Comments: Patentsin2015 are patents issued in 2015 Total/TotalN is the total number of patent attorneys and agents (they’re the same) PopulationEstimate2016 is the estimated population in 2016 StateN = 6 is California StateN = 8 is D.C. . regress Patentsin2015 TotalN Source | SS df MS Number of obs = 51 -------------+------------------------------ F( 1, 49) = 263.88 Model | 1.4287e+09 1 1.4287e+09 Prob > F = 0.0000 Residual | 265299047 49 5414266.27 R-squared = 0.8434 -------------+------------------------------ Adj R-squared = 0.8402 Total | 1.6940e+09 50 33880093.7 Root MSE = 2326.9 ------------------------------------------------------------------------------ Patents~2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- TotalN | 3.963567 .2439971 16.24 0.000 3.473236 4.453897 _cons | -620.6591 386.7269 -1.60 0.115 -1397.816 156.4976 ------------------------------------------------------------------------------ . regress Patentsin2015 TotalN if StateN != 6 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 112.25 Model | 185466609 1 185466609 Prob > F = 0.0000 Residual | 79306458.9 48 1652217.89 R-squared = 0.7005 -------------+------------------------------ Adj R-squared = 0.6942 Total | 264773068 49 5403531.99 Root MSE = 1285.4 ------------------------------------------------------------------------------ Patents~2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- TotalN | 2.237985 .2112312 10.59 0.000 1.813276 2.662694 _cons | 429.3409 235.4417 1.82 0.074 -44.04643 902.7282 ------------------------------------------------------------------------------ . regress Patentsin2015 Total if StateN != 8 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 365.71 Model | 1.4913e+09 1 1.4913e+09 Prob > F = 0.0000 Residual | 195731688 48 4077743.51 R-squared = 0.8840 -------------+------------------------------ Adj R-squared = 0.8816 Total | 1.6870e+09 49 34428927.6 Root MSE = 2019.3 ------------------------------------------------------------------------------ Patents~2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- Total | 4.094715 .214118 19.12 0.000 3.664202 4.525228 _cons | -565.6115 335.8819 -1.68 0.099 -1240.947 109.7244 ------------------------------------------------------------------------------ **** . regress TotalN PopulationEstimate2016 Source | SS df MS Number of obs = 51 -------------+------------------------------ F( 1, 49) = 157.50 Model | 69363646.8 1 69363646.8 Prob > F = 0.0000 Residual | 21579600.4 49 440400.007 R-squared = 0.7627 -------------+------------------------------ Adj R-squared = 0.7579 Total | 90943247.2 50 1818864.94 Root MSE = 663.63 ---------------------------------------------------------------------------------------- TotalN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0001626 .000013 12.55 0.000 .0001366 .0001886 _cons | -176.4206 123.99 -1.42 0.161 -425.5879 72.74674 ------------------------------------------------------------- . regress TotalN PopulationEstimate2016 if StateN != 6 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 69.76 Model | 21936135.5 1 21936135.5 Prob > F = 0.0000 Residual | 15093664.1 48 314451.335 R-squared = 0.5924 -------------+------------------------------ Adj R-squared = 0.5839 Total | 37029799.5 49 755710.194 Root MSE = 560.76 ---------------------------------------------------------------------------------------- TotalN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0001202 .0000144 8.35 0.000 .0000913 .0001491 _cons | 26.00376 113.8573 0.23 0.820 -202.9216 254.9292 ---------------------------------------------------------------------------------------- . regress Total PopulationEstimate2016 if StateN != 8 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 218.46 Model | 72921321.2 1 72921321.2 Prob > F = 0.0000 Residual | 16022053.9 48 333792.79 R-squared = 0.8199 -------------+------------------------------ Adj R-squared = 0.8161 Total | 88943375.1 49 1815170.92 Root MSE = 577.75 ---------------------------------------------------------------------------------------- Total | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0001678 .0000114 14.78 0.000 .0001449 .0001906 _cons | -256.1138 109.6974 -2.33 0.024 -476.6752 -35.55236 ---------------------------------------------------------------------------------------- *** . regress Patentsin2015 PopulationEstimate2016 Source | SS df MS Number of obs = 51 -------------+------------------------------ F( 1, 49) = 127.71 Model | 1.2243e+09 1 1.2243e+09 Prob > F = 0.0000 Residual | 469737235 49 9586474.19 R-squared = 0.7227 -------------+------------------------------ Adj R-squared = 0.7170 Total | 1.6940e+09 50 33880093.7 Root MSE = 3096.2 ---------------------------------------------------------------------------------------- Patentsin2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0006831 .0000604 11.30 0.000 .0005616 .0008046 _cons | -1564.709 578.4856 -2.70 0.009 -2727.219 -402.1982 ---------------------------------------------------------------------------------------- . regress Patentsin2015 PopulationEstimate2016 if StateN != 6 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 119.37 Model | 188836706 1 188836706 Prob > F = 0.0000 Residual | 75936361.3 48 1582007.53 R-squared = 0.7132 -------------+------------------------------ Adj R-squared = 0.7072 Total | 264773068 49 5403531.99 Root MSE = 1257.8 ---------------------------------------------------------------------------------------- Patentsin2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0003526 .0000323 10.93 0.000 .0002877 .0004175 _cons | 12.59279 255.3809 0.05 0.961 -500.8848 526.0704 ---------------------------------------------------------------------------------------- . regress Patentsin2015 PopulationEstimate2016 if StateN != 8 Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 1, 48) = 124.98 Model | 1.2189e+09 1 1.2189e+09 Prob > F = 0.0000 Residual | 468135275 48 9752818.22 R-squared = 0.7225 -------------+------------------------------ Adj R-squared = 0.7167 Total | 1.6870e+09 49 34428927.6 Root MSE = 3123 ---------------------------------------------------------------------------------------- Patentsin2015 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------+---------------------------------------------------------------- PopulationEstimate2016 | .0006859 .0000614 11.18 0.000 .0005625 .0008092 _cons | -1607.495 592.9567 -2.71 0.009 -2799.714 -415.2757 ----------------------------------------------------------------------------------------