Table 4.2, page 114
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear correlate income water80 educat retire peop81 cpeop water81 (obs=496) | income water80 educat retire peop81 cpeop water81 -------------+--------------------------------------------------------------- income | 1.0000 water80 | 0.3371 1.0000 educat | 0.3463 0.0982 1.0000 retire | -0.3806 -0.2919 -0.1742 1.0000 peop81 | 0.3113 0.5251 0.0587 -0.3757 1.0000 cpeop | 0.0911 -0.0312 0.0055 -0.0585 0.1443 1.0000 water81 | 0.4178 0.7648 0.0404 -0.2731 0.6183 0.0661 1.0000
Figure 4.1, page 115. The option symbol(p) means that a small plus sign will be used, and the half option means that only the lower half of the graph will be displayed.
graph matrix income water80 educat retire peop81 cpeop water81, half msymbol(p)
Figure 4.2, page 115
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/nations, clear
graph matrix encon85 popgro85 fert84 birthr85, half
Figure 4.3, page 116 The yline(0) option draws a horizontal line at 0.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear regress water81 income water80 educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | (dropped) cpeop | 344.6506 80.80625 4.27 0.000 185.8803 503.4209 peop80 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ rvfplot,yline(0) ylabel(-4000(2000)4000) xlabel(0(2000)8000)
Figure 4.4, page 117
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear
regress water81 income water80 educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | (dropped) cpeop | 344.6506 80.80625 4.27 0.000 185.8803 503.4209 peop80 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict yhat predict e, residual gen abse = abs(e) graph twoway (scatter abse yhat) (mband abse yhat, bands(6) )
Figure 4.5, page 119
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord2, clear
graph twoway line H2Ouse time, ylabel(3.5(.5)5.5) xlabel(1 20(20)120) xline(127)
Figure 4.6, page 121
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord2, clear
regress H2Ouse temp rain educ Source | SS df MS Number of obs = 137 -------------+------------------------------ F( 3, 133) = 21.57 Model | 8.40906094 3 2.80302031 Prob > F = 0.0000 Residual | 17.2802366 133 .129926591 R-squared = 0.3273 -------------+------------------------------ Adj R-squared = 0.3122 Total | 25.6892976 136 .188891894 Root MSE = .36045 ------------------------------------------------------------------------------ H2Ouse | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- temp | .0128571 .0016975 7.57 0.000 .0094995 .0162147 rain | -.0474281 .021229 -2.23 0.027 -.0894182 -.005438 educ | -.2469767 .1134846 -2.18 0.031 -.4714448 -.0225086 _cons | 3.828001 .1006446 38.03 0.000 3.62893 4.027072 ------------------------------------------------------------------------------ predict resid, residual tsset time time variable: time, 1 to 137 ac resid, lags(25) xlabel(0(2)24) ylabel(-.2(.2)1)
Figure 4.7, page 122 The c(s) option is short for connect(s), and the s stands for smooth.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord2, clear
regress H2Ouse temp rain educ Source | SS df MS Number of obs = 137 -------------+------------------------------ F( 3, 133) = 21.57 Model | 8.40906094 3 2.80302031 Prob > F = 0.0000 Residual | 17.2802366 133 .129926591 R-squared = 0.3273 -------------+------------------------------ Adj R-squared = 0.3122 Total | 25.6892976 136 .188891894 Root MSE = .36045 ------------------------------------------------------------------------------ H2Ouse | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- temp | .0128571 .0016975 7.57 0.000 .0094995 .0162147 rain | -.0474281 .021229 -2.23 0.027 -.0894182 -.005438 educ | -.2469767 .1134846 -2.18 0.031 -.4714448 -.0225086 _cons | 3.828001 .1006446 38.03 0.000 3.62893 4.027072 ------------------------------------------------------------------------------ predict e, resid graph twoway line e time, ylabel(-.8(.2).8) xlabel(0 20(20)120) yline(0)
Figure 4.8, page 122
Graph 1:
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord2, clear
regress H2Ouse temp rain educ Source | SS df MS Number of obs = 137 -------------+------------------------------ F( 3, 133) = 21.57 Model | 8.40906094 3 2.80302031 Prob > F = 0.0000 Residual | 17.2802366 133 .129926591 R-squared = 0.3273 -------------+------------------------------ Adj R-squared = 0.3122 Total | 25.6892976 136 .188891894 Root MSE = .36045 ------------------------------------------------------------------------------ H2Ouse | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- temp | .0128571 .0016975 7.57 0.000 .0094995 .0162147 rain | -.0474281 .021229 -2.23 0.027 -.0894182 -.005438 educ | -.2469767 .1134846 -2.18 0.031 -.4714448 -.0225086 _cons | 3.828001 .1006446 38.03 0.000 3.62893 4.027072 ------------------------------------------------------------------------------ predict e, resid graph twoway line e time, ylabel(-.8(.2).8) xlabel(1 20(20)120) yline(0)
Graph 2:
gen e1 = e[_n-1]/3 + e[_n]/3 + e[_n+1]/3 (2 missing values generated) graph twoway line e1 time, ylabel(-.8(.2).8) xlabel(1 20(20)120) yline(0)
Graph 3:
gen e2 = e1[_n-1]/3 + e1[_n]/3 + e1[_n+1]/3 (4 missing values generated) graph twoway line e2 time, ylabel(-.8(.2).8) xlabel(1 20(20)120) yline(0)
Graph 4:
gen e3 = e2[_n-1]/3 + e1[_n]/3 + e1[_n+1]/3 (5 missing values generated) gen e4 = e3[_n-1]/3 + e1[_n]/3 + e1[_n+1]/3 (6 missing values generated) gen e5 = e4[_n-1]/3 + e1[_n]/3 + e1[_n+1]/3 (7 missing values generated) graph twoway line e5 time, ylabel(-.8(.2).8) xlabel(1 20(20)120) yline(0)
Figure 4.9, page 124.
Histogram: The bin option allows you to select how many bins the histogram will have.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear regress water81 income water80 educat retire peop81 cpeop Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 cpeop | 96.4536 80.51903 1.20 0.232 -61.75235 254.6596 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict e, residual histogram e, fraction norm bin(13) xlabel(-4000(2000)4000) ylabel(0(.1).4)
Boxplot:
graph box e, yline(0) ylabel(-4000(2000)4000)
Symmerty plot:
symplot e, xlabel(0 2000 4000) ylabel(0 2000 4000)
Quantile normal plot:
qnorm e, ylabel(-4000(2000)4000) xlabel(-2000 0 2000)
Table 4.3, page 127.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear
regress water81 income water80 educat retire peop81 cpeop Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 cpeop | 96.4536 80.51903 1.20 0.232 -61.75235 254.6596 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict DBincome, dfbeta(income) predict DBwtr80, dfbeta(water80) predict DBeducat, dfbeta(educat) predict DBretire, dfbeta(retire) predict DBpeop81, dfbeta(peop81) predict DBcpeop, dfbeta(cpeop) summarize DBincome DBwtr80 DBeducat DBretire DBpeop81 DBcpeop Variable | Obs Mean Std. Dev. Min Max -------------+----------------------------------------------------- DBincome | 496 .0004404 .0907714 -.248154 1.340371 DBwtr80 | 496 -.0002074 .0895012 -1.38789 .6845321 DBeducat | 496 -.0001973 .0434508 -.3601133 .1023189 DBretire | 496 .0000682 .0445025 -.216704 .2785343 DBpeop81 | 496 .0000747 .0612796 -.4263415 .4554408 DBcpeop | 496 -.0000535 .0406626 -.23371 .3507265
Figure 4.10, page 127.
regress water81 income water80 educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | (dropped) cpeop | 344.6506 80.80625 4.27 0.000 185.8803 503.4209 peop80 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ avplot income, xlabel(-20(20)60) ylabel(-4000(2000)4000)
Figure 4.11, page 128. The DFBETAs need to be scaled according to the endnote. The [w=rcd] option does this.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear regress water81 income water80 educat retire peop81 cpeop Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 cpeop | 96.4536 80.51903 1.20 0.232 -61.75235 254.6596 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict DBincome, dfbeta(income) regress water81 water80 educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 5, 490) = 184.54 Model | 714043771 5 142808754 Prob > F = 0.0000 Residual | 379194939 490 773867.223 R-squared = 0.6531 -------------+------------------------------ Adj R-squared = 0.6496 Total | 1.0932e+09 495 2208563.05 Root MSE = 879.70 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- water80 | .5218759 .0268043 19.47 0.000 .4692104 .5745414 educat | -17.03541 13.01692 -1.31 0.191 -42.61128 8.540463 retire | 47.74677 95.39495 0.50 0.617 -139.6869 235.1804 peop81 | 263.9229 29.62926 8.91 0.000 205.7068 322.139 cpeop | 134.9 83.13626 1.62 0.105 -28.44755 298.2475 peop80 | (dropped) _cons | 291.3458 214.0905 1.36 0.174 -129.3028 711.9944 ------------------------------------------------------------------------------ predict yresid, residual regress income water80 educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 5, 490) = 39.56 Model | 24271.7315 5 4854.3463 Prob > F = 0.0000 Residual | 60129.3572 490 122.712974 R-squared = 0.2876 -------------+------------------------------ Adj R-squared = 0.2803 Total | 84401.0887 495 170.50725 Root MSE = 11.078 ------------------------------------------------------------------------------ income | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- water80 | .0014278 .0003375 4.23 0.000 .0007646 .002091 educat | 1.184248 .1639156 7.22 0.000 .8621833 1.506312 retire | -6.745725 1.201261 -5.62 0.000 -9.105983 -4.385467 peop81 | .7500293 .3731065 2.01 0.045 .0169433 1.483115 cpeop | 1.833663 1.046893 1.75 0.080 -.2232916 3.890617 peop80 | (dropped) _cons | 2.342986 2.695935 0.87 0.385 -2.954032 7.640004 ------------------------------------------------------------------------------ predict xresid, residual gen rcd = DBincome replace rcd = . if abs(DBincome) > 2 (0 real changes made) replace rcd = [(99/18)*abs(DBincome)*((abs(DBincome))+1)^2]+1 (496 real changes made) replace rcd = 2 if abs(DBincome) ==. (0 real changes made) graph twoway (scatter yresid xresid [w=rcd], msymbol(oh)) (lfit yresid xresid), /// ylabel(-4000(2000)4000) xlabel(-20(20)60)
Figure 4.12, page 129.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear regress water81 income water80 educat retire peop81 cpeop Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 cpeop | 96.4536 80.51903 1.20 0.232 -61.75235 254.6596 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict DBwtr80, dfbeta(water80) regress water81 income educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 5, 490) = 79.31 Model | 488996056 5 97799211.3 Prob > F = 0.0000 Residual | 604242653 490 1233148.27 R-squared = 0.4473 -------------+------------------------------ Adj R-squared = 0.4417 Total | 1.0932e+09 495 2208563.05 Root MSE = 1110.5 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 33.10548 4.448118 7.44 0.000 24.36574 41.84522 educat | -42.21332 17.28474 -2.44 0.015 -76.17467 -8.251971 retire | 84.66143 124.019 0.68 0.495 -159.0132 328.3361 peop81 | (dropped) cpeop | 376.5361 105.6257 3.56 0.000 169.0009 584.0713 peop80 | 491.5161 33.46848 14.69 0.000 425.7566 557.2755 _cons | 586.0337 269.3883 2.18 0.030 56.73503 1115.332 ------------------------------------------------------------------------------ predict yresid, residual regress water80 income educat retire peop81 cpeop peop80 Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 5, 490) = 47.23 Model | 500781798 5 100156360 Prob > F = 0.0000 Residual | 1.0392e+09 490 2120731.64 R-squared = 0.3252 -------------+------------------------------ Adj R-squared = 0.3183 Total | 1.5399e+09 495 3110990.51 Root MSE = 1456.3 ------------------------------------------------------------------------------ water80 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 24.67473 5.833263 4.23 0.000 13.21344 36.13602 educat | -.7069974 22.66721 -0.03 0.975 -45.24391 43.82992 retire | -212.4708 162.6385 -1.31 0.192 -532.0258 107.0841 peop81 | (dropped) cpeop | 64.81579 138.5176 0.47 0.640 -207.3459 336.9775 peop80 | 494.6113 43.89057 11.27 0.000 408.3744 580.8482 _cons | 698.8928 353.2758 1.98 0.048 4.770461 1393.015 ------------------------------------------------------------------------------ predict xresid, residual gen rcd1 = DBwtr80 replace rcd1 = . if abs(DBwtr80) > 2 (0 real changes made) replace rcd1 = [(99/18)*abs(DBwtr80)*((abs(DBwtr80))+1)^2]+1 (496 real changes made) replace rcd1 = 2 if abs(DBwtr80) ==. graph twoway (scatter yresid xresid [w=rcd1], msymbol(oh)) (lfit yresid xresid), /// ylabel(-2000(2000)6000) xlabel(-2000(0)8000)
Figure 4.13, page 129. These are done the same as above, dropping the different variables.
Figure 4.14, page 131. We use the regpt program to make graphs similar to the left and right panel of figure 4.14. You can download regpt from within Stata by typing search regpt (see How can I use the search command to search for programs and get additional help? for more information about using search).
regpt
Table 4.4, page 133.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear regress water81 income water80 educat retire peop81 cpeop Source | SS df MS Number of obs = 496 -------------+------------------------------ F( 6, 489) = 171.08 Model | 740477522 6 123412920 Prob > F = 0.0000 Residual | 352761188 489 721393.022 R-squared = 0.6773 -------------+------------------------------ Adj R-squared = 0.6734 Total | 1.0932e+09 495 2208563.05 Root MSE = 849.35 ------------------------------------------------------------------------------ water81 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | 20.96699 3.463719 6.05 0.000 14.16138 27.7726 water80 | .49194 .0263478 18.67 0.000 .440171 .5437089 educat | -41.86552 13.22031 -3.17 0.002 -67.84114 -15.8899 retire | 189.1843 95.02142 1.99 0.047 2.483674 375.885 peop81 | 248.197 28.7248 8.64 0.000 191.7578 304.6363 cpeop | 96.4536 80.51903 1.20 0.232 -61.75235 254.6596 _cons | 242.2204 206.8638 1.17 0.242 -164.2312 648.6721 ------------------------------------------------------------------------------ predict DBincome, dfbeta(income) predict DBwtr80, dfbeta(water80) predict e, residual predict h, leverage predict z, rstandard predict t, rstudent predict D, cooksd list case e h z t D DBincome DBwtr80 if D>=.15 Observation 94 case 101 e -4037.047 h .0817331 z -4.960134 t -5.08462 D .3128368 DBincome .0629841 DBwtr80 -1.38789 Observation 118 case 127 e 3315.585 h .061611 z 4.029793 t 4.094227 D .1523151 DBincome .980374 DBwtr80 -.1809267 Observation 125 case 134 e 3687.116 h .0903783 z 4.551666 t 4.646505 D .2940669 DBincome 1.340371 DBwtr80 .2510464
Table 4.5, page 134.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/concord1, clear quietly regress water81 income water80 educat retire peop81 cpeop * Stata 8 code. vif * Stata 9 code and output. estat vif Variable | VIF 1/VIF -------------+---------------------- peop81 | 1.55 0.643154 water80 | 1.48 0.674804 income | 1.40 0.712424 retire | 1.29 0.775514 educat | 1.15 0.872996 cpeop | 1.04 0.956972 -------------+---------------------- Mean VIF | 1.32