Question: An experiment was designed by a market researcher to study the effects of two types of promotional expenditures on sales of a line of food products sold in supermarkets. Sixteen locations were selected at random for the test. The researcher collected data on three factors. The data is given below, where y = sales volume ($ ten thousands), x₁ = media expenditures ($ thousands), and x₂ = point-of-sale expenditures ($ thousands).

y: 8.74 10.53 10.99 11.97 12.74 12.83 14.69 15.30 16.11

x₁: 2 2 2 2 3 3 3 3 4

x₂: 2 3 4 5 2 3 4 5 2

y: 16.31 16.46 17.69 19.65 18.86 19.93 20.51

x₁: 4 4 4 5 5 5 5

x₂: 3 4 5 2 3 4 5

The following model is proposed:

Y = b₀ + b₁x₁ + b₂x₂ + e

Carry out a “complete” multiple regression analysis of this model. In addition

predict y for x₁ = 3, and x₂ = 3, and give a 95% C.I. for both Y|X, and E[Y|X].