Question

Explain the importance of linearity when measuring the relationship between two continuous variables. If the relationship is not linear, what test would be advisable? List and explain two continuous variables that are unlikely to have a linear relationship.

Answer 1

Linear relationship between two variables depends on nature of the variables.

As to exists linear relationship there should be systematic increase of two variables. That is y=mx+c

This linear relationship doesn't exists when y will not be explained through x but some functions of x say g(x)

So for example ,

1)

year is x and population is our y in this case linear regression doesn't hold. The model should be exponential that is log(y)= mx+c

2)

For a sleep medicine, response y is length of sleep and x is dose of medicine. Here also linearity doesn't hold.