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

Answer 1

A linear representation is the best way to represent the data because the given equation f(x) = -0.15x + 20.1 is a linear equation.

Step-by-step explanation:

A linear representation is the best way to represent the data because the given equation f(x) = -0.15x + 20.1 is a linear equation. This equation represents a straight line relationship between the independent variable x and the dependent variable f(x). The slope of the line is -0.15, which represents the rate of change of f(x) with respect to x. The y-intercept of the line is 20.1, which represents the value of f(x) when x=0.

Answer 2

The r-value for the linear function related to the ordered pairs is very close to zero, so it is not a good representation of the data. A quadratic model would better represent the data because there is a turning point within the data set. The data increases then decreases, which is what the graph of a quadratic does.

Step-by-step explanation: