Question

charlie used a regression calculator to generate the equation ( f(x)=-0.15x + 20.1 ) for the ordered pairs ( (2,15) ), ( (4,21) ), ( (6,26) ), ( (8,20) ), and ( (10,14) ). is a linear representation the best way to represent the data? if it is, explain why. if not, explain why and suggest a better alternative.

Explanation:

A linear representation is not the best way. The data points do not follow a consistent linear trend. For example, when \(x = 2\), \(y=15\); when \(x = 4\), \(y = 21\) (an increase), but when \(x=10\), \(y = 14\) (a decrease). A quadratic regression might be a better alternative as the data seems to have a non - linear (up - then - down) pattern.

Answer:

A linear representation is not the best way. The data does not follow a consistent linear trend. A quadratic regression could be a better alternative.