In this video, we will assess the accuracy of the model that we have created, that we have established
the relationship between X and Y, but we want to know how well does the predicted values with the actual
Y values.
So assess the quality of it.
We will look at two related qualities.
One is the digital standard edit and the other is called R Square.
Let us first look at the standard error.
We saw earlier that the visitors center that it is on the route are assessed by and minus two, which
can also be written like this, a summation of squared of difference between actual value and predictive
value.
Roughly speaking, Oddisee is the average amount that the response will deviate from the true regression
line.
As you can see in the results shown below, this is the result we got when we ran the model and software,
it is straightaway giving us the standard error, which is six point five minutes of for this model
on 504 degrees of freedom.
This 504 we are getting from minus two and this or to minus two is 504.
And this is called the degrees of Freedom.
So for these many degrees of freedom, we are getting a standard error of six point nine seven.
And in other words, even if the model was correct and true values of zero and we were never known exactly
the predicted value of house price from this model.
They'll still be off by six point five nine seven units on an average.
Therefore, Odyssey can also be considered as a measure of lack of fear 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 R-squared statistic, The Odyssey provides an absolute measure of lack of it, but since
it is measured in the units of light, it is not always clear what constitutes a good odyssey.
So R-squared provides us with an alternative.
Oscar is 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, squaddies versus minus Odyssey's upon basis that
assesses total sum of squares and Odyssey's vegetables are Moscowitz.
DSF is measuring the amount of variability inherent in the response that is porras house prices data.
The price of each house itself is varying about the mean house price.
So if you find a difference of actual Osprey's from the man of the house price.
Square these values and add them up, you get total sum of squares, so this total sum of square value
is giving you the total amount of variability in how space.
How much of this is explained by the model that we constructed or that we will use Odyssey's Odyssey's
is measuring the amount of variability that is not explained by our model of the degradation and the
assessed minus.
Odyssey's is giving us the variability of light, which is explained by our model.
Therefore, as good measures, the proportion of explained variance from the total variance.
Oscar winning 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 the regression
did not explain much of the variability.
This can occur either because our linear model is wrong or because linear was not the right choice for
this relationship between X and Y or both of these reasons for our model.
The result given by the software packages that started at about six point forty nine.
R-squared value is zero point forty.
So it is somewhere between zero and one, nearly 50 percent of the variability of the response variable
is handled by the model that reconstructed.
There is another value, we just called it just R-squared, which you can see from the model result,
the difference between this R-squared and this adjusted R-squared is that in adjusted R-squared will
be also 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 Oscar value
will increase by 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 and the model, the adjusted R-squared increases only the new term improved the model more
than would be expected.
By chance, it decreases when the predictor improves the model by less than expected by chance.
So just did.
R-squared is a more preferred term over R-squared.
Now 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 have.
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 linear assumption
is also a rough approximation of the relationship.
These letters are going to be large.
In such a case, even smaller Oscar values can be acceptable generally, Oscar, better than point five
can be considered as a good fit model.