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Regression Model Fitting With Quadratic Term Leads to Different Conclusion in Economic Analysis of Washington State Smoking Ban

Quarter/Year	Sales in Millions, $	Linear	Quadratic
1/02	96.5	89.2	101.0
2/02	98.7	90.0	98.8
3/02	99.7	90.8	96.7
4/02	95.1	91.6	95.0
1/03	91.1	92.4	93.6
2/03	91.9	93.3	92.5
3/03	93.3	94.1	91.6
4/03	92.6	94.9	91.0
1/04	90.0	95.7	90.7
2/04	92.2	96.5	90.7
3/04	97.1	97.3	90.9
4/04	93.4	98.2	91.5
1/05	91.5	99.0	92.3
2/05	96.6	99.8	93.4
3/05	99.3	100.6	94.8
4/05	96.9	101.4	96.4
1/06	91.8	102.2	98.4
2/06	96.3	103.1	100.6
3/06	99.4	103.9	103.1
4/06	97.6	104.7	105.9
1/07	100.3	105.5	108.9
2/07	114.1	106.3	112.3
3/07	126.0	107.1	115.9
4/07	124.2	108.0	119.8

Figure. Comparison of regression fit to taxable retail sales in bars and taverns in Washington State after the implementation of a smoke-free law, from the first quarter of 2002 (1/02) through the fourth quarter of 2007 (4/07). Values are adjusted for inflation to the Consumer Price Index (www.bls.gov/cpi/). The figure displays 2 regression equations for the quadratic fitting (y = 0.1405x² − 2.4969x + 103.58, R² = 0.7811) and the linear fitting (y = 0.8166x + 88.359, R² = 0.367) .

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