Question

Experience with a certain type of plastic indicates that a relation exists between the hardness (measured in Brinell units) of items molded from the plastic (Y) and the elapsed time since ter- mination of the molding process (X). It is proposed to study this relation by means of regression analysis. A participant in the discussion objects, pointing out that the hardening of the plastic "is the result of a natural chemical process that doesn't leave anything to chance, so the relation must be mathematical and regression analysis is not appropriate." Evaluate this objection.

Answer 1

Answer:

Step-by-step explanation:

The regression analysis is a mathematical measure of the average relationship between two or more variable in terms of the original units of data.

Liner regression: If the regression curve is a straight line then there is a linear regression between the variables.

Non-linear regression: If the regression curve is not a straight line then there is a non-linear regression between the variables.

The correct answer is: a specific mathematical model my not be appropriate in this case.

The argument is the results of natural chemical process that doesn’t leave anything to chance, so the relation must be mathematical and regression analysis is not appropriate.

From the available information, the relation exists between the hardness of items moulded from the plastic $\left( y \right)$ and the elapsed time $\left( x \right)$.

The argument is the results of natural chemical process that doesn’t leave anything to chance, so the relation must be mathematical and regression analysis is not appropriate.

The hardness of items moulded by plastic is dependent on so many other variables, such as material quality (impurities in the plastic), which in turn may change the relation between $x{\rm{ and }}$.

Also there can be chance of wrong measurement (not purely chance cause). So obviously, there are many effects which are affecting the relation between the variables. So, a specific mathematical model my not be appropriate in this case.

There can be chance of wrong measurement (not purely chance cause). So obviously, there are many effects which are affecting the relation between the variables. So, a specific mathematical model my not be appropriate in this case.