Exercise: Head circumference and height, answer 9

Question 9: The equation of the regression line is:

        head circumference = 372 + 0.114 height

What is a regression line and what does it tell us? In what units are 0.114 and 372 reported?

Suggested answer

A regression line predicts the mean value of the outcome variable, head circumference, for any given value of the predictor variable, height. It is the prediction which minimises the sum of squares of the differences between the observed outcome and that predicted by the equation.

0.114 is the slope or gradient of the line, the amount by which the mean measurement of head circumference of students of any given measured height exceeds that for students whose measured height is one millimetre less. It is the difference in head circumference measured in millimetre for a difference of one unit of height measured in millimetres. Hence its units are millimetre per millimetre.

372 is the intercept or constant term, the value of the outcome variable when the predictor variable is zero. In this case it does not have any meaning other than to get the line in the right place. As it is the mean head circumference in millimetre for students with zero height, the units are millimetres.


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