So that's great.
That's the first thing to notice.
And then what I was telling you
is that for each of the coefficient we have different information.
We have actually the coefficient in the linear regression equation.
Then we have the standard error, then the t value,
then the p value here, and then the significance level.
So the most important info, by looking at this are the last two columns
the p value and the significance level.
Because these columns tell us about the statistical
significance of the independent variable onto the dependent variable.
That means it tells us if each of the independent variable
has a significant impact on the dependent variable.
Okay.
So let me first explain what the p value is.
The most important thing to understand is that the lower the p value is
and the mode statistically significant, your independent variable is going to be.
That means that the
lower the p value is, the more impact or effect
your independent variable is going to have on the dependent variable.
And generally a good threshold to use is the 5% threshold.
That means that if your p value is lower than 5%, then that means
that your independent variable would be highly statistically significant.
And the more it is about 5%, the less it will be statistically significant.
So that's how you must interpret the p value.
And then we have this last column,
which is just a faster way of interpreting the coefficients.
Because as you can see we have this line here that explains us about the stars.
And basically what the stars means is that when the p value is
between 0 and 0.1%, then there's going to be three stars,
which means the highly statistical significance of your independent variable.
If the p value is between 0.1 percent and 1%,
then it's a quite high level of statistical significance.
Then if your p value is between 1% and 5%,
then the independent variable is still statistically significant,
but will have a less strong effect than the first categories.
And then if your p value is between 5% and 10%, it's borderline.
The independent variable might have a certain level
of statistical significance, but not that much anyway, a lot
less than those independent variables that have three stars or two stars.
And then if your p value is between 10% and one,
then there is absolutely no statistical significance.
That means that your independent variable
won't have any effect on the dependent variable.
So that's very interesting because when we look at our independent
variables here, we notice that only one variable has
a high statistical significance onto the dependent variable.
It's the R&D spend.
So it looks like the profit is mainly governed by the R&D spend.
That means that it's the R&D spend that has the only strong effect on the profit.
So that's a very important information for our investors because they now know
that they shouldn't only be looking at the profit itself by, you know,
just looking at the maximum profit to decide where to invest.
But also it should be looking at the R&D spend variable.
It should be looking at the amount spent in R&D
to add another criterion in their investment decisions.
So that's a very good info and basically what it means.
What all this means is that among all the independent variables here,
the only predictor, the only strong predictor of the profit is the R&D spend.
The rest is absolutely like any useful.
So actually what this means is that we could
we could
rewrite this multiple linear regression equation
and turn it into a simple linear regression.
Because since the only independent variable
that has an effect on the profit dependent variable is the R&D spend,
then the formula could be profit equals r that the dot spent.
And that would be okay.
That would actually give us the same prediction okay.
So you learned a lot of stuff in this tutorial.
But that's very important things to know in linear regression.
So congratulations.
We only have one tutorial left where we will be predicting the test set results.
So I look forward to seeing you there.
And until then enjoy machine learning.