We saw simple linear regression with only one predictor variable.
However, in practice, that is really the case.
And we usually have more than one predictor variable.
Even in our house pricing data, we have 16 variables lived after data processing.
Let us now try to extend our analysis to accommodate multiple variables.
Mathematically, for multiple linear regression, the equation can be transformed as below.
Why is equal to does it all?
Plus, we don't want names x1 defoe's predictor.
Plus we our two times x2.
The second predictor and so on.
The last predictor here B is giving us the number of predictors and etr this last term.
Iida, is the error dumb, the error from Deve of this predicted away from the actual way.
And for our dataset, this equation.
Can we model like this?
Price is equal to Bedazzler, which is a constant plus beta one times.
The first variable.
Plus, beta, two 22nd preliterate able with this split population and so on.
And the 16 valuable.
So for any debt predictor, bita of that Geertz predictor is giving the average effect of one unit increase
in the value of that predictor on why?
With the assumption that we are hauling all other predators fixed, for example, if we increase poor
population by one unit, price will increase by Bider to units.
If we increase average distance by one unit, price will increase by redoes 16 unit to the coefficients
are giving us the amount of increase and the response would be able.
So when we are estimating the regression coefficient in a multiple linear model, the logical flaw remains
the same.
We first get the rest to some Oscars by this formula.
So this is the square of difference between the predicted and actual values.
And for all the data points, it is some.
So we tried to minimize this value, this artist's value.
We will again use calculus and matrix algebra to get the coefficients.
But the multiple regression coefficients are a bit complicated.
So we are not providing them here.
Our software will be handling that part again for us below.
I have given the result of the multiple linear regression model run on our dataset.
It includes all the predictable variables, the BDA estimates, the coefficient, then the standard
error.
We saw how to calculate standard error before we did simple linear regression and the corresponding
P and P values.
Against these P values, depending on their significance.
We have these tarmac's so we said that we can have a threshold of one percent if we have a threshold
of one percent.
We'll get two stars if we have a total of five or 10.
We'll get one star.
So these two are having a confidence interval of 95 percent.
And these three are having a confidence interval of more than point one percent.
And in the end, these are the values for the complete model.
So these are values for individual variables and these values are for the complete model.
So here is the multiple R squared, which is point seven two.
That is seventy two percent of the variance in the values of Y in the values of house price is explained
by our model.
Adjusted R-squared is taking into account the number of variables.
So the number of variables is 16.
So it is taking into account that we have 16 variables.
So, correspondingly, the adjusted R-squared is point seven one, which is nearly the same as R-squared.
And we can say that this model is pretty good in explaining the variance of why.
Remember that this is just it isn't in a separate video.
I will show you how to get this result.
How do I know multiple linear regression model in this software package.
And there will be discussing the whole result again and the meaning of each and every coefficient and
the P values and this are scored an F statistic.
The aim of showing, you heard is that when we run a multiple linear regression, this is the type of
result that we get.
We get the beta coefficient and the corresponding P values for each of the predictive variables.
And we get some other values which are for the whole model.