
What we want is we want our
null hypothesis to be true,

67
00:05:05,910 --> 00:05:09,480
that these are all equal to zero

68
00:05:09,480 --> 00:05:12,480
both individually and jointly.

69
00:05:12,480 --> 00:05:16,470
If that is true, we have homoscedasticity

70
00:05:16,470 --> 00:05:19,560
and that's a good thing and
we don't have to deal with it.

71
00:05:19,560 --> 00:05:23,100
If we cannot reject our null,

72
00:05:23,100 --> 00:05:25,980
then we do have heteroscedasticity

73
00:05:25,980 --> 00:05:28,020
and we need to deal with it

74
00:05:28,020 --> 00:05:30,570
as we learned with to do inference

75
00:05:30,570 --> 00:05:33,660
and to get a more efficient model.

76
00:05:33,660 --> 00:05:35,820
Let's see what this says.

77
00:05:35,820 --> 00:05:36,653
Boom.

78
00:05:38,310 --> 00:05:42,150
We do see just barely
these are significant.

79
00:05:42,150 --> 00:05:44,670
It's kind of a borderline case.

80
00:05:44,670 --> 00:05:48,180
It looks like it's not a very severe case.

81
00:05:48,180 --> 00:05:50,970
And for things like weighted least squares

82
00:05:50,970 --> 00:05:55,320
that we might wanna see,
what is the culprit of that?

83
00:05:55,320 --> 00:06:00,320
And the only one that
is significant is educ.

84
00:06:00,900 --> 00:06:03,510
Again, this is kind of a borderline case.

85
00:06:03,510 --> 00:06:07,710
It's a significant, the
.08, so it wouldn't be

86
00:06:07,710 --> 00:06:12,710
at a P less than .05,
but it is less than .1.

87
00:06:15,840 --> 00:06:19,170
It might be good to
sort of do it both ways,

88
00:06:19,170 --> 00:06:21,600
compute the standard errors

89
00:06:21,600 --> 00:06:24,303
or weighted least squares or FGLS.

90
00:06:25,590 --> 00:06:28,980
And let's do the other test to see

91
00:06:28,980 --> 00:06:31,350
if that gives us anything else.

92
00:06:31,350 --> 00:06:35,790
Now, we're gonna do a linear regression

93
00:06:35,790 --> 00:06:40,790
and instead of regressing
it on the regressors,

94
00:06:42,870 --> 00:06:46,503
we're gonna do it on Y hat squared,

95
00:06:49,050 --> 00:06:50,253
on Y hat,

96
00:06:54,330 --> 00:06:56,910
and Y hat squared.

97
00:06:56,910 --> 00:06:59,850
Then let's turn off, it keeps saving 'em

98
00:06:59,850 --> 00:07:04,110
because we didn't tell it not to.

99
00:07:04,110 --> 00:07:09,110
And again, we want this
to be not significant.

100
00:07:09,300 --> 00:07:12,660
We want all our betas to be jointly zero.

101
00:07:12,660 --> 00:07:17,660
And we look and we find that they are.

102
00:07:18,870 --> 00:07:22,140
The whole thing is not significant.

103
00:07:22,140 --> 00:07:26,730
And so again, these are, so again,

104
00:07:26,730 --> 00:07:29,250
this is kind of a borderline case,

105
00:07:29,250 --> 00:07:34,250
but that shows you how to do
the the Breusch-Pagan test

106
00:07:36,030 --> 00:07:40,140
and the second version of the white test

107
00:07:40,140 --> 00:07:41,793
for heteroscedasticity.