Question

Under what conditions might it make better sense to use a linear function rather than a quadratic or cubic function that fits a few data points more​ closely?

Answer 1

Explanation:

When data points are plotted between two variables, seeing the scatter plot we can form idea about the curve which is close to all points.

In other words, using least squares method, the curve of best fit would be the curve which has squares of deviations form the observed points a minimum

Thus conditions are

i) The scatter plot suggests a linear relationship

ii) Pearson correlation coefficient has value near to 1 or -1 suggesting linearlity

iii) There seems to be constant increase of y for unit increase in x

Under the above linear line fits

In all the other cases, quadratic or cubic function fits well.