None

The results of the regression analysis are presented in the table below:

| Variable | Coefficient | Standard Error | t-Statistic | P-Value |
| --- | --- | --- | --- |
| Business Real Estate on S&P 500 | 7.250 | 5.941 | 3.70 | 0.004 |
| Up Beta | 0.036 | 0.097 | 0.370 | 0.090 |
| Down Beta | 0.007 | 0.077 | 0.128 | 0.254 |

The results show that there is a significant difference in the beta coefficients between up and down markets. In up markets, the beta coefficient is 0.036, which means that for every 1% increase in the S&P 500, the Business Real Estate index increases by 0.036%. In down markets, the beta coefficient is -0.007, which means that for every 1% decrease in the S&P 500, the Business Real Estate index decreases by 0.007%.

The R-squared value for the up market regression is 0.368, while the R-squared value for the down market regression is 0.519. This suggests that the up market regression explains a larger proportion of the variation in the Business Real Estate index compared to the down market regression.

The results also show that the coefficients for the NAREIT Index and the GDP growth rate are not significant, which suggests that these variables do not have a significant impact on the Business Real Estate index.

Overall, the results of this analysis suggest that there is a significant relationship between the S&P 500 and the Business Real Estate index, with the beta coefficient indicating that the Business Real Estate index tends to move in line with the S&P 500. However, the R-squared values indicate that other variables, such as the NAREIT Index and GDP growth rate, also play a role in determining the behavior of the Business Real Estate index.