Question

Using a series of 40 annual observations, a student estimated a model that included the following variables:

            Y = yearly Dow Jones Industrial Average

            X₁ = ratio of annual corporate profit to annual corporate sales

            X₂ = index of industrial production

            X₃ = corporate bond yield

            X₄ = disposable income per capita

            X₅ = consumer price index.

The results included the following:           R² = .885        dw = 1.046

a.    Is there evidence of a linear relationship between the Dow Jones and any of the independent variables? Use alpha =.05.

b. Should we conclude that 1st order autocorrelation is a problem? Use alpha = .05.

Answer 1

Using a series of 40 annual observations, a student estimated a model that included the following variables:

            Y = yearly Dow Jones Industrial Average

            X₁ = ratio of annual corporate profit to annual corporate sales

            X₂ = index of industrial production

            X₃ = corporate bond yield

            X₄ = disposable income per capita

            X₅ = consumer price index.

The results included the following:           R² = .885        dw = 1.046

a.    Is there evidence of a linear relationship between the Dow Jones and any of the independent variables? Use alpha =.05.

Degrees of freedom for toal 40-1=39

DF for regression= 5

Df for error = 34

=(0.885/5)/((1-0.885)/34)

=52.33

Critical F( 5,34) at 0.05 of significance = 2.494

Calculated F 52.33 > critical F. Ho is rejected.

There is evidence to conclude that there is a linear relationship between the Dow Jones and any of the independent variables.

b. Should we conclude that 1st order autocorrelation is a problem? Use alpha = .05.

Durbin Watson test reports a test statistic=1.046

Critical value of Durbin Watson test at 0.05 level =(1.230, 1.786)

The calculated test value is below the lower limit. Therefore there is concern about positive autocorrelation.