In this video, we will assess the accuracy of the model that we have created.
Now we have established the relationship between X and Y.
What do we want to know?
How well does he predicted by values with the actual Y values?
So to assess the quality of it, we will look at two related quantities.
One is it is a double standard edit and the other is called R Square.
Let us first look at residual standard edit.
We saw earlier that there's a double standard edit is on the road odysseys by and minus two, which
can also be written like this, either summation or squared off difference between actual value and
predicted value.
Roughly speaking, Oddisee is the average amount that the response will deviate from the true regression
line.
As you can see in the desert shown below.
This is the design we got when we landed more than an assortment.
It is totally giving us details.
Do a standard edit with is six point five minutes of.
This model on 504 degrees of freedom.
This 504.
We are getting from minus two.
And it's 506.
And minus two is 504.
And this is called the degrees of Freedom.
So for these many degrees of freedom, we are getting a standard at all six point nine seven.
And in other words, even if a model was correct and through values of redoes, it wouldn't be the one
well known.
Exactly.
The predicted value of house price from this model.
We'll still be off by six point five nine seven unit on an average.
Therefore, Odyssey can also be considered as a measure of lack of fit of this model to the data.
So this six point five nine seven value is telling you on an average by how many units your predictive
value is missing, the actual value.
Next is the Oswestry stick.
The Odyssey provides an absolute measure of lack of food, but since it is measured in the units of
light, it is not always clear what constitutes a good odyssey.
So our R-squared provides us with an alternative squid as a proportion.
The proportion of total variance explained by our model.
So it always lies between zero and one.
It is the mathematical formula for Askwith.
R-squared is VSS minus Artosis upon basis would be assessed as total sum of squares.
And Odyssey's is legitimate sum of squares.
Yes, this is measuring the amount of variability inherent in the response.
That is what our house prices data.
The price of each house itself is writing about dimino space.
So if you find the difference of actual house price from the mean of the house price.
Square these values and add them up.
You get those small squares.
So this sort of sum of squared value is giving you the total amount of variability in whole space.
How much of this is explained by the model that we call constructed or that we will use odysseys, Odyssey's
is measuring the amount of variability that is not explained by our model of prediction and the assessed
minus.
Odyssey's is giving us the variability of way, which is explained by our model.
Therefore, R-squared measures the proportion of explained variance from the total variance.
R-squared venue, close to one, indicates that a large proportion of the variability in the response
variable has been explained by the regression model.
If it is close to zero, it indicates that regression did not explain much of divide evenly.
This can occur either because out of linear model is wrong or because Linnean was not the right choice
for this relationship between X and Y or both of these reasons or our model.
The result given by the software packages that led to a standard error was six point five nine.
R-squared value is zero point forty eight.
So it is somewhere between zero and one.
Nearly 50 percent of the video of the response variable is handled by the model that we constructed.
There is an added value.
We just call it just did R-squared, which you can see from the model result.
The difference between this R-squared and this adjusted R-squared is that an adjusted R-squared will
be altered, taking into account the total number of variables which are actually impacting the model.
The reason behind doing this is if you keep on adding variables to your model, Osgoode value simply
keeps on increasing.
Even if the variable is not significantly related with the response variable.
Still, the R-squared value will increase by less by a small amount.
So the adjusted R-squared is a modified version of R-squared that has been adjusted for the number of
predictors in the model, the adjusted R-squared increase is only the new term, improved the model
more than would be expected by chance.
It decreases when they predict that improves the model by less than expected by tons.
So adjusted R-squared is a more preferred term.
Or what?
R-squared.
We have a value of R-squared, but what value of R-squared will be considered as a good value of R-squared?
This will generally depend on the type of application that you get.
If the data is coming from a science experiment and the relationship is supposed to be actually linear
in such a case, Oscar should be very close to one.
But if it is a marketing data and we are missing a lot of unmeasured factors and the lenient assumption
is also a rough approximation of the relationship.
The residual errors are going to be large.
In such a case, even smaller R-squared values can be acceptable.
Generally, Oscar seventeen point five can be considered as a corporate model.