Question: Regression Analysis In trying to find new locations for their restaurants, fast food chains such as McDonald's or Wendy's usually consider a number of factors. A company researcher is developing a model for site selection. Since high sales is the objective in site selection, the dependent variable in an analysis of sites will be annual gross sales. The independent variables will be mean annual household income (INC) and mean age of children (AGE) in the area surrounding the site. Twenty five currently operating sites with approximately 5,000 in population and one major competitor were randomly selected. A complete second-order model was used in the study. The model is of the form:

where:

y = annual gross sales

INC = mean annual household income

AGE = mean age of children in the area surrounding the site

The following least squares model is obtained:

with:

the standard error of b₁ = 49.6

the standard error of b₂ = 47.2

the standard error of b₃ = 0.54

the standard error of b₄ = 1.17

the standard error of b₅ = 0.94

R² = 0.91

F = 36.9 with 5 and 19 df.

A. Perform tests to determine if the quadratic terms are appropriate.

B. Is there significant interaction between incoMeand mean age of children? Test an appropriate hypothesis.

C. At what level of income does sales reach an optimum (peak or trough) when mean age is 10 years?

D. An area under consideration for a restaurant has a median income of $35,000 and the average age of children is ten years, use this model to predict Sales in this area.