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Interpretations

Once we have a model, it is important to understand the real world interpretations of the slope and of the intercepts.  Understanding how to interpret these will give us a better feel for the power and limitations of modeling.

Our Model y = 1.01755752x - 1.309866458

a.) An interpretation of the slope of your model.

The slope of our model is 1.01755752.  For our particular situation, the interpretation is:

For each additional inch of height, the arm span increases by 1.01755752 inches.

Generally: For each additional unit of 1 in the x, the y increases (or decreases) by m.

b.) An interpretation of both intercepts of your model.

i.) The y-intercept of our model is y = -1.309866458.  For our particular situation, the interpretation is:

If a person has a height of 0 inches, then his or her arm span is -1.309866458 inches.

ii.) The x-intercept is 1.309866458/1.01755752  = 1.287265272.  For our particular situation, the interpretation is:

If a person's arm span is 0 inches, then his or her height is 1.287265272 inches.

c.) While these interpretations may seem a bit odd - after all - no one has a negative arm span, they do show you some limitations in modeling.  A model that makes perfectly good sense in some situations may have major limitations elsewhere.  

d.) This brings up the difference between interpolation and extrapolation.

i.) Interpolation is using a model to estimate values among the observed values.

ii.) Extrapolation is using a model to estimate values outside the observed data.

  last modified September 05, 2007