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).

Question

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 1

In this case, a linear representation may not be the best way to represent the data.

Looking at the ordered pairs provided, it is clear that the relationship between the input x and the output f(x) is not linear, as the output values do not follow a straight line. Instead, the data points seem to follow a more curved pattern, possibly a quadratic or exponential relationship.

A better alternative would be to use a quadratic or exponential regression model to better fit the data. By using a regression calculator to generate a quadratic or exponential equation, we can more accurately represent the relationship between the x values and the f(x) values. This would provide a better representation of the data and would likely produce more accurate predictions for other values of x.