Another Example with Dummy Variables

Suppose we want to predict a restaurant’s sales from traffic flow going past the restaurant and the city in which the restaurant is located.

First, we plot the sales vs. the traffic flow, but in a special way. We create the plot so that the points are broken up by the city. So, on the plot, seeing a `1` means this is the sales for a restaurant in city 1 with the specified traffic flow.

Does it appear that a different line is needed to describe sales in each city?

If so, does each line need a different slope and intercept?

Begin with a model that only uses traffic flow to predict sales:

Regression Analysis: Sales versus Flow

# Some output deleted

The regression equation is

Sales = 0.018 + 0.108 Flow

S = 0.5957 R-Sq = 93.4% R-Sq(adj) = 93.1%

Analysis of Variance

Source DF SS MS F P

Regression 1 111.34 111.34 313.75 0.000

Residual Error 22 7.81 0.35

Total 23 119.15

Now, try a model which uses the city variable, with no flow*city interaction. This gives parallel lines that have different y-intercepts.

Regression Analysis: Sales versus Flow, City1, City2, City3

# Some output deleted

The regression equation is

Sales = 1.08 + 0.104 Flow - 1.22 City1 - 0.531 City2 - 1.08 City3

S = 0.3623 R-Sq = 97.9% R-Sq(adj) = 97.5%

Analysis of Variance

Source DF SS MS F P

Regression 4 116.656 29.164 222.17 0.000

Residual Error 19 2.494 0.131

Total 23 119.150

Finally, set up a model with interaction terms, so the lines will have differing slopes and intercepts.

Regression Analysis: Sales versus Flow, City1, ...

# Some output deleted

The regression equation is

Sales = 0.709 + 0.109 Flow - 0.252 City1 - 0.618 City2 - 1.20 City3

- 0.0156 FlowCity1 + 0.0055 FlowCity2 + 0.0049 FlowCity3

S = 0.3418 R-Sq = 98.4% R-Sq(adj) = 97.7%

Analysis of Variance

Source DF SS MS F P

Regression 7 117.280 16.754 143.39 0.000

Residual Error 16 1.870 0.117

Total 23 119.150