Similar to stocks, knowing time-series correlation for sales data can be incredibly valuable as well. Suppose a man has a hot dog stand called PCA Hot Dogs and he would like to know how it is doing relative to industry-wide performance of all hot dog stands. The sales data for PCA Hot Dogs is attached. Construct a simple linear regression for PCA Hot Dogs' sales to industry sales, and plot the residuals over time. Use the Durbin-Watson test to determine whether there is positive autocorrelation in the errors. Draw conclusions about the existence of autocorrelation and use them to inform on the performance of PCA Hot Dogs. Include a correlogram.

Follow-Up Discussion:Other than the simple linear time regression, what other models might we consider here to better fit this data? What business questions might we ask next after these analyses?

Month PCA HotDogs Sales Industry-Wide Sales

1 5 0.318

2 5.06 0.33

3 5.12 0.356

4 5.1 0.334

5 5.35 0.386

6 5.57 0.455

7 5.61 0.46

8 5.8 0.527

9 6.04 0.598

10 6.16 0.65

11 6.22 0.685

12 6.31 0.713

13 6.38 0.724

14 6.54 0.775

15 6.68 0.78

16 6.73 0.796

17 6.89 0.8598

18 6.97 0.88

19 7.1 0.89

20 6.8 0.91

21 7.2 0.95

22 7.3 1.1