Question

What is the least squares regression model for the following data points?: (1,3), (2,6), (3,19), (2,7), (8,9), (10,25)

Answer 1

`y=1,5721x+4,6875`

Explanation:

Essentially the least squares method places the best possible straight line fit through a given data set.

We may use a calculator in stat mode and enter all these data points and the calculator will output the gradient and y-intercept of the corresponding least squares line.

Doing so, I obtain :

Gradient = 1,5721
y-intercept = 4,6875

Coefficient of correlation, r = 0,68285,
Since r is not all that close to 1, it implies that a straight line does not approximate this data set very well, ie lots of data points are far off the least squares line of best approximation in this case.

Graphically, the least squares line, `y=1,5721x+4,6875` looks as follows

graph{1.5721x+4.6875 [-41.1, 41.13, -20.55, 20.56]}