Table 7.

Panel regression test results of DIRS and DIRS² on ROA and ROE.

	Coefficient	t-statistics	p-value
Panel A: ROA (fixed effects)
Constant	0.1884	0.2302	0.8181
DIRS	0.0895	1.9784	0.0510*
DIRS2	−0.0018	−2.7829	0.0057**
F-statistic = 37.4328 Prob. (F-statistic) = 0.0000**			Adjusted R2 = 0.4645 DW = 1.8372
Panel B: ROA (fixed effects)
Constant	13.7315	1.8660	0.0629
DIRS	0.1008	2.0864	0.0376*
DIRS2	−0.0019	−2.9837	0.0031**
SIZE	−0.9243	−1.8469	0.0656
ΔSALES	0.0230	4.9458	0.0000**
F-statistic = 35.3098 Prob. (F-statistic) = 0.0000**			Adjusted R2 = 0.5082 DW = 1.7911
Panel C: ROE (fixed effects)
Constant	0.0115	0.0101	0.9863
DIRS	0.1340	1.9784	0.0446*
DIRS2	−0.0025	−2.7234	0.0068**
F-statistic = 35.2436 Prob. (F-statistic) = 0.0000**			Adjusted R2 = 0.4491 DW = 1.8057
Panel D: ROE (fixed effects)
Constant	27.4822	2.6902	0.0075**
DIRS	0.1488	2.2201	0.0271**
DIRS2	−0.0026	−3.0045	0.0029**
SIZE	−1.8785	−2.7040	0.0072**
ΔSALES	0.0319	4.9282	0.0000**
F-statistic = 35.1215 Prob. (F-statistic) = 0.0000**			Adjusted R2 = 0.4994 DW = 1.7912

Note: DW is the Durbin–Watson (1950) statistic, $DW={\sum }_{t=2}^N{({\hat{e}}_t-{\hat{e}}_{t-1})}^2/{\sum }_{t=1}^N{\hat{e}}_t^2$ and ${\hat{e}}_t$ are the least squares residuals from the regression equation under consideration. Based on the Durbin–Watson bounds test, there is no residual autocorrelation if DW is greater than the upper critical value bound, which approximately equals 1.78 at the 5% significance level.

^*Represent the significance level of 5%.

^**Represent the significance level of 1%.