Brendan Dennehy, CFA, works for Transon Investments, Plc., a Dublin-based hedge fund with significant equity investments in technology companies in Asia. North America, and Europe. Transon is concerned by the recent poor performance of one of the fund's Chinese investments, Winston Communications, an assembler of telecommunications equipment. Transon's chief of information technology (IT) is Sean Malloy. Yesterday, Winston's IT office sent Malloy data relating to the assembly process and a printout of an analysis of the number of defective assemblies per hour, Winston's IT people believe that the number of defective assemblies per hour is a function of the outside air temperature and the speed (production rate) of the assembly lines. Malloy recalls that Dennehy has had substantial training in statistics while working on his MBA. He asks Dennehy to help him interpret the regression results supplied by Winston.

Using the data provided in Exhibit 1，Dennehy tests the hypothesis that the coefficients for outside air temperature and assembly line speed are significantly different from zero, using a significance level of 5%.

Next Dennehy would like to confirm that nonstationarity is not a problem. To test for this he conducts Dickey-Fuller tests for a unit root on each of the time series. The results are reported in Exhibit 2.

Dennehy tells Malloy about the Dickey-Fuller test results, stating:

We can safely use regression to estimate the relationship between the dependent variable and the independent variables if:

1. none of the three time series exhibit a unit root, or

2. all three series exhibit a unit root but they are also mutually cointegrated.

Malloy disagrees in part with Dennehy's statement, He agrees with Dennehy about the use of regression if none of the time series exhibit a unit root. But Malloy believes that it is safe to estimate the regression if only the independent variables exhibit unit roots but are cointegrated, and the dependent variable does not exhibit a unit root.