So you would have noticed that there is one value of this outpoured that we have still not discussed
and that value is called F statistic, and in this video we'll be discussing about F statistic.
Now, if you see the result for each of the coefficient.
There is a corresponding P-value, which is telling us whether each individual predictor is related
to the response, I'm talking about these P values and probability values.
These two columns.
So since at least one of them has a small p value here, we have six of them to, since at least one
of them has a small P value corresponding to their T value, we may think that shortly at least one
of the predictors are related to the response.
Therefore, we will say that there is a relationship between this point and political variables that
is not all of the conditions of the variables, that is the we do have to be to be.
Ardito, so all of them are not Dettol.
So this argument may sound okay, but it is actually not, especially if we have a large number of variables.
Let me put it mathematically for you first, what I'm saying is the null hypothesis is that all of them
are zero.
I want to prove that this is not the case.
I want to say that at least one of the Beatles is definitely not.
That is the predictor that I am selected, have some relationship with the response.
To now, suppose if my model is saying that any one of the predictors say here we got sakes, suppose
it was giving that only one of them to room number is significantly littered with Osprey's, which is
the P value and the rest are not.
Now, can I say with confidence that since bit of room number is significantly limited, I am confident
that the predictors in this model are impacting the response variable.
The answer is no, I cannot say that.
Let me show you how to suppose I toss a coin five times and I say that, that if I get five heads in
a row, I will turn that coin as a biased coin.
Now, if this is my criteria of saying that the coin is biased, what is the probability that I will
classify a fair coin as a biased coin?
As you can see, probability of head in one toss of a coin is half.
So what is the probability that in all the five doses, I'll get all the heads half into half into half
and half and half five times, that is harvestable fail, which comes out three point zero three one
two fail.
This means that there is nearly three percent chance that I will wrongly classify a fair coin as a biased
coin.
Now, if I toss 100 fair coins five times.
What is the probability of at least one of them getting all five head?
So these are 100 coins, the probability of getting ahead is point five again.
What is the probability that at least one of them is wrongly classified as a biased coin?
So this we can calculate using this formula that I've shown here, it is first finding out the probability
of getting all heads and none of these and we are finding one minus that probability.
And that is coming out to be 95 percent.
You do not need to know how this came out, but the result is important.
The point that I am trying to make is, although the probability of calling a fair coin as a bad coin
was only three percent.
But if you are doing this experiment 100 times, it is almost certain that you will wrongly classify
at least one of the Queen's.
By almost certain, I mean, there is more than 95 percent probability.
You know, this is similar to this statistic in the sense I said that we are 95 percent sure that we
that there is not zero.
When I saw it devalue and P-value.
So we are nearly five percent unsure.
So there is a five percent chance of a beta, which is zero being classified as a non-zero beta.
Not if we have a large number of variables.
All having five percent chance of getting wrongly guessed as significant, it is almost certain that
at least one of them is actually wrongly saying that we have got that very well known.
So if we depend on individual P values, there is a very high chance that we will incorrectly conclude
that there is a relationship between predictor variables and irresponsible.
The solution to this problem is to adjust for the number of predictors and then find the p value.
This new statistic, which adjust just for the number of predictors, is called a statistic.
This includes the number of variables in the form of this be.
So all this then we run a multiple regression model, give a statistic value for the model and the corresponding
P value.
So this P-value must be checked against the threshold that whether there is a relationship between model
predictors and the response, if there is, then we will look at the disvalue and P-value of each individual
variable to identify which of the variables is significantly.
I hope you understand the concept.
I'll briefly summarize it.
The idea is, instead of looking at individual variables.
And saying that the model predictors are significantly impacting the response variable, we will look
at a different statistic which takes into account the number of variables that we have.
This ensures that we do not make the mistake of saying that the models have a significant relationship
with predictor.
If we got that, we are not to worry about positively impacting the response by chance.
So to avoid that chant, we are using this new statistic, which is called a statistic, we look at
its value and we look at the corresponding P value.
If this P value is lower than the threshold value, say, one percent or five percent.
Again, we say that the model predictors are significantly impacting the response.
After that, we will look at the individual predictors and their estimate and P values, although not
like I have told you earlier.
Also, even if you do not understand the whole concept behind this statistic, the concept that you
should take away from this video lesson is just that you have to check whether your P value of F statistic
is lower than a threshold of five percent.
You do not need to understand all of the concept behind Aphoristic.
This will ensure that the model predicts that you used are having some significant impact on the response
that responsivity will.