1
00:00:00,066 --> 00:00:00,633
So that's great.

2
00:00:00,633 --> 00:00:01,800
That's the first thing to notice.

3
00:00:01,800 --> 00:00:02,900
And then what I was telling you

4
00:00:02,900 --> 00:00:06,533
is that for each of the coefficient
we have different information.

5
00:00:06,533 --> 00:00:10,233
We have actually the coefficient
in the linear regression equation.

6
00:00:10,800 --> 00:00:13,600
Then we have the standard error,
then the t value,

7
00:00:13,600 --> 00:00:16,800
then the p value here,
and then the significance level.

8
00:00:17,333 --> 00:00:21,600
So the most important info, by looking at
this are the last two columns

9
00:00:22,000 --> 00:00:24,700
the p value and the significance level.

10
00:00:24,700 --> 00:00:28,000
Because these columns
tell us about the statistical

11
00:00:28,000 --> 00:00:31,966
significance of the independent variable
onto the dependent variable.

12
00:00:32,466 --> 00:00:35,533
That means it tells us
if each of the independent variable

13
00:00:35,700 --> 00:00:39,100
has a significant impact
on the dependent variable.

14
00:00:40,133 --> 00:00:40,433
Okay.

15
00:00:40,433 --> 00:00:43,033
So let me first explain what
the p value is.

16
00:00:43,033 --> 00:00:47,700
The most important thing to understand
is that the lower the p value is

17
00:00:48,100 --> 00:00:52,366
and the mode statistically significant,
your independent variable is going to be.

18
00:00:53,366 --> 00:00:54,033
That means that the

19
00:00:54,033 --> 00:00:58,200
lower the p value
is, the more impact or effect

20
00:00:58,200 --> 00:01:01,400
your independent variable is going to have
on the dependent variable.

21
00:01:02,333 --> 00:01:06,633
And generally a good threshold to use
is the 5% threshold.

22
00:01:07,200 --> 00:01:11,733
That means that if your p value
is lower than 5%, then that means

23
00:01:11,733 --> 00:01:15,300
that your independent variable
would be highly statistically significant.

24
00:01:15,633 --> 00:01:19,866
And the more it is about 5%, the less
it will be statistically significant.

25
00:01:20,400 --> 00:01:23,333
So that's how you must interpret
the p value.

26
00:01:23,333 --> 00:01:25,000
And then we have this last column,

27
00:01:25,000 --> 00:01:28,500
which is just a faster way
of interpreting the coefficients.

28
00:01:28,933 --> 00:01:33,066
Because as you can see we have this line
here that explains us about the stars.

29
00:01:33,633 --> 00:01:37,233
And basically what the stars means is
that when the p value is

30
00:01:37,233 --> 00:01:42,300
between 0 and 0.1%,
then there's going to be three stars,

31
00:01:42,300 --> 00:01:46,966
which means the highly statistical
significance of your independent variable.

32
00:01:47,533 --> 00:01:51,833
If the p value is between 0.1
percent and 1%,

33
00:01:52,133 --> 00:01:55,566
then it's a quite high level
of statistical significance.

34
00:01:56,000 --> 00:01:59,366
Then if your p value is between 1% and 5%,

35
00:01:59,500 --> 00:02:03,000
then the independent variable
is still statistically significant,

36
00:02:03,266 --> 00:02:06,600
but will have a less strong effect
than the first categories.

37
00:02:07,333 --> 00:02:11,400
And then if your p value is between 5%
and 10%, it's borderline.

38
00:02:11,700 --> 00:02:14,600
The independent variable
might have a certain level

39
00:02:14,600 --> 00:02:19,133
of statistical significance,
but not that much anyway, a lot

40
00:02:19,133 --> 00:02:23,066
less than those independent variables
that have three stars or two stars.

41
00:02:23,700 --> 00:02:27,000
And then if your p value is between
10% and one,

42
00:02:27,000 --> 00:02:30,400
then there is absolutely no
statistical significance.

43
00:02:30,400 --> 00:02:32,166
That means that your independent variable

44
00:02:32,166 --> 00:02:35,166
won't have any effect
on the dependent variable.

45
00:02:35,400 --> 00:02:40,166
So that's very interesting
because when we look at our independent

46
00:02:40,166 --> 00:02:43,200
variables
here, we notice that only one variable has

47
00:02:43,200 --> 00:02:46,833
a high statistical significance
onto the dependent variable.

48
00:02:47,300 --> 00:02:49,000
It's the R&D spend.

49
00:02:49,000 --> 00:02:54,100
So it looks like the profit
is mainly governed by the R&D spend.

50
00:02:54,100 --> 00:02:59,700
That means that it's the R&D spend that
has the only strong effect on the profit.

51
00:03:00,233 --> 00:03:04,166
So that's a very important information
for our investors because they now know

52
00:03:04,166 --> 00:03:07,833
that they shouldn't only be looking
at the profit itself by, you know,

53
00:03:08,166 --> 00:03:11,800
just looking at the maximum profit
to decide where to invest.

54
00:03:12,100 --> 00:03:14,866
But also it should be looking at the R&D
spend variable.

55
00:03:14,866 --> 00:03:17,866
It should be looking at the amount
spent in R&D

56
00:03:17,866 --> 00:03:21,300
to add another criterion
in their investment decisions.

57
00:03:21,600 --> 00:03:24,300
So that's a very good info
and basically what it means.

58
00:03:24,300 --> 00:03:27,900
What all this means is that among
all the independent variables here,

59
00:03:28,133 --> 00:03:33,300
the only predictor, the only strong
predictor of the profit is the R&D spend.

60
00:03:33,533 --> 00:03:36,666
The rest is absolutely like any useful.

61
00:03:37,166 --> 00:03:39,433
So actually
what this means is that we could

62
00:03:40,533 --> 00:03:40,966
we could

63
00:03:40,966 --> 00:03:44,900
rewrite this multiple linear
regression equation

64
00:03:44,900 --> 00:03:48,100
and turn it into a simple linear
regression.

65
00:03:48,100 --> 00:03:51,233
Because
since the only independent variable

66
00:03:51,233 --> 00:03:55,133
that has an effect on the profit
dependent variable is the R&D spend,

67
00:03:55,133 --> 00:04:00,433
then the formula could be profit equals
r that the dot spent.

68
00:04:01,366 --> 00:04:02,266
And that would be okay.

69
00:04:02,266 --> 00:04:05,500
That would actually give us
the same prediction okay.

70
00:04:05,500 --> 00:04:07,700
So you learned a lot of stuff
in this tutorial.

71
00:04:07,700 --> 00:04:10,966
But that's very important things to know
in linear regression.

72
00:04:11,300 --> 00:04:12,766
So congratulations.

73
00:04:12,766 --> 00:04:16,566
We only have one tutorial left where we
will be predicting the test set results.

74
00:04:16,866 --> 00:04:18,466
So I look forward to seeing you there.

75
00:04:18,466 --> 00:04:21,466
And until then enjoy machine learning.