Describe about how to place a regression line?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Describe about how to place a regression line?
The most common method for placing a regression line is Least squares method. In this method the basic concept is to minimize the squares of the error or residual terms using the method of minima and finding the relations (or normal equations) for estimating the parameters (coefficients).
Let us suppose that we have two variables X and Y (say) with values (xi, yi), i=1,2,...,n. There has been observed a dependence between these two, such that Y is dependent and X is explanatory then the line of regression will be
where ei is the error or residual.
In order to fit the line 
, we have to minimize total ei. To do so, the principle of maxima and minima is used.
Accordingly we have to determine a and b so that
is minimum. For this we take the partial derivatives w.r.t. a and b and equate them to zero as:
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