Pualine:
what if you log the regressand only?
what if you log the regressand only?
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Kind regards,
Carlo
(Stata 19.0) -
Hello Carlo,
I followed the advice from Clyde (see above) , as log transform my regressand was my initial bet. If I do that the impact becomes very low
Code:Linear regression Number of obs = 974 F(8, 139) = 99.42 Prob > F = 0.0000 R-squared = 0.6090 Root MSE = .08558 (Std. err. adjusted for 140 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust lndownloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- daily_vaccinations | -4.20e-08 6.43e-09 -6.53 0.000 -5.47e-08 -2.93e-08 new_cases | 9.96e-08 2.51e-08 3.97 0.000 5.00e-08 1.49e-07 stay_at_home_policy | .0059275 .0116929 0.51 0.613 -.0171914 .0290464 facial_coverings | .0162332 .0067554 2.40 0.018 .0028767 .0295897 residential | -.0174582 .0023205 -7.52 0.000 -.0220462 -.0128703 workplaces | .0042913 .0008878 4.83 0.000 .0025359 .0060467 grocery_and_pharmacy | .0027483 .0010341 2.66 0.009 .0007038 .0047929 leisure | -.0092535 .0009861 -9.38 0.000 -.0112032 -.0073038 _cons | 12.64769 .0214231 590.38 0.000 12.60533 12.69004 --------------------------------------------------------------------------------------leisure and residential are Google mobility data during covid, to see if there are any changes if public places are closed vs openCode:* Example generated by -dataex-. For more info, type help dataex clear input long downloads_market float lndownloads_market long new_cases float lnnew_cases long daily_vaccinations float lndaily_vaccinations byte(facial_coverings leisure residential) 341189 12.740191 164238 12.009072 1482195 14.209035 4 -27 7 276702 12.530697 138823 11.840955 1487034 14.212294 4 -29 14 273405 12.51871 111938 11.6257 1493026 14.216315 4 -26 13 261750 12.475145 129043 11.7679 1523847 14.23675 4 -20 11 258194 12.461467 121330 11.70627 1579060 14.27234 4 -23 11 271123 12.510328 108669 11.596062 1642312 14.311616 4 -24 11 335024 12.721957 122620 11.716846 1683043 14.336114 4 -21 6 331554 12.711546 124827 11.734684 1680143 14.33439 4 -31 6 268429 12.50034 110180 11.60987 1704200 14.348606 4 -26 11 258350 12.46207 92931 11.439612 1742649 14.370917 4 -25 12 258774 12.46371 80726 11.298816 1766134 14.384303 4 -22 11 258242 12.461653 91417 11.423186 1775339 14.389502 4 -26 13 272266 12.514535 98339 11.496176 1809237 14.408416 4 -24 13 337155 12.728298 99548 11.508395 1833702 14.421847 4 -23 8 343975 12.748324 97431 11.4869 1854830 14.433304 4 -24 7 278952 12.538795 85221 11.353004 1799377 14.40295 4 -34 18 261930 12.475833 67413 11.118593 1748582 14.374315 4 -33 16 253641 12.443675 58066 10.969336 1699474 14.34583 4 -27 13 252157 12.437807 56871 10.94854 1619739 14.297775 4 -33 17 265697 12.490112 63770 11.063038 1529221 14.24027 4 -26 14 334151 12.719348 68568 11.13558 1505355 14.22454 4 -19 6 339249 12.73449 73576 11.206074 1506831 14.22552 4 -19 5 264264 12.484704 65510 11.089958 1545559 14.250896 4 -22 11 249671 12.4279 56628 10.94426 1591287 14.280054 4 -18 10 243892 12.40448 55821 10.929906 1671486 14.329224 4 -15 10 242057 12.39693 70162 11.158562 1826222 14.41776 4 -17 10 251278 12.434315 72358 11.189382 1990581 14.503937 4 -18 10 311802 12.650124 71998 11.184394 2088405 14.55191 4 -15 5 308777 12.640374 73274 11.201962 2124824 14.5692 4 -16 4 239650 12.386935 68298 11.131636 2214511 14.610542 4 -17 9 224399 12.32118 52570 10.8699 2289948 14.64404 4 -16 10 220762 12.30484 51114 10.841814 2344331 14.66751 4 -12 9 223473 12.317046 53761 10.892303 2381996 14.68345 4 -15 9 239508 12.386342 66043 11.098062 2399133 14.690618 4 -16 9 293563 12.589848 64859 11.07997 2409485 14.694923 4 -13 4 293945 12.591148 64094 11.068106 2420479 14.699476 4 -12 3 231257 12.351285 57710 10.963185 2431384 14.70397 4 -16 9 219047 12.297042 43758 10.68643 2467021 14.718522 4 -14 9 216059 12.283307 42703 10.662024 2499757 14.731704 4 -13 9 223494 12.31714 54088 10.898368 2536720 14.746383 4 -14 9 240834 12.391863 61755 11.03093 2566875 14.7582 4 -14 9 300223 12.61228 59764 10.998158 2585933 14.765597 4 -10 3 306224 12.632072 64222 11.0701 2593402 14.76848 4 -11 4 247223 12.418046 52274 10.864254 2608866 14.774426 4 -14 10 229951 12.34562 47230 10.762785 2633115 14.783678 4 -11 9 219173 12.297617 43532 10.681252 2637533 14.785355 4 -4 8 219060 12.2971 51806 10.85526 2628017 14.78174 4 -10 10 237601 12.378348 59588 10.99521 2609056 14.7745 4 -10 8 297082 12.601764 63099 11.05246 2603838 14.772497 4 -6 2 303143 12.62196 62022 11.035244 2609841 14.7748 4 -4 2 248635 12.42374 58456 10.97603 2620473 14.778866 4 -9 8 258886 12.464143 45228 10.719472 2644185 14.787873 4 -9 8 251465 12.43506 48228 10.783695 2698082 14.808052 4 -9 9 244261 12.405993 57684 10.962735 2758421 14.83017 4 -10 9 252701 12.439962 68021 11.127572 2828803 14.855364 4 -10 8 315511 12.66195 65367 11.087772 2873156 14.870922 4 -8 2 318479 12.67131 74834 11.223027 2899438 14.880028 4 -8 3 255835 12.452288 63203 11.054107 2967615 14.90327 4 -8 8 241676 12.395353 53256 10.882866 3043800 14.928617 4 -7 8 235200 12.368192 58014 10.96844 3132209 14.95725 4 -6 8 234764 12.366336 61789 11.03148 3240378 14.9912 4 -4 8 279313 12.54009 69567 11.150045 3216591 14.983832 4 -6 10 341929 12.742358 73685 11.207555 3192561 14.976334 4 -6 2 347939 12.759783 70446 11.162601 3128761 14.956147 4 -28 1 263302 12.481057 63695 11.06186 3167217 14.968364 4 -6 8 247202 12.41796 45722 10.730335 3221788 14.985447 4 -6 7 239936 12.388127 56400 10.940225 3248620 14.99374 4 -4 7 240578 12.3908 63657 11.061265 3237451 14.990297 4 -6 8 261429 12.473918 74627 11.220258 3333157 15.01943 4 -10 7 326151 12.695116 75434 11.231013 3417042 15.044286 4 -7 2 320046 12.67622 76415 11.243935 3508126 15.070593 4 -6 2 258481 12.462578 68111 11.128894 3497188 15.06747 4 -9 7 244370 12.40644 53239 10.882546 3427241 15.047266 4 -8 7 243909 12.40455 60435 11.009324 3334168 15.019733 4 -7 8 244612 12.40743 72206 11.18728 3228039 14.987386 4 -10 8 259203 12.465366 70654 11.16555 3127921 14.95588 4 -11 8 326913 12.69745 71498 11.177424 3052968 14.931624 4 -8 2 331781 12.71223 71074 11.171477 3014943 14.91909 4 -5 2 254606 12.447473 77212 11.25431 2952878 14.89829 4 -10 8 239776 12.38746 49337 10.80643 2917771 14.88633 4 -8 8 236824 12.375072 35281 10.4711 2886773 14.87565 4 -9 8 237560 12.378176 57318 10.95637 2850998 14.86318 4 -9 8 256040 12.45309 63049 11.051667 2807666 14.847864 4 -11 7 323971 12.68841 61479 11.02645 2785657 14.839994 4 -9 2 322041 12.682434 62419 11.041625 2765597 14.832767 4 -6 2 265313 12.488666 51698 10.853174 2738301 14.822848 4 -9 7 253175 12.441836 40847 10.61759 2690417 14.805206 4 -8 7 249020 12.425288 30199 10.315564 2634173 14.78408 4 -7 7 246365 12.41457 50313 10.826018 2570304 14.759535 4 -8 8 260354 12.469797 54396 10.904046 2515052 14.737804 4 -8 6 330265 12.70765 55643 10.926712 2466030 14.71812 4 -6 1 332922 12.715664 55311 10.920727 2449788 14.711512 4 -4 1 251693 12.435966 48352 10.786263 2388627 14.68623 4 -8 7 239938 12.388136 36593 10.507612 2332468 14.662437 4 -7 7 234723 12.36616 32953 10.402838 2256142 14.629167 4 -4 7 231805 12.353652 42552 10.658483 2180771 14.59519 4 -6 6 250938 12.432961 44541 10.704165 2123268 14.568467 4 -7 6 304681 12.62702 42692 10.661767 2076177 14.54604 4 -3 0 309428 12.64248 44641 10.706408 2038290 14.527622 4 -2 0 258221 12.46157 37021 10.51924 1986770 14.50202 4 -9 7 end
Thank you! This is such a great help.
Comment
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If I insert the interaction term (e.g., If I am assuming a moderating effect of new cases combined with vaccinations)
I'll get this result
When introducing other variables as well this effect becomes again insignificant, what do you suggest? I plotted the residuals but can't figure out "the right way" of doing this..Code:reg downloads_market lndaily_vaccinations lnnew_cases Int_cases_vacc, vce(cluster week_cluster) Linear regression Number of obs = 628 F(3, 89) = 65.19 Prob > F = 0.0000 R-squared = 0.1347 Root MSE = 35297 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | 29690.39 18415.31 1.61 0.110 -6900.442 66281.23 lnnew_cases | 61040.06 22296.62 2.74 0.007 16737.15 105343 Int_cases_vacc | -3768.773 1670.475 -2.26 0.027 -7087.972 -449.5736 _cons | -231914 245800.3 -0.94 0.348 -720314 256486.1 --------------------------------------------------------------------------------------
Code:. reg downloads_market lndaily_vaccinations lnnew_cases Int_cases_vacc stay_at_home_policy facial_coverings residential workplaces grocer > y_and_pharmacy leisure, vce(cluster week_cluster) Linear regression Number of obs = 623 F(9, 89) = 70.81 Prob > F = 0.0000 R-squared = 0.6277 Root MSE = 23246 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | -53346.56 22611.26 -2.36 0.020 -98274.65 -8418.473 lnnew_cases | -40070.24 26212.51 -1.53 0.130 -92153.95 12013.47 Int_cases_vacc | 3846.079 1985.015 1.94 0.056 -98.10229 7790.261 stay_at_home_policy | 5121.802 3486.443 1.47 0.145 -1805.686 12049.29 facial_coverings | 9676.553 2465.764 3.92 0.000 4777.134 14575.97 residential | -8046.373 1100.117 -7.31 0.000 -10232.28 -5860.464 workplaces | 379.8358 390.1568 0.97 0.333 -395.3975 1155.069 grocery_and_pharmacy | 474.6654 462.9559 1.03 0.308 -445.218 1394.549 leisure | -2123.055 405.7492 -5.23 0.000 -2929.27 -1316.84 _cons | 873973.1 295998.8 2.95 0.004 285829.7 1462116 --------------------------------------------------------------------------------------Comment
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Pauline:
what did -linktest- tell you after wach regression that you ran?Kind regards,
Carlo
(Stata 19.0)Comment
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When you are working with continuous variables, you cannot judge the "impact" by the absolute size of the regression coefficient. Yes, -4.20e-08 looks like a very small number. But you have to consider that it is a ratio of ln downloads to daily vaccinations. But daily vaccinations, once the vaccine was introduced is a huge number, in the millions (106), and ln downloads is a very modest number, in the low teens (101). So any regression coefficient is going to have to be of order of magnitude 10-5 just to bring the result into the right order of magnitude. Then when you consider that, especially early in the vaccination campaign, vaccines were targeted to the elderly, whereas downloads of dating apps would be targeted to the young, you can't expect the relationship to be all that strong.If I do that the impact becomes very low
Never judge a coefficient of a continuous variable (or the coefficient of a discrete variable when the outcome variable is continuous) without thinking about the scale of the continuous variable(s).Comment
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Carlo,
This is the linktest if running only the two main independent variables:
This is the linktest when including an interaction term:Code:. reg downloads_market lndaily_vaccinations lnnew_cases Int_cases_vacc, vce(cluster week_cluster) Linear regression Number of obs = 628 F(3, 89) = 65.19 Prob > F = 0.0000 R-squared = 0.1347 Root MSE = 35297 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | 29690.39 18415.31 1.61 0.110 -6900.442 66281.23 lnnew_cases | 61040.06 22296.62 2.74 0.007 16737.15 105343 Int_cases_vacc | -3768.773 1670.475 -2.26 0.027 -7087.972 -449.5736 _cons | -231914 245800.3 -0.94 0.348 -720314 256486.1 -------------------------------------------------------------------------------------- Linear regression Number of obs = 628 F(2, 89) = 86.34 Prob > F = 0.0000 R-squared = 0.1311 Root MSE = 35341 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | -11962.97 1236.974 -9.67 0.000 -14420.81 -9505.128 lnnew_cases | 10441.25 1162.287 8.98 0.000 8131.814 12750.69 _cons | 327125.5 20953.09 15.61 0.000 285492.2 368758.9 -------------------------------------------------------------------------------------- . end of do-file . linktest Source | SS df MS Number of obs = 628 -------------+---------------------------------- F(2, 625) = 47.88 Model | 1.1937e+11 2 5.9685e+10 Prob > F = 0.0000 Residual | 7.7910e+11 625 1.2466e+09 R-squared = 0.1329 -------------+---------------------------------- Adj R-squared = 0.1301 Total | 8.9847e+11 627 1.4330e+09 Root MSE = 35307 ------------------------------------------------------------------------------ downloads_~t | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- _hat | -3.731911 4.256555 -0.88 0.381 -12.09079 4.626972 _hatsq | 8.37e-06 7.53e-06 1.11 0.267 -6.41e-06 .0000232 _cons | 666850.5 600391.9 1.11 0.267 -512179.2 1845880
And this is the linktest when including all variablesCode:. reg downloads_market lndaily_vaccinations lnnew_cases Int_cases_vacc, vce(cluster week_cluster) Linear regression Number of obs = 628 F(3, 89) = 65.19 Prob > F = 0.0000 R-squared = 0.1347 Root MSE = 35297 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | 29690.39 18415.31 1.61 0.110 -6900.442 66281.23 lnnew_cases | 61040.06 22296.62 2.74 0.007 16737.15 105343 Int_cases_vacc | -3768.773 1670.475 -2.26 0.027 -7087.972 -449.5736 _cons | -231914 245800.3 -0.94 0.348 -720314 256486.1 -------------------------------------------------------------------------------------- . linktest Source | SS df MS Number of obs = 628 -------------+---------------------------------- F(2, 625) = 49.13 Model | 1.2206e+11 2 6.1030e+10 Prob > F = 0.0000 Residual | 7.7641e+11 625 1.2422e+09 R-squared = 0.1359 -------------+---------------------------------- Adj R-squared = 0.1331 Total | 8.9847e+11 627 1.4330e+09 Root MSE = 35246 ------------------------------------------------------------------------------ downloads_~t | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- _hat | -2.64874 4.038392 -0.66 0.512 -10.5792 5.28172 _hatsq | 6.41e-06 7.09e-06 0.90 0.366 -7.52e-06 .0000203 _cons | 517863.5 573703.6 0.90 0.367 -608756.5 1644484 ------------------------------------------------------------------------------ .
Code:. reg downloads_market lndaily_vaccinations lnnew_cases Int_cases_vacc stay_at_home_policy facial_coverings residential leisure, vce(clu > ster week_cluster) Linear regression Number of obs = 623 F(7, 89) = 74.41 Prob > F = 0.0000 R-squared = 0.6249 Root MSE = 23294 (Std. err. adjusted for 90 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust downloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | -60499.93 22316.58 -2.71 0.008 -104842.5 -16157.36 lnnew_cases | -48598.88 25800 -1.88 0.063 -99862.94 2665.175 Int_cases_vacc | 4546.102 1958.324 2.32 0.023 654.953 8437.251 stay_at_home_policy | 6518.087 3319.346 1.96 0.053 -77.38212 13113.56 facial_coverings | 9684.859 2408.872 4.02 0.000 4898.482 14471.24 residential | -9157.487 599.9015 -15.26 0.000 -10349.48 -7965.496 leisure | -1787.785 359.5429 -4.97 0.000 -2502.189 -1073.381 _cons | 958239.1 292745.7 3.27 0.002 376559.6 1539919 -------------------------------------------------------------------------------------- . end of do-file . linktest Source | SS df MS Number of obs = 623 -------------+---------------------------------- F(2, 620) = 869.55 Model | 6.5591e+11 2 3.2795e+11 Prob > F = 0.0000 Residual | 2.3384e+11 620 377155106 R-squared = 0.7372 -------------+---------------------------------- Adj R-squared = 0.7363 Total | 8.8974e+11 622 1.4305e+09 Root MSE = 19420 ------------------------------------------------------------------------------ downloads_~t | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- _hat | -4.433885 .3349531 -13.24 0.000 -5.091665 -3.776104 _hatsq | 9.67e-06 5.94e-07 16.27 0.000 8.50e-06 .0000108 _cons | 755080.8 46990.94 16.07 0.000 662800.1 847361.5 ------------------------------------------------------------------------------
Maybe you can shortly explain how to compare these results and draw a conclusion of it, this helps me a lot in making sense of my struggles. Thank you all!Comment
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Clyde, this makes absolutely sense. You are right.
But isn't this explanation the perfect reason why to switch the ln on the dependent variable? As if the magnitudes are incredibly small I can not draw reasonable conclusions from it.
Prior in our discussion you explained that the relationship looks more linear if I log the independent variables - how do I recognize which transformation makes more "sense"?
Thank you - This is very helpful - very much appreciated
Comment
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As you are working with simple linear regression, in the absence of any good prior knowledge of what it should be, you should use the one that gives the most linear relationship. I think a good way to decide that is graphically. Use the -rvfplot- postestimation command to see which way of specifying your model gives you the best plot (which, in the ideal situation, is a more or less rectangular smear of points). If you have more than one model that gives a good -rvfplot- then you can focus more strongly on the role of specific variables with the -rvpplot- postestimation command. (See -help rvpplot- for details.)how do I recognize which transformation makes more "sense"?
If you are uncomfortable with graphical methods, the -linktest- command that Carlo has urged you to use can be helpful, though it only detects certain specific kinds of non-linearity. (I think the only methods that are sensitive to all kinds of non-linearity are the graphical ones.)
Turning to judging the strength of an effect, and the problem that the coefficient's magnitude is sensitive to the scale of continuous variables, another way to assess this is to run the model with and without the predictor (making sure not to change the estimation sample because of the vagaries of missing values in the data) and see how large the change in R2 is. So
This change in R2 statistic tells you how much of the variance in the outcome is attributable to your variable of interest over and above what all the other variables in the model contribute to it. This statistic is not sensitive to scale and is a much better measure of the "importance" of a variable's effect.Code:regress ... variable_with_small_coefficient ... local full_r2 = e(r2) regress ... if e(sample) // EXCLUDE variable_with_small_coefficient FROM VARLIST local delta = `full_r2' - e(r2) display "Change in R2 = " %03.2f `delta'
Comment
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Clyde,
before applying the log, I added 1 to vaccinations, and cases, as there are some observations which are obviosly zero, I think thereby I can also solve the problem of the ratio problem, at least I've read this approach in a comparable study about app downloads.
I followed your advice, and ran a regression for each variable and even though I detected some patterns, it doesn't really change about my indecisiveness using a Log-Log model or not.
For the variable new cases I rather assume a U -shape - see attached 1) normal - log 2) log-log
For daily vaccinations I don't know what to do at all (picture 3 & 4) After I solved this problem - I will continue with focusing on strength as you said, Clyde.
Thank you - I am really grateful to receive advice.
Comment
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Update to my post above - I tried to test the U-shape relationship but R-squared decreases after application - see below:
Including squared term - linear coefficient and non-linear coefficient become insignificant:
Including only the square term:Code:. reg lndownloads_market lnnew_cases lnnew_cases_squared lndaily_vaccinations stay_at_home_policy residential leisure, vce(cluster week_ > cluster) Linear regression Number of obs = 974 F(6, 139) = 98.46 Prob > F = 0.0000 R-squared = 0.5806 Root MSE = .08854 (Std. err. adjusted for 140 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust lndownloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lnnew_cases | -.0165251 .013141 -1.26 0.211 -.0425072 .0094569 lnnew_cases_squared | .0004549 .0006193 0.73 0.464 -.0007696 .0016794 lndaily_vaccinations | -.0031087 .0012676 -2.45 0.015 -.0056149 -.0006025 stay_at_home_policy | .0174767 .0120255 1.45 0.148 -.0062998 .0412532 residential | -.0297468 .001476 -20.15 0.000 -.0326652 -.0268284 leisure | -.0091931 .0009454 -9.72 0.000 -.0110624 -.0073239 _cons | 12.81617 .0480136 266.93 0.000 12.72124 12.9111 --------------------------------------------------------------------------------------
Code:Linear regression Number of obs = 974 F(5, 139) = 102.10 Prob > F = 0.0000 R-squared = 0.5794 Root MSE = .08862 (Std. err. adjusted for 140 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust lndownloads_market | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lnnew_cases_squared | -.0002666 .0001164 -2.29 0.024 -.0004969 -.0000364 lndaily_vaccinations | -.002627 .0011574 -2.27 0.025 -.0049154 -.0003387 stay_at_home_policy | .0118005 .0113109 1.04 0.299 -.0105632 .0341642 residential | -.0300365 .0014743 -20.37 0.000 -.0329515 -.0271216 leisure | -.009119 .0009289 -9.82 0.000 -.0109556 -.0072823 _cons | 12.74831 .0170782 746.47 0.000 12.71455 12.78208 --------------------------------------------------------------------------------------
Additional I tested the strength of the effect by applying Clyde's proposed option (Thank you!!)
So judging from an R2 delta of 0.2 I assume the strength of lnnew_cases is quite significant - How can I explain this rationale in my thesis? Do I interpret the regression at all? Or should I explain the the issue of judging the strength of an effect, if the coefficient's magnitude is sensitive to the scale of the continuous variable "daily app downloads".Code:reg lnnew_cases lndaily_vaccinations stay_at_home_policy residential leisure, vce(cluster week_cluster) Linear regression Number of obs = 974 F(4, 139) = 39.31 Prob > F = 0.0000 R-squared = 0.6058 Root MSE = 1.6514 (Std. err. adjusted for 140 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust lnnew_cases | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | .2839621 .0450929 6.30 0.000 .1948053 .3731188 stay_at_home_policy | 1.710963 .5413445 3.16 0.002 .640629 2.781298 residential | -.0454098 .0112976 -4.02 0.000 -.0677471 -.0230725 leisure | -.0219784 .0157013 -1.40 0.164 -.0530226 .0090658 _cons | 10.67888 1.433494 7.45 0.000 7.844606 13.51315 -------------------------------------------------------------------------------------- . local full_r2 = e(r2) . reg lndaily_vaccinations stay_at_home_policy residential leisure, vce(cluster week_cluster) Linear regression Number of obs = 974 F(3, 139) = 27.70 Prob > F = 0.0000 R-squared = 0.4069 Root MSE = 7.0083 (Std. err. adjusted for 140 clusters in week_cluster) ------------------------------------------------------------------------------------- | Robust lndaily_vaccinati~s | Coefficient std. err. t P>|t| [95% conf. interval] --------------------+---------------------------------------------------------------- stay_at_home_policy | -7.859408 .9495217 -8.28 0.000 -9.736781 -5.982035 residential | -.0214445 .0608805 -0.35 0.725 -.141816 .098927 leisure | .0419233 .0550766 0.76 0.448 -.0669729 .1508195 _cons | 23.55035 1.547445 15.22 0.000 20.49077 26.60992 ------------------------------------------------------------------------------------- . local delta = `full_r2' - e(r2) . display "Change in R2 = " %03.2f `delta' Change in R2 = 0.20
(The impact of lndaily_vaccination is even stronger, see below)
Code:. reg lnnew_cases lndaily_vaccinations stay_at_home_policy residential leisure, vce(cluster week_cluster) Linear regression Number of obs = 974 F(4, 139) = 39.31 Prob > F = 0.0000 R-squared = 0.6058 Root MSE = 1.6514 (Std. err. adjusted for 140 clusters in week_cluster) -------------------------------------------------------------------------------------- | Robust lnnew_cases | Coefficient std. err. t P>|t| [95% conf. interval] ---------------------+---------------------------------------------------------------- lndaily_vaccinations | .2839621 .0450929 6.30 0.000 .1948053 .3731188 stay_at_home_policy | 1.710963 .5413445 3.16 0.002 .640629 2.781298 residential | -.0454098 .0112976 -4.02 0.000 -.0677471 -.0230725 leisure | -.0219784 .0157013 -1.40 0.164 -.0530226 .0090658 _cons | 10.67888 1.433494 7.45 0.000 7.844606 13.51315 -------------------------------------------------------------------------------------- . local full_r2 = e(r2) . reg lnnew_cases stay_at_home_policy residential leisure, vce(cluster week_cluster) Linear regression Number of obs = 974 F(3, 139) = 6.95 Prob > F = 0.0002 R-squared = 0.0328 Root MSE = 2.5855 (Std. err. adjusted for 140 clusters in week_cluster) ------------------------------------------------------------------------------------- | Robust lnnew_cases | Coefficient std. err. t P>|t| [95% conf. interval] --------------------+---------------------------------------------------------------- stay_at_home_policy | -.5208105 .3225056 -1.61 0.109 -1.158461 .1168403 residential | -.0514992 .0180318 -2.86 0.005 -.0871513 -.0158472 leisure | -.0100738 .0254498 -0.40 0.693 -.0603927 .0402451 _cons | 17.36628 .7748165 22.41 0.000 15.83433 18.89823 ------------------------------------------------------------------------------------- . . . local delta = `full_r2' - e(r2) . display "Change in R2 = " %03.2f `delta' Change in R2 = 0.57Comment
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Please ignore the part about strength - I did not use it in the correct way - I will restructure my Assumptions.
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Pauline:
adding a constant to value=0 before logging, is not a good idea.
Kind regards,
Carlo
(Stata 19.0)Comment
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