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And this video will assess the accuracy of these coefficients because it can be done that we have calculated.

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I will start by restating the situation that we are in.

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In the world, millions of House transactions were happening.

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We picked a small set or a small sample of 506 such observations and decided to identify the relationship

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between house place and number of rooms.

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When I use the formula shown in previous video, we get the values of B does yellow and Beethoven.

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This line is minimizing the squared error on the sample of five under six points.

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If we had selected some other 506 observations, we may have got some other values of B does it when

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we do one.

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If we take all the million observations of the world and then get a line, this line will be called

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the population regression line.

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This line may or may not be seen as this simple regression line.

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You can see in this graph, this blue line, it is simple regression line, which is minimizing the

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error on these data points.

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D sample datapoint.

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But this red line reality population, the green line, which would have come if I would have thought

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the least good at a for all the data points of the population.

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These two de Nazeem.

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Now, the problem is this, we do not have all the observations.

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Therefore, we cannot get population immigration lane.

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We have sample data so we can get only December regression line.

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We want to use the coefficient of symbol regression lane as an estimate for the population gratingly.

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How far off release empl estimate?

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That is.

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But as you look up and be done, Cap will be from the population coefficients which are be you won't

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be done for this.

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We will use a quantity called standard error of bedazzling redone.

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The standard error of BW and Weedman is calculated using these formulas again.

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I'm showing you these formulas and discussing the intuition behind them.

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You need not memorize them or know their derivation for practical purposes.

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But since these quantities will be part of the output of the model from us or to it, we need to understand

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their meaning.

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So in this formula.

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Delta Sigma squared, sigma squared is the variance of population residuals.

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Remember, we discussed residuals, Duell is the value, which is the difference of actual way from

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the estimated value of the population.

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Sigma squared is the variance of these values for all the data points of the population.

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Since population Diggnation Lane is not known.

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The Sigma squad is also not known.

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We need to estimate it from our sample data to this estimate is given by this formula, which is Oddisee

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is equal to under route RSS by and minus to here.

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Odyssey is called residual standard error.

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Odyssey's is did a little small squares.

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We discussed this only last video, which is sum of all the squares.

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So for all the data points, we get the errors.

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That is the residuals.

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We squared them and we add them.

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That is the Odyssey's.

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We divide Odyssey's by N minus two.

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And is the number of observations.

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So for our dataset, it is by winders six will divided by five under six, minus two.

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Then we find it on the road.

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We get there's a dual standard at a.

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We'll use this residual standard error as a proxy for Sigma.

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Also, notice that if X is more spread out in this formula, B, does it go and be done?

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Standard error of bedazzling reduction will be small, which intuitively means that we have more leverage

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while estimating the slope in such a case.

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Now, what is the practical take away from the S.

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E calculations?

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Standard error will be used to give us a confidence interval, that is, or linear regression.

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There is a 95 percent chance that provably of bidone lies in the interval.

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Redoubling gap minus two time standard at it, if we don't do bidone gap.

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Plus two things gender identity reduction.

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So within this interval, we had Lawwell use this and hired will use this.

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We are 95 percent confident that the actual reduction lies in this interval.

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Similarly, what we does zero, the 95 percent confidence interval will be the estimates.

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We do zero minus two days.

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Standard error.

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This.

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Standard edit of BW.

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And the higher value will be be does he look plus two times standard at at all?

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What does he do?

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To summarize, what we have done here is we had two lines.

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One line we got from dissemble regression that we did.

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The other one is a hypothetical line, which is the true line between the population of all the points.

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We wanted to show whether we can approximate this sample line as the population line.

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For that, we found out the confidence interval.

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Within which the population coefficient will lay.

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So, Debbie, does it all of the population line really between.

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These two values that we get from dissemble regression and the slope of the population regression relay.

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Between these two values of the sample equation.

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And we have a signed up probably of how confident we are.

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We are saying that there is a 95 percent chance that the population Diggnation corporations lie within

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these intervals, that we are not using sampling.

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Another use of standard error is to establish that whether X and Y actually have a relationship or not.

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In a linear model, this relationship is given by Biederman.

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We are saying that.

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Why is be the one times X plus constant?

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So if beta one is zero, it means that there is no relationship.

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If there is no relationship, then the variable X cannot be used to predict like.

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So we need to show that the probability of beta one being zero is negligible.

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Let me tell you the contempt first, and after that, I'll show you the way, how you will find it in

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every other statistical book.

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The concept is this Biederman has some value.

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That is the most probable value found by the formula we saw in the previous videos.

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Now, if you want to see that we are sufficiently confident that it cannot be zero.

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It has two parts to it.

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First, most probable value should be fired from zero and taken.

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The standard error of Weeda, which is giving us the interval in which the rule lays, should be small.

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So basically, we want Z2 not to lie in this whole interval in which be delays.

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I hope you get the idea.

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Let's do it the proper way, no, this this method is called hypothesis testing.

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We will construct two hypotheses.

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One is at zero, that is there is no relationship between X and Y.

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And its alternative, which is written as it is that there is a literature between X and Y.

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So it is Weedman is equal, Luisito.

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It is between is not equal, Luisito.

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And we want to disprove a digital.

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To disprove at zero.

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We will calculate something known as B statistic, which is given as BS equal to be done cap minus zero

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divided by standard A. B double.

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So you can see what this what this is representing here, enumerator.

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It says how far Bita one is from zero.

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And when you divided by standard at it, you go the distance is how many times?

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Standard edit.

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So using this formula will go to devalue.

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No, we want this devalue to be large.

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By the way, it is called P-value, because it is based on B distribution, which is similar to normal

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distribution.

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Basically, tea distribution is another prohibited distribution.

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And if you have P-value, you can get the probability of observing any value equal to absolutely or

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logit.

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The probability that you will get from this distribution is called P-value.

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Now, this P-value has meaning.

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We can interpret P-value as follows.

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Small value of B will mean that it is highly unlikely that there is no relationship between preterm

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response.

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Which means that we can reject the null hypothesis and declare that there is a relationship between

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X and Y.

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Typically, we use.

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A value like five percent or one percent as the cutoff value for P, that is, if P is listin point

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zero one, then the variable X is significantly impacting Y.

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There does look at deserts of of sample.

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Or that this is a desert which we have received from the software package that we are using and the

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course, there is a separate video where you you will learn how to run this analysis and get this result.

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I'm just discussing the result here as an example to all to read that we just covered.

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So in the last video, we had just seen the beta one and Bedazzler values this intercept, this debate,

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as you know.

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And this room, numb with evil, has this slope.

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This nine point zero nine is the beta one for this very evil.

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The first thing that we covered is the standard error.

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What does he do when we done?

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The formula that I showed you earlier was used to calculate the standard error of Bedazzler and be done

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how the standard elegant me use this.

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You can make this statement that for the sample of five, six observations, the beads that you calculated

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for minimum error was nine point zero nine.

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But you are 95 percent confident that for the global data of how spacing the be done will lay between

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nine point zero nine minus two times zero point for one.

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Do nine point zero nine plus two times zero point four to.

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So this interval is giving you that the estimated B does that you have here.

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Can be used to make this statement that deep-Rooted aggression coalitions will lie in the interval given

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by the standard error.

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The next thing we discussed will be when you and BP will you?

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This devaluing p value.

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We said that we have one hypothesis.

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We're just saying that there is no relationship.

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To disprove that hypothesis, we calculated or devalue.

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Which was given by this formula.

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So to get the value of this be done, we will put the bit of uncapped value divided by the S.

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E, so nine point zero nine divided by zero point forty one gives you this devalue.

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So corresponding to this devalue, we calculate a P value, which is it as probability of getting a

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P value, which is greater than equal to this?

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The that we call ridded.

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This property value is coming out to be very small.

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It's a it's an exponential with a bout of minus 16 to this value is very small.

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So if this value is very small, we can see that it is unlikely that there is no relationship, which

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means that there is some relationship.

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And therefore, we are confident that room number variable is impacting the house pricing and the relationship

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between them is given by this coefficient.

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So the takeaway from this lecture is we have be done and B, does it all values calculated for the simple.

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We calculated a standard error, which is helping us in determining two things.

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One is or does the event in which the true value of Beta one and B, does it relate?

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And the second thing is whether there is actually a relationship between these predictor.

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And the response variables.

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To establish that there is a listenership we calculated at P-value using these two things, using a

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T value, we calculated a P value.

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And if this P value is less than a threshold of one percent or five percent, whichever you like to

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use, then we see that there is a relationship.

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So far, our model, there is a relationship of hose pricing with room them, and that relationship

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is this between which is main point you don't make.