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 left after data preprocessing.
Let us not try to extend our analysis to accommodate multiple variables.
Mathematically, for multiple linear regression, the equation can be transformed as below.
Why is he going to be the zero plus one times X one defense predictor?
Plus, we are two times X2, the second predictor and so on.
The last predictor here, B is giving us the number of predictors.
And it's this last item is the erratum the error from the of this predicted Y from the actual Y.
And for our dataset, this equation can be modelled like this price is equal to be zero, which is a
constant plus the times the first variable.
Plus, we two times the second level with this poor population and so on, the 16 variable.
So for any date predictor beta of that date predictor is giving the average effect of one unit increase
in the value of that predictor on why.
With the assumption that we are holding all other predators fixed, for example, if we increase poor
population by one unit, price will increase by better two units.
If we increase resistance by one unit, price will increase by 16 units to the corporations are giving
us the amount of increase in the response variable.
So when we are estimating the regression coefficient in a multiple linear model, the logical flaw remains
the same.
We first get the results of 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 something.
So we try to minimize this value, this odysseys 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 beta estimates, the capuchin and then the standard
error, we saw how to calculate standard error before we did a simple linear regression and the corresponding
PNB values.
Against these people use 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 will get two stars.
If we have a threshold of five percent, we will 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 two 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 seven to 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 did Square 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, they ask where it is pointing and one which is nearly the same as our square.
And we can say that this model is pretty good in explaining the variance of why.
Remember that this is just the result in a separate video, I'll show you how to get this resolved,
how to run a multiple linear regression model in the 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 squared and F statistic.
The aim of showing you here 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.