Regression and Time Series Data: Seasonal Variation

Textbook: Section 13.8 (8^th edition)

Example: Canadian Monthly Fresh Fruit Imports (millions $), 1980-2000.

Regression Analysis: FruitImpM versus Time, Jan, ...

The regression equation is

FruitImpM = 40.1 + 0.390 Time - 14.1 Jan - 12.5 Feb + 1.31 Mar + 1.94 Apr

+ 14.6 May + 33.4 Jun + 23.0 Jul + 4.34 Aug + 1.53 Sep - 4.09 Oc

+ 1.85 Nov

Predictor Coef SE Coef T P

Constant 40.134 2.107 19.04 0.000

Time 0.389586 0.007080 55.02 0.000

Jan -14.138 2.642 -5.35 0.000

Feb -12.513 2.642 -4.74 0.000

Mar 1.312 2.641 0.50 0.620

Apr 1.941 2.641 0.73 0.463

May 14.617 2.641 5.53 0.000

Jun 33.445 2.641 12.66 0.000

Jul 23.009 2.641 8.71 0.000

Aug 4.336 2.641 1.64 0.102

Sep 1.527 2.641 0.58 0.564

Oc -4.088 2.641 -1.55 0.123

Nov 1.847 2.641 0.70 0.485

S = 8.758 R-Sq = 93.6% R-Sq(adj) = 93.2%

Analysis of Variance

Source DF SS MS F P

Regression 12 279467 23289 303.61 0.000

Residual Error 251 19254 77

Total 263 298721

Source DF Seq SS

Time 1 234467

Jan 1 8133

Feb 1 8252

Mar 1 1030

Apr 1 1073

May 1 699

Jun 1 15860

Jul 1 9103

Aug 1 359

Sep 1 85

Oc 1 368

Nov 1 38

Durbin-Watson statistic = 1.77