## 3 Regression Analysis of Price (USD/MWh) Data for West, North, and Houston Regions in ERCOT
### Analysis of Hourly Models for North and Houston Price Data  
Since the inferences for the North and Houston regions are almost identical, we treat them together. Consider Tables 5 and 6, which correspond to the parameter estimates for the North and Houston regions, respectively. * WSapp18 at 4 PM: The WSapp81 variable results in a significant reduction in price per MWh in both regions--6.2% in the North, and 5.4% in Houston. * MOE at 4 pm: Solar generation (Sgen) is significant, but positive, in both regions. Importantly, these marginal solar effects are negligible. The conflicting positive coefficient sign is once again the result of very little solar energy in the ERCOT grid at 4 PM, when compared to the energy present from nuclear and wind sources. This is yet another reason we chose to combine wind and solar active applications in the models. Over time, it may become viable to separate solar and wind applications in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Normal Regression Coefficients** & **Hour 3 AM** & **Hour 11 AM** & **Hour 4 PM** \\ \hline WSapp18 & 0.0007 & \(-\)0.0841 * & \(-\)0.1572 * \\  & (0.0179) & (0.0235) & (0.0263) \\  & \(-\)2.6998 * & - & - \\  & (0.0235) & - & - \\  & 1.3815 * & - & - \\  & (0.0327) & - & - \\  & & 1.3162 * & \\  & (0.0401) & - & - \\  & - & (0.0450) & - \\  & 0.3036 * & 0.4993 * & 0.3114 * \\ Ln(NGprice) & (0.0421) & (0.0462) & (0.0522) \\  & \(-\)0.2664 * & \(-\)0.2371 * & \(-\)0.3339 * \\  & (0.0103) & (0.0083) & (0.0112) \\  & - & \(-\)0.0201 & 0.0275 \\  & (0.0127) & (0.0115) \\  & \(-\)0.1749 * & \(-\)0.0752 & \(-\)0.1148 \\  & (0.0387) & (0.0428) & (0.0495) \\  & 0.1440 & 0.4031 * & 0.8271 * \\  & (0.0843) & (0.1129) & (0.1198) \\ Ln(REload) & 0.7441 * & 0.5791* & 0.7455 * \\  & (0.0555) & (0.0642) & (0.0699) \\  & \(-\)2.0414 * & \(-\)3.2873 * & \(-\)6.6572 * \\  & (0.5050) & (0.5144) & (0.5099) \\ \hline \hline \end{tabular} Legend: * \(p\) < 0.0001.  
\end{table} 
Table 4: West region normal regression estimates. the modeling process. The nuclear generation coefficient estimates for the North and Houston regions are \(-0.1188\%\) and \(-0.1967\%\), and for wind generation, the estimates are \(-0.0931\%\) and \(-0.0717\%\), respectively. * WSupp18 at 11 AM: The WSupps18 variable results in a statistically significant (\(p<0.0001\)) reduction in price per MWh in both regions--3.80% in the North, and 3.95% in Houston. * MOE at 11 AM: Solar generation (Sgen) is significant in both regions, but the marginal effects are almost zero. This is not surprising, since, as noted before, solar energy is still in its infancy in the ERCOT. The nuclear generation coefficient estimates for the North and Houston regions are \(-0.1124\%\) and \(-0.1695\%\), and for wind generation, the estimates are \(-0.0917\%\) and \(-0.0666\%\), respectively, with \(p<0.0001\). * WSupp18 at 3 AM: The WSupps18 variable results in a statistically significant (\(p<0.0001\)) reduction in price per MWh in both regions--2.31% in the North, and 3.1% in Houston. * MOE at 3 AM: The nuclear generation coefficient estimates for the North and Houston regions are \(-0.1592\%\) and \(-0.1760\%\), and for wind generation, the estimates are \(-0.0965\%\) and \(-0.0824\%\), respectively, with \(p<0.0001\). * Finally, the price dummies, natural gas price, North load, Houston load, and rest of the ERCOT load, in the North and Houston regions are generally consistent with the inferences described above for the West region. Likewise, the normal regression analyses are similar to that for the West region, and is thus omitted in this paper. In summary, based on the regression analyses of the three regions, this paper empirically validates the conjecture that offering tax incentives to increase the number of active wind and solar applications is associated with meaningful reductions in the wholesale price of electricity in the ERCOT.