Least Squares Consider the four points 2001950 4001650 6001

Least Squares - Consider the four points (200,1950), (400,1650), (600,1800) and (800,1600). The least squares line is y = 1975 - 0.45x. Explain what \"least squares\" means, using these data as a specific example.

Solution

A line of best fit is a straight line that is the best approximation of the given set of data.

It is used to study the nature of the relation between two variables
Y = 1975 - 0.45 x
=>
When x = 200
Y = 1975 - 0.45(200) = 1885
When x = 400
Y = 1975 - 0.45(400) = 1795
When x = 600
Y = 1975 - 0.45(600) = 1705
When x = 800
Y = 1975 - 0.45(800) = 1615

With the curve fot we receive the data set as (200, 1885) ( 400,1795) ( 600,1705) (800,1615 ), We estimate the Y values at the best approximation of every X value. Though \'Y\' values produced are diffrent in the problem it gives the best approxmation for the given set of data