Question

A market researcher, having collected data on breakfast cereal expenditures by families with one, two, three, four, or five children living at home, plans to use an ordinary regression model to estimate the mean expenditures at each of these five family size levels. However, the researcher is undecided between fitting a linear or a quadratic regression model, and the data do not give clear evidence in favor of one model or the other. A colleague suggests: "For your purposes, you might simply use an ANOVA model." Is this a useful suggestion? Explain.

Answer 1

Answer and Step-by-step explanation:

ANOVA model is mathematical model describe relationship between response and treatment.

One way ANOVA is given by:

YIJ = µ + Ti +Єij

Where, yij represent jth observation on ith treatment.

In this question, researcher collected data on the breakfast expenditure of a family whose size is five.

Yes, we can use ANOVA model. ANOVA can be used even if there is quadratic nonlinear relationship between expenditure and family size.

Since, the family size is five; we have to compare their mean expenditure on food.

The ANOVA one way model is:

YIJ = µ + Ti +Єij

For i=1, 2,3,4,5 and j= 1, 2,3,4,5

With hypothesis,

H01 : µ1 are equal.

H11 : at least two i not equal to j.

Answer 2

Answer:

Yes it is a useful suggestion

Step-by-step explanation:

Using the ANOVA model is a good idea because using it would give allowance For us to compare the five means of the five different family sizes. By this, during investigation there would be no confusion as to if a quadratic or linear relationship exists between the variables family size and breakfast cereal expenditure.

We would be comparing the mean expenditure of food of these 5 different family size levels so anova is useful.