Question

How would you interpret the relationship between two numeric variables when the estimated least squares regression line for them is essentially horizontal (slope 0)?

Answer 1

We know that the least square regression line is given by the equation:

y = a+b x

Here is the Y-intercept of the line and is the slope of the line that is, angle made with the horizontal axis or corresponding change in Y when X increases by one unit. This implies that the least square regression lines are completely determined by the slope and the intercept as given in the above equation.

Now if this line is found to be horizontal as shown in the figure below then it can be easily observed from the figure that the horizontal least square regression line makes no angle with the horizontal axis of the independent variable and thus is parallel to it.