Should Seasonal Variables Be Included

Should Seasonal Variables Be Included - DETERMINING WHETHER...

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DETERMINING WHETHER TO INCLUDE DUMMY SEASONAL VARIABLES IN REGRESSION MODELS BACKGROUND Consider the following model with Trend and Seasons S 1 , S 2 , S 3 and S 4 . Note: one less season is included in the model: Y = β 0 + β 1 t + β 2 S 1 + β 3 S 2 + β 4 S 3 + ε CASE 1: The p-values for all t-tests for β 1 , β 2 , β 3 , β 4 were low. CONCLUSION: USE THE SEASONAL VARIABLE MODEL! Low Significance F At least one of t, S 1 , S 2 , S 3 is significant All p-values are LOW! t, S 1 , S 2 , S 3 are all significant

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al) MSE(Season Ho) in Terms of (Number ) SSE - (SSE F Seasonal Period = CASE 2: Not all the p-values for all t-tests for β 1 , β 2 , β 3 , β 4 were low. Use Partial F-test comparing the seasonal model to the period only model. Seasonal Model: Y = β 0 + β 1 t + β 2 S 1 + β 3 S 2 + β 4 S 3 + ε Period Only Model: Y = β 0 + β 1 t + ε Strategy: Perform the Partial F-test on the following: H 0 : β 2 = β 3 = β 4 = 0 H 1 : At least one of β 2 , β 3 , β 4 0 And the test is: Reject H 0 if F > F α , # terms in Ho, DFE(Seasonal) where CASE 2a: Not all p's low, but include Seasonal Variables Regression With Seasonal Variables Low Significance F At least one of t, S 1 , S 2 , S 3 is significant Low p- High p-values MSE

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