linear_regression.txt

Linear Regression Line:
A linear line showing the relationship between the dependent and independent variable is called a regression line.
Types of relations in the regression line:
1) Positive Linear relationship 
2) Negative Linear Relationship

1) Positive Linear Relationship--> increase in both the x and y axes independent variables and dependent variables respectively.
2) Negative Linear Relationship--> when there is increase in the x axis and decrease in the y axis that is independent and dependent variable respectively.

Finding the best fit line :
basically our main focus in the best fit line is that the error between the predicted value and the actual value should be minimized.
The best fit line will have the minimum error
why the word "cost function " is used in machine learning and that in linear regression?

ans: to find the best values for the coefiicients (a0 and a1 ) in linear regression for example y= a0 + a1x (a0 and a1 are coefficients )
and this will further help us to find the best fit .

what are the benefits of using the cost function?
ans:
optimizes the regression coefficients 
measures how a linear regression model is performing.

find the accuracy of mapping function-->maps the input variable with the output variable.
In linear regression we use the mean squared error between the predicted value and the actual value .

what are residuals ?
ans:
The distance between the predicted and the actual value .
If the observed points will be far away from the regression line then the residual will be high
and if the observed points are close to the regression line then the residuals are low and so the cost function.'

Gradient Descent:
it is used to minimize the Mean Squared Error by calculating the gradient of the cost function.
to update the coefficients of the line by reducing the cost function.
random selection of values of coeeficients and then iteratively update the values to reach the minimum cost function.

Model Performance:
Optimizations: to find the best out of the various models 
1) R-Squared Method:
determines goodness of fit.
measures the strength of the relationship between the dependent and independent variables on a scale of 0-100%
The high value of R-Squared method shows less difference between the predicted and the actual value and hence represents it as a good model.
it is also called coefficient of determination and coefficient of multi determination for multiple regression.
R-squared = expected variation/ total variation

Assumptions of Linear Regression :
1) Linear relationship between the features and the target.
2) small or no multicolinearities between the features.
3) Homoscedactisity assumption:
4)