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Linear Regression - part 1
Linear correlation and linear regression are very close to each other. When you measure the linear correlation of two variables, what you are doing is laying out a straight line that best fits the average of these two variables. That line is spoken of as the regression line, and its utility is not only as a device for helping us to visualize the relationship between the two variables. It can also serve very usefully as a basis for making predictions.
In this section we will focus on 'Time Series' (as opposite to Cross Sections), meaning data for variables at different point in time (as it is the case when you get historical quotes on a stock exchange).
The line is called the regression line or least squares line, because it is determined such that the sum of the squared distances of all the data points from the line is the lowest possible.
If we have two variables X and Y), the regression line will have the following form:
X = a + b Y
where a is called the intercept, and b the slope as illustrated hereunder:
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