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.

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.

Vocaloid · Answer

calculate the R^2 value for this model and data (typically we use regression software for this, if you have a graphing calculator you can calculate the R^2 value, if not you can find regression calculators online). the closer to 1 that the R^2 value is, the better the model represents the data.

try a few models: linear, quadratic, cubic, exponential, logarithmic, etc.  see if there are any better fits than linear.