charlie used a regression calculator to generate the equation $f(x)= - 0.15x + 20.1$ for the ordered pairs…

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.

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.

Answer

Answer:

No, a linear representation is not the best way to represent the data.

Explanation:

Step1: Analyze data pattern

Plot the ordered - pairs ((2,15)), ((4,21)), ((6,26)), ((8,20)), ((10,14)) on a graph.

Step2: Observe non - linearity

The data does not follow a straight - line pattern. The values first increase from (x = 2) to (x=6) ((y) from (15) to (26)) and then decrease from (x = 6) to (x = 10) ((y) from (26) to (14)).

Step3: Suggest alternative

A quadratic representation might be a better alternative as quadratic functions can model data that has a single peak or valley, which seems to be the case here.