1
00:00:01,640 --> 00:00:06,500
Let's determine if either the number of classes attended or the number of hours studied are individually
2
00:00:06,510 --> 00:00:11,270
irrelevant in our regression equation at the 5% significance level.
3
00:00:13,990 --> 00:00:21,100
We can actually determine if our variables are relevant.
4
00:00:21,110 --> 00:00:22,910
Although they may be included,
5
00:00:22,910 --> 00:00:28,600
we can go through our analysis and take all of our variables,
6
00:00:28,600 --> 00:00:33,870
and we can actually determine if they are even relevant, and would affect our Y.
7
00:00:34,040 --> 00:00:36,310
This is something that is not totally obvious.
8
00:00:36,310 --> 00:00:40,770
There's no black or white answer for especially when you're using multiple variables,
9
00:00:40,780 --> 00:00:44,220
it's hard to tell which one is not important.
10
00:00:44,230 --> 00:00:48,000
This following formula and procedure can help with that.
11
00:00:48,010 --> 00:00:50,760
We're going to check both of our variables.
12
00:00:51,140 --> 00:00:53,370
We're going to check if they are relevant.
13
00:00:53,380 --> 00:00:55,870
First thing we're gonna have to do,
14
00:00:56,240 --> 00:00:58,400
we need to set a critical value... actually...
15
00:00:58,830 --> 00:01:00,950
why don't we set a hypothesis test first?
16
00:01:01,540 --> 00:01:06,200
Our H0, are null hypothesis, would be
17
00:01:06,200 --> 00:01:11,100
that the variable B and this would
18
00:01:11,100 --> 00:01:12,700
be another variable,
19
00:01:12,700 --> 00:01:14,020
the first one in the second one.
20
00:01:14,020 --> 00:01:16,980
But would equal zero.
21
00:01:16,990 --> 00:01:22,830
basically, that there is no relevance.
22
00:01:22,910 --> 00:01:28,190
Those variables have no actual meaning to the equation.
23
00:01:28,200 --> 00:01:33,250
Our alternative hypothesis ,
24
00:01:34,040 --> 00:01:39,450
is that they don't equal zero.
25
00:01:39,460 --> 00:01:43,660
Forgive my bad strike through here just to get the point across...
26
00:01:44,340 --> 00:01:45,450
They don't equal zero.
27
00:01:47,740 --> 00:01:49,930
Now we need to determine our T value.
28
00:01:50,100 --> 00:01:55,170
If you have a look at our formula sheet,
29
00:01:55,170 --> 00:02:01,370
you see our degrees of freedom are N minus K minus one.
30
00:02:02,140 --> 00:02:07,040
We have degrees of freedom that equal five
31
00:02:07,310 --> 00:02:08,990
minus two columns minus one.
32
00:02:09,010 --> 00:02:10,550
Gives us a degrees of freedom of two.
33
00:02:11,840 --> 00:02:13,910
If we head over to our T value,
34
00:02:13,910 --> 00:02:15,150
we're looking for degrees of freedom.
35
00:02:15,280 --> 00:02:17,910
This is a 5% significance level.
36
00:02:17,930 --> 00:02:22,690
We know that this is a two tails situation because it's not equal to zero.
37
00:02:22,690 --> 00:02:26,740
Variables can have a negative impact or they can have a positive impact,
38
00:02:26,750 --> 00:02:30,770
But it's not greater or less. It's a two tails because it could go either direction.
39
00:02:32,040 --> 00:02:34,350
We'll pull up our T table.
40
00:02:41,440 --> 00:02:43,660
Here we see our two tails.
41
00:02:46,540 --> 00:02:51,960
We are going to choose our 5% significance on two tails,
42
00:02:51,970 --> 00:02:52,930
two degrees of freedom,
43
00:02:52,930 --> 00:02:55,060
and we have 4.303 .
44
00:03:03,740 --> 00:03:15,858
We've set our critical T value at 4.303.
45
00:03:17,440 --> 00:03:25,160
That means that if our T value is
46
00:03:26,440 --> 00:03:37,970
between negative 4.303 to positive 4.303
47
00:03:43,040 --> 00:03:45,470
we can reject our null hypothesis.
48
00:03:51,140 --> 00:03:55,760
By rejecting our null hypothesis we are saying that the variable is not equal to zero,
49
00:03:55,760 --> 00:03:58,250
and it does have an impact, either positive or negative.
50
00:04:03,240 --> 00:04:08,550
To do that we need to determine a T value for both variables.
51
00:04:09,590 --> 00:04:11,760
We're gonna need to use the following formula.
52
00:04:14,440 --> 00:04:24,500
Now B one is our slope that we've already determined.
53
00:04:25,040 --> 00:04:30,350
This would be the standard deviation of our B one or our column.
54
00:04:30,840 --> 00:04:33,378
We haven't determined our standard deviation yet.
55
00:04:33,388 --> 00:04:35,760
I'll just do that in Excel with you right now.
56
00:04:38,040 --> 00:04:46,550
We can do our standard deviation using a basic formula,
57
00:04:47,440 --> 00:04:54,650
equals STDEV.S because this is for a sample.
58
00:04:56,220 --> 00:04:59,360
And we can include our column here.
59
00:05:00,340 --> 00:05:01,570
For our first variable,
60
00:05:02,540 --> 00:05:07,540
we get a standard deviation of 2.7 and I can slide it right,
61
00:05:07,810 --> 00:05:10,660
and I get a 2.68 .
62
00:05:17,440 --> 00:05:23,250
Let's do our study time variable.
63
00:05:28,640 --> 00:05:32,290
Our study time had a 2.70 standard deviation.
64
00:05:35,440 --> 00:05:41,340
So T equals 2.79.
65
00:05:41,590 --> 00:05:50,610
We have scroll up to our first where we've set that slope at 2.79.
66
00:05:50,610 --> 00:05:51,560
That's our B.
67
00:05:54,440 --> 00:05:56,960
You can also find it in your spreadsheet.
68
00:05:59,540 --> 00:06:01,760
2.79 to your coefficient
69
00:06:05,540 --> 00:06:06,560
minus zero.
70
00:06:07,940 --> 00:06:09,860
Divided by 2.7.
71
00:06:12,840 --> 00:06:14,200
So we would get a T.
72
00:06:14,200 --> 00:06:16,457
That equals 1.3.
73
00:06:16,467 --> 00:06:20,970
Our class attended variable.
74
00:06:24,040 --> 00:06:28,950
We have our slope of 4.84 minus zero
75
00:06:30,910 --> 00:06:36,060
divided by 2.68 which is our standard deviation.
76
00:06:40,740 --> 00:06:45,720
Just to make sure we're following our BEDMAS rules, I put those in brackets.
77
00:06:45,720 --> 00:06:51,670
We get a T value of 1.81. What does this mean?
78
00:06:52,140 --> 00:06:56,460
Both variables are within our critical value range here.
79
00:06:57,040 --> 00:07:01,580
That means for both variables we can reject our null hypothesis.
80
00:07:01,590 --> 00:07:04,060
Both of them are irrelevant to our equation.
81
00:07:04,740 --> 00:07:09,270
If we had more than two variables we had 3,4,5,6 or more.
82
00:07:09,640 --> 00:07:12,330
We would continue this process for each one,
83
00:07:12,410 --> 00:07:16,510
and we would just drop the variables out that didn't fit in the equation.
84
00:07:16,520 --> 00:07:18,010
That would fit our data.
85
00:07:18,020 --> 00:07:23,950
This is how we can determine which variables are relevant and then keep them within our equation.
86
00:07:24,440 --> 00:07:27,480
Sometimes with multiple various variables,
87
00:07:27,480 --> 00:07:28,390
that could be a lot of work.
88
00:07:28,390 --> 00:07:30,050
They all have to be done individually.
89
00:07:30,640 --> 00:07:33,280
These are not linked answers into this.
90
00:07:33,290 --> 00:07:37,570
These air just individual testing the variables to our critical T value.