Question

When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as:______.
A) Y = β0 + β1X + (β2X)2 + ε
B) Y = β0 + β1X + β2X2 + ε
C) Y = β0 + β1X + β2X
D) Y = β0 + β1X2 + β2X2 + ε

Answer 1

Answer:

A

Step-by-step explanation:

The linear model can be assessed by the checking the independent variables having power 1 which shows the linear relationship between x and y. For example, as in the option B, C and D, the power of Xi's is one. Whereas the non linear model has the power for independent variables greater than 1. For example, as in option  A the model is a quadratic model because X associated with β2 has a power of a 2.

Thus the nonlinear model can be expressed as

Y = β0 + β1X + (β2X)2 + ε.