3. The following estimated equation was obtained by OLS regression using quarterly data for 1958 to 1976 inclusive:

| November 19, 2015


Yt = 2.20 + 0.104X1t − 3.48X2t + 0.34X3t.

(3.4) (0.005) (2.2) (0.15)

Standard errors are in parentheses. The explained sum of squares is 80 and the residual sum of squares 40.

Test the hypothesis that the coecient on X2t equals −4.

When three seasonal dummy variables are added and the equation reestimated, the explained sum of squares rose to 90. Define the seasonal dummy variables and write down the regression equation (using β’s for coecients). Test the null hypothesis of no seasonality.

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