Regression @ Grocery Store.
Let suppose, you made up a list to buy grocery, say, - crate of eggs (X 1 ), bread(X 2 ), orange juice(X 3 ), and toilet roll(X 4 ). Before you go to the store you want to be able to predict your expenditure, Total Cost(Y) to you. Y is the dependent variable, because the cost depends on what you buy, X's, called the independent variables. We determine the unit price of each item based on our past purchases (observed data). In general, there will be price variation at different grocery stores or on different days at the same store - think about sales or occasional discounts. Therefore we are only able to estimate the unit costs.
In simple regression, the model for each X will be: Y= b 0 +b 1 X 1 , where b 1 is unit price of X 1 to be estimated. Suppose, using regression regression, we estimate the unit cost of eggs, bread, orange juice, toilet roll, and soap to be 2.10, 2.95, 3.95, 6.99, respectively. We say that, a unit increase in the number eggs purchased will increase your Total Cost(Y) by S2.10 and so on for the other items.
The multiple regression model has the equation: Y=b 0 +b 1 X 1 +b 3 X 3 +b 4 X 4 ; where b i s represent adjusted unit prices of each item. We usually use statistical software, such as Excel, MegaStat, SPSS, SAS, etc to get the estimates. Suppose there has been a long ongoing promotion, that shows that for each purchase of orange juice, you get crate of eggs free. Note that if you pick only eggs, you pay $2.95 for it, similarly for the other items. However, if you buy the orange juice and eggs together, you practically get the eggs free.
Statistically, we say the price of eggs depends on the purchase of orange juice or the adjusted price of eggs is insignificant. This is the essence of multiple regression-how much will the unit price of one item influence that of another item.
Questions: Suppose in this example b 0 =3.5.
How do you interpret b 0 ? Does it have a meaning if you don't buy anything?