So you would have noticed that there is one value of this outpoured that we are 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 in the desert 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, too.
Since at least one of them has a small P value corresponding to their devalue.
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 bond and predictor variables.
That is not all of the coefficients of the variables that has been one.
We do appear to be.
Ardito.
So all of them are not deedle.
This argument may sound OK, 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 Z2.
I want to prove that this is not the case.
I want to say that at least one of DBI does is definitely non-zero.
That is the predictor that I have selected have some relationship with the response.
Now, suppose if my model is saying that any one of the predictors say, hey, we got six.
Suppose it was giving that only one of them to a room them is significantly littered with host praise.
This is the P value and the rest are not.
Now, can I say with confidence that since bit of room them is significantly lifted, I am confident
that the predictors in this model are impacting the response variable.
The answer is no.
I cannot see that.
Let me show you how.
So suppose I toss a coin five times and I say that that I figured five heads in a row.
I will thumb that going as a biased coin.
Now, if this is my criteria of saying that the coin is biased or does the probability that I will classify
a fair coin as a biased coin?
As you can see, probably 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?
So half into half into half and half and half five times.
There it is, harvestable fail become, which comes out to me.
Point zero three one two, fail.
This means that there is nearly three percent chance that I will wrongly call classify a fair coin as
a biased coin.
Now, if I was hundred feared grains five times.
What is the probability of at least one of them getting all five head?
So these are hundred fed grains.
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 going?
So this weekend, calculate using this formula that I've shown here, it is first finding out the probability
of getting all heads in 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'm trying to make is, although the probably of calling a fair coin as a bad coin was
only three percent.
But if you're doing this experiment a hundred times, it is almost certain that you will wrongly classify
at least one of the coins.
By almost Artane, I mean, there is more than 95 percent probability.
You know, this is similar to the T statistic in the sense I said that we are 95 percent sure that we
today is not zero.
When I saw it, P-value and P-value.
So we had nearly five percent unsure.
So there is a five percent chance of a BITA, which is zero being classified as a nondurable bita.
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 of for that variable
is non-zero.
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 predictive variables and they respond to real.
The solution to this problem is to adjust for the number of predictors and then find the value.
This new statistic, which I just for the number of predictors, is called F statistic.
This includes the number of variables in the form of this be.
So Alz of when we run a multiple regression model, give a F 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 P-value and P-value of each individual variable to identify which
of the variables is significant.
Delegate.
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 these models have a significant relationship
with predicted, if we got that, we're not too deeply into variables versus individually impacting
the response.
By chance.
So to avoid that jaunt, 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 estimates and P values, although not
like I have told you a little.
Also, even if you do not understand the whole concept behind this statistic, the concept that you
should take away from this, we do listen is just that you have to check whether your P value of F statistic
is lower than attracts your low five percent.
You do not need to understand all of the concept behind me after Ristic.
This will ensure that the model predictors that you used are having some significant impact on the response
that you would.