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01:22

# The Linear Regression Model. Geometrical Representation

01:22
/ The Linear Regression Model. Geometrical Representation

## The simple linear regression model. Geometrical representation

Letâ€™s check out the simple linear regression model equation. Here it is.

You have probably heard about the regression line, right? When we plot the data points on an x-y plane, the regression line is the best-fitting line through the data points.

Okay. Hereâ€™s a plot with some data points. We plot the line based on the regression equation.

The grey points that are scattered are the observed values.

B zero, as we said earlier, is a constant and is the intercept of the regression line with the y axis.

B one is the slope of the regression line. It shows how much y changes for each unit change of x.

The distance between the observed values and the regression line is the estimator of the error term epsilon. Itâ€™s point estimate is called residual.

Now, if you draw a perpendicular from an observed point to the regression line, the intercept between that perpendicular and the regression line is a point with a y value equal to y hat. As we said earlier, given an x, y hat is the value predicted by the regression line.