And this video will assess the accuracy of these coefficients because it can be done that we have calculated.
I will start by restating the situation that we are in.
In the world, millions of House transactions were happening.
We picked a small set or a small sample of 506 such observations and decided to identify the relationship
between house place and number of rooms.
When I use the formula shown in previous video, we get the values of B does yellow and Beethoven.
This line is minimizing the squared error on the sample of five under six points.
If we had selected some other 506 observations, we may have got some other values of B does it when
we do one.
If we take all the million observations of the world and then get a line, this line will be called
the population regression line.
This line may or may not be seen as this simple regression line.
You can see in this graph, this blue line, it is simple regression line, which is minimizing the
error on these data points.
D sample datapoint.
But this red line reality population, the green line, which would have come if I would have thought
the least good at a for all the data points of the population.
These two de Nazeem.
Now, the problem is this, we do not have all the observations.
Therefore, we cannot get population immigration lane.
We have sample data so we can get only December regression line.
We want to use the coefficient of symbol regression lane as an estimate for the population gratingly.
How far off release empl estimate?
That is.
But as you look up and be done, Cap will be from the population coefficients which are be you won't
be done for this.
We will use a quantity called standard error of bedazzling redone.
The standard error of BW and Weedman is calculated using these formulas again.
I'm showing you these formulas and discussing the intuition behind them.
You need not memorize them or know their derivation for practical purposes.
But since these quantities will be part of the output of the model from us or to it, we need to understand
their meaning.
So in this formula.
Delta Sigma squared, sigma squared is the variance of population residuals.
Remember, we discussed residuals, Duell is the value, which is the difference of actual way from
the estimated value of the population.
Sigma squared is the variance of these values for all the data points of the population.
Since population Diggnation Lane is not known.
The Sigma squad is also not known.
We need to estimate it from our sample data to this estimate is given by this formula, which is Oddisee
is equal to under route RSS by and minus to here.
Odyssey is called residual standard error.
Odyssey's is did a little small squares.
We discussed this only last video, which is sum of all the squares.
So for all the data points, we get the errors.
That is the residuals.
We squared them and we add them.
That is the Odyssey's.
We divide Odyssey's by N minus two.
And is the number of observations.
So for our dataset, it is by winders six will divided by five under six, minus two.
Then we find it on the road.
We get there's a dual standard at a.
We'll use this residual standard error as a proxy for Sigma.
Also, notice that if X is more spread out in this formula, B, does it go and be done?
Standard error of bedazzling reduction will be small, which intuitively means that we have more leverage
while estimating the slope in such a case.
Now, what is the practical take away from the S.
E calculations?
Standard error will be used to give us a confidence interval, that is, or linear regression.
There is a 95 percent chance that provably of bidone lies in the interval.
Redoubling gap minus two time standard at it, if we don't do bidone gap.
Plus two things gender identity reduction.
So within this interval, we had Lawwell use this and hired will use this.
We are 95 percent confident that the actual reduction lies in this interval.
Similarly, what we does zero, the 95 percent confidence interval will be the estimates.
We do zero minus two days.
Standard error.
This.
Standard edit of BW.
And the higher value will be be does he look plus two times standard at at all?
What does he do?
To summarize, what we have done here is we had two lines.
One line we got from dissemble regression that we did.
The other one is a hypothetical line, which is the true line between the population of all the points.
We wanted to show whether we can approximate this sample line as the population line.
For that, we found out the confidence interval.
Within which the population coefficient will lay.
So, Debbie, does it all of the population line really between.
These two values that we get from dissemble regression and the slope of the population regression relay.
Between these two values of the sample equation.
And we have a signed up probably of how confident we are.
We are saying that there is a 95 percent chance that the population Diggnation corporations lie within
these intervals, that we are not using sampling.
Another use of standard error is to establish that whether X and Y actually have a relationship or not.
In a linear model, this relationship is given by Biederman.
We are saying that.
Why is be the one times X plus constant?
So if beta one is zero, it means that there is no relationship.
If there is no relationship, then the variable X cannot be used to predict like.
So we need to show that the probability of beta one being zero is negligible.
Let me tell you the contempt first, and after that, I'll show you the way, how you will find it in
every other statistical book.
The concept is this Biederman has some value.
That is the most probable value found by the formula we saw in the previous videos.
Now, if you want to see that we are sufficiently confident that it cannot be zero.
It has two parts to it.
First, most probable value should be fired from zero and taken.
The standard error of Weeda, which is giving us the interval in which the rule lays, should be small.
So basically, we want Z2 not to lie in this whole interval in which be delays.
I hope you get the idea.
Let's do it the proper way, no, this this method is called hypothesis testing.
We will construct two hypotheses.
One is at zero, that is there is no relationship between X and Y.
And its alternative, which is written as it is that there is a literature between X and Y.
So it is Weedman is equal, Luisito.
It is between is not equal, Luisito.
And we want to disprove a digital.
To disprove at zero.
We will calculate something known as B statistic, which is given as BS equal to be done cap minus zero
divided by standard A. B double.
So you can see what this what this is representing here, enumerator.
It says how far Bita one is from zero.
And when you divided by standard at it, you go the distance is how many times?
Standard edit.
So using this formula will go to devalue.
No, we want this devalue to be large.
By the way, it is called P-value, because it is based on B distribution, which is similar to normal
distribution.
Basically, tea distribution is another prohibited distribution.
And if you have P-value, you can get the probability of observing any value equal to absolutely or
logit.
The probability that you will get from this distribution is called P-value.
Now, this P-value has meaning.
We can interpret P-value as follows.
Small value of B will mean that it is highly unlikely that there is no relationship between preterm
response.
Which means that we can reject the null hypothesis and declare that there is a relationship between
X and Y.
Typically, we use.
A value like five percent or one percent as the cutoff value for P, that is, if P is listin point
zero one, then the variable X is significantly impacting Y.
There does look at deserts of of sample.
Or that this is a desert which we have received from the software package that we are using and the
course, there is a separate video where you you will learn how to run this analysis and get this result.
I'm just discussing the result here as an example to all to read that we just covered.
So in the last video, we had just seen the beta one and Bedazzler values this intercept, this debate,
as you know.
And this room, numb with evil, has this slope.
This nine point zero nine is the beta one for this very evil.
The first thing that we covered is the standard error.
What does he do when we done?
The formula that I showed you earlier was used to calculate the standard error of Bedazzler and be done
how the standard elegant me use this.
You can make this statement that for the sample of five, six observations, the beads that you calculated
for minimum error was nine point zero nine.
But you are 95 percent confident that for the global data of how spacing the be done will lay between
nine point zero nine minus two times zero point for one.
Do nine point zero nine plus two times zero point four to.
So this interval is giving you that the estimated B does that you have here.
Can be used to make this statement that deep-Rooted aggression coalitions will lie in the interval given
by the standard error.
The next thing we discussed will be when you and BP will you?
This devaluing p value.
We said that we have one hypothesis.
We're just saying that there is no relationship.
To disprove that hypothesis, we calculated or devalue.
Which was given by this formula.
So to get the value of this be done, we will put the bit of uncapped value divided by the S.
E, so nine point zero nine divided by zero point forty one gives you this devalue.
So corresponding to this devalue, we calculate a P value, which is it as probability of getting a
P value, which is greater than equal to this?
The that we call ridded.
This property value is coming out to be very small.
It's a it's an exponential with a bout of minus 16 to this value is very small.
So if this value is very small, we can see that it is unlikely that there is no relationship, which
means that there is some relationship.
And therefore, we are confident that room number variable is impacting the house pricing and the relationship
between them is given by this coefficient.
So the takeaway from this lecture is we have be done and B, does it all values calculated for the simple.
We calculated a standard error, which is helping us in determining two things.
One is or does the event in which the true value of Beta one and B, does it relate?
And the second thing is whether there is actually a relationship between these predictor.
And the response variables.
To establish that there is a listenership we calculated at P-value using these two things, using a
T value, we calculated a P value.
And if this P value is less than a threshold of one percent or five percent, whichever you like to
use, then we see that there is a relationship.
So far, our model, there is a relationship of hose pricing with room them, and that relationship
is this between which is main point you don't make.