ARE 107_ Assignment #3
Meghna Advani
2022-06-02
##Load/Install Packages
install.packages("gdata")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages( "AER" )## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages( "car")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages( "lmtest" )## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages( "zoo" )## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages("plm")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages("stargazer")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages("forecast")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages("glmnet")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)library(gdata)## gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.## ## gdata: read.xls support for 'XLSX' (Excel 2007+) files ENABLED.##
## Attaching package: 'gdata'## The following object is masked from 'package:stats':
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## nobs## The following object is masked from 'package:utils':
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## object.size## The following object is masked from 'package:base':
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## startsWithlibrary(AER)## Loading required package: car## Loading required package: carData## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
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## as.Date, as.Date.numeric## Loading required package: sandwich## Loading required package: survivallibrary(car)
library(lmtest)
library(zoo)
library (plm)##
## Attaching package: 'plm'## The following object is masked from 'package:gdata':
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## nobslibrary(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerlibrary(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(glmnet)## Loading required package: Matrix## Loaded glmnet 4.1-4#Download Data
load("/cloud/project/Guns.Rdata")
guns = mydataI. Empirical Exercise: Shall-Carry Laws and Violent Crime Rates. Using the Guns Data and the Guns P rogram provided to you, replicate the two tables on pages 24 and 28 in Lecture 12.
Part A) Write down the regression equation as well as the R commands to obtain each column of the table on p. 24.
Column #1 : vio_it = 542.2377 − 161.1868shall_it + \(\epsilon\)_it.
#Column #1
regpols<-lm(vio~shall,data=mydata)
summary (regpols)##
## Call:
## lm(formula = vio ~ shall, data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -495.24 -228.84 -63.64 134.06 2379.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 542.24 10.98 49.386 < 2e-16 ***
## shall -161.19 22.27 -7.236 8.32e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 327.2 on 1171 degrees of freedom
## Multiple R-squared: 0.0428, Adjusted R-squared: 0.04199
## F-statistic: 52.36 on 1 and 1171 DF, p-value: 8.319e-13Column #2 : vio_it = 558.1739 + 57.0242shall_it + \(\hat{\alpha}\)_i + \(\epsilon\)_it.
#Column 2
regfes<-lm(vio~shall+factor(stateid),data=mydata)
summary(regfes)##
## Call:
## lm(formula = vio ~ shall + factor(stateid), data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -637.28 -54.24 -5.75 46.49 872.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 558.174 22.642 24.652 < 2e-16 ***
## shall 57.024 10.349 5.510 4.45e-08 ***
## factor(stateid)2 26.225 32.100 0.817 0.414113
## factor(stateid)4 37.525 32.100 1.169 0.242651
## factor(stateid)5 -129.691 32.072 -4.044 5.62e-05 ***
## factor(stateid)6 319.309 32.021 9.972 < 2e-16 ***
## factor(stateid)8 -75.387 32.021 -2.354 0.018730 *
## factor(stateid)9 -137.500 32.021 -4.294 1.91e-05 ***
## factor(stateid)10 6.183 32.021 0.193 0.846932
## factor(stateid)11 1490.804 32.021 46.557 < 2e-16 ***
## factor(stateid)12 411.309 32.473 12.666 < 2e-16 ***
## factor(stateid)13 12.611 32.336 0.390 0.696605
## factor(stateid)15 -298.739 32.021 -9.329 < 2e-16 ***
## factor(stateid)16 -317.844 32.276 -9.848 < 2e-16 ***
## factor(stateid)17 269.991 32.021 8.432 < 2e-16 ***
## factor(stateid)18 -215.329 33.652 -6.399 2.30e-10 ***
## factor(stateid)19 -310.574 32.021 -9.699 < 2e-16 ***
## factor(stateid)20 -166.465 32.021 -5.199 2.38e-07 ***
## factor(stateid)21 -230.916 32.050 -7.205 1.06e-12 ***
## factor(stateid)22 200.431 32.223 6.220 7.00e-10 ***
## factor(stateid)23 -448.754 33.030 -13.586 < 2e-16 ***
## factor(stateid)24 295.461 32.021 9.227 < 2e-16 ***
## factor(stateid)25 58.543 32.021 1.828 0.067774 .
## factor(stateid)26 137.039 32.021 4.280 2.03e-05 ***
## factor(stateid)27 -280.909 32.021 -8.773 < 2e-16 ***
## factor(stateid)28 -224.962 32.276 -6.970 5.40e-12 ***
## factor(stateid)29 24.478 32.021 0.764 0.444766
## factor(stateid)30 -394.530 32.223 -12.244 < 2e-16 ***
## factor(stateid)31 -257.439 32.021 -8.040 2.27e-15 ***
## factor(stateid)32 186.944 32.072 5.829 7.29e-09 ***
## factor(stateid)33 -484.350 33.652 -14.393 < 2e-16 ***
## factor(stateid)34 -5.352 32.021 -0.167 0.867286
## factor(stateid)35 185.696 32.021 5.799 8.66e-09 ***
## factor(stateid)36 383.143 32.021 11.965 < 2e-16 ***
## factor(stateid)37 -41.696 32.072 -1.300 0.193844
## factor(stateid)38 -524.880 32.635 -16.083 < 2e-16 ***
## factor(stateid)39 -112.722 32.021 -3.520 0.000448 ***
## factor(stateid)40 -76.504 32.072 -2.385 0.017225 *
## factor(stateid)41 -84.149 32.276 -2.607 0.009252 **
## factor(stateid)42 -199.511 32.336 -6.170 9.53e-10 ***
## factor(stateid)44 -188.774 32.021 -5.895 4.94e-09 ***
## factor(stateid)45 234.653 32.050 7.322 4.67e-13 ***
## factor(stateid)46 -435.523 32.635 -13.345 < 2e-16 ***
## factor(stateid)47 10.112 32.100 0.315 0.752806
## factor(stateid)48 47.045 32.050 1.468 0.142420
## factor(stateid)49 -306.896 32.551 -9.428 < 2e-16 ***
## factor(stateid)50 -481.989 33.652 -14.323 < 2e-16 ***
## factor(stateid)51 -245.139 32.072 -7.643 4.53e-14 ***
## factor(stateid)53 -167.476 33.652 -4.977 7.48e-07 ***
## factor(stateid)54 -394.206 32.336 -12.191 < 2e-16 ***
## factor(stateid)55 -332.891 32.021 -10.396 < 2e-16 ***
## factor(stateid)56 -283.070 32.100 -8.818 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 108.6 on 1121 degrees of freedom
## Multiple R-squared: 0.8991, Adjusted R-squared: 0.8945
## F-statistic: 195.8 on 51 and 1121 DF, p-value: < 2.2e-16Column #3: vio_it = 447.5616 − 2.2071shall_it + \(\hat{\alpha}\)_i + \(\hat{\lambda}\)_t + \(\epsilon\)_it.
#Column 3
regfesy<-lm(vio~shall + factor(stateid)+factor(year),data=mydata)
summary(regfesy)##
## Call:
## lm(formula = vio ~ shall + factor(stateid) + factor(year), data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -545.86 -43.12 -1.31 41.29 761.59
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 447.562 22.478 19.911 < 2e-16 ***
## shall -2.207 10.388 -0.212 0.831782
## factor(stateid)2 39.102 26.589 1.471 0.141690
## factor(stateid)4 50.402 26.589 1.896 0.058279 .
## factor(stateid)5 -119.390 26.555 -4.496 7.66e-06 ***
## factor(stateid)6 319.309 26.493 12.053 < 2e-16 ***
## factor(stateid)8 -75.387 26.493 -2.846 0.004516 **
## factor(stateid)9 -137.500 26.493 -5.190 2.50e-07 ***
## factor(stateid)10 6.183 26.493 0.233 0.815520
## factor(stateid)11 1490.804 26.493 56.271 < 2e-16 ***
## factor(stateid)12 442.212 27.042 16.353 < 2e-16 ***
## factor(stateid)13 38.364 26.875 1.427 0.153726
## factor(stateid)15 -298.739 26.493 -11.276 < 2e-16 ***
## factor(stateid)16 -294.667 26.803 -10.994 < 2e-16 ***
## factor(stateid)17 269.991 26.493 10.191 < 2e-16 ***
## factor(stateid)18 -156.097 28.457 -5.485 5.12e-08 ***
## factor(stateid)19 -310.574 26.493 -11.723 < 2e-16 ***
## factor(stateid)20 -166.465 26.493 -6.283 4.77e-10 ***
## factor(stateid)21 -223.190 26.528 -8.413 < 2e-16 ***
## factor(stateid)22 221.033 26.738 8.267 3.94e-16 ***
## factor(stateid)23 -402.399 27.712 -14.521 < 2e-16 ***
## factor(stateid)24 295.461 26.493 11.152 < 2e-16 ***
## factor(stateid)25 58.543 26.493 2.210 0.027327 *
## factor(stateid)26 137.039 26.493 5.173 2.74e-07 ***
## factor(stateid)27 -280.909 26.493 -10.603 < 2e-16 ***
## factor(stateid)28 -201.784 26.803 -7.528 1.07e-13 ***
## factor(stateid)29 24.478 26.493 0.924 0.355716
## factor(stateid)30 -373.928 26.738 -13.985 < 2e-16 ***
## factor(stateid)31 -257.439 26.493 -9.717 < 2e-16 ***
## factor(stateid)32 197.245 26.555 7.428 2.21e-13 ***
## factor(stateid)33 -425.119 28.457 -14.939 < 2e-16 ***
## factor(stateid)34 -5.352 26.493 -0.202 0.839937
## factor(stateid)35 185.696 26.493 7.009 4.17e-12 ***
## factor(stateid)36 383.143 26.493 14.462 < 2e-16 ***
## factor(stateid)37 -31.394 26.555 -1.182 0.237359
## factor(stateid)38 -488.826 27.237 -17.947 < 2e-16 ***
## factor(stateid)39 -112.722 26.493 -4.255 2.27e-05 ***
## factor(stateid)40 -66.203 26.555 -2.493 0.012810 *
## factor(stateid)41 -60.971 26.803 -2.275 0.023111 *
## factor(stateid)42 -173.758 26.875 -6.465 1.52e-10 ***
## factor(stateid)44 -188.774 26.493 -7.125 1.87e-12 ***
## factor(stateid)45 242.379 26.528 9.137 < 2e-16 ***
## factor(stateid)46 -399.470 27.237 -14.666 < 2e-16 ***
## factor(stateid)47 22.988 26.589 0.865 0.387457
## factor(stateid)48 54.770 26.528 2.065 0.039190 *
## factor(stateid)49 -273.418 27.136 -10.076 < 2e-16 ***
## factor(stateid)50 -422.758 28.457 -14.856 < 2e-16 ***
## factor(stateid)51 -234.838 26.555 -8.844 < 2e-16 ***
## factor(stateid)53 -108.245 28.457 -3.804 0.000150 ***
## factor(stateid)54 -368.453 26.875 -13.710 < 2e-16 ***
## factor(stateid)55 -332.891 26.493 -12.565 < 2e-16 ***
## factor(stateid)56 -270.194 26.589 -10.162 < 2e-16 ***
## factor(year)78 19.196 17.791 1.079 0.280847
## factor(year)79 62.216 17.791 3.497 0.000489 ***
## factor(year)80 92.394 17.791 5.193 2.46e-07 ***
## factor(year)81 96.457 17.791 5.422 7.26e-08 ***
## factor(year)82 77.582 17.793 4.360 1.42e-05 ***
## factor(year)83 46.798 17.793 2.630 0.008653 **
## factor(year)84 45.879 17.793 2.579 0.010052 *
## factor(year)85 57.702 17.793 3.243 0.001218 **
## factor(year)86 86.316 17.802 4.849 1.42e-06 ***
## factor(year)87 75.363 17.810 4.231 2.51e-05 ***
## factor(year)88 102.277 17.821 5.739 1.23e-08 ***
## factor(year)89 123.007 17.821 6.903 8.62e-12 ***
## factor(year)90 179.334 17.866 10.038 < 2e-16 ***
## factor(year)91 202.854 17.932 11.312 < 2e-16 ***
## factor(year)92 214.570 17.987 11.929 < 2e-16 ***
## factor(year)93 221.847 17.987 12.333 < 2e-16 ***
## factor(year)94 201.980 17.987 11.229 < 2e-16 ***
## factor(year)95 188.945 18.125 10.424 < 2e-16 ***
## factor(year)96 152.480 18.347 8.311 2.78e-16 ***
## factor(year)97 131.382 18.506 7.099 2.24e-12 ***
## factor(year)98 98.756 18.506 5.337 1.15e-07 ***
## factor(year)99 66.747 18.506 3.607 0.000324 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 89.84 on 1099 degrees of freedom
## Multiple R-squared: 0.9323, Adjusted R-squared: 0.9278
## F-statistic: 207.2 on 73 and 1099 DF, p-value: < 2.2e-16Column #4: vioit = −747.8744 + 2.2258shall_it + \(\hat{\alpha}\)_i +\(\hat{\lambda}\)_t + \(\hat{\gamma}\)_it + \(\epsilon\)_it.
#Column 4
regfesyt<-lm(vio~shall+factor(stateid)+factor(year)+factor(stateid):year, data=mydata)
summary (regfesyt)##
## Call:
## lm(formula = vio ~ shall + factor(stateid) + factor(year) + factor(stateid):year,
## data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -668.38 -33.05 0.79 28.15 629.07
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -747.87436 280.54200 -2.666 0.007798 **
## shall 2.22577 12.15726 0.183 0.854769
## factor(stateid)2 80.96916 298.65178 0.271 0.786355
## factor(stateid)4 640.47785 298.65178 2.145 0.032217 *
## factor(stateid)5 -178.17148 297.69555 -0.599 0.549634
## factor(stateid)6 942.11739 295.25289 3.191 0.001460 **
## factor(stateid)8 1367.33477 295.25289 4.631 4.09e-06 ***
## factor(stateid)9 651.72612 295.25289 2.207 0.027506 *
## factor(stateid)10 -303.86086 295.25289 -1.029 0.303644
## factor(stateid)11 -365.85642 295.25289 -1.239 0.215575
## factor(stateid)12 378.21271 301.98929 1.252 0.210702
## factor(stateid)13 328.41711 301.98929 1.088 0.277060
## factor(stateid)15 691.80875 295.25289 2.343 0.019310 *
## factor(stateid)16 642.13981 301.66021 2.129 0.033513 *
## factor(stateid)17 399.21739 295.25289 1.352 0.176628
## factor(stateid)18 -23.35615 295.50308 -0.079 0.937017
## factor(stateid)19 -0.23476 295.25289 -0.001 0.999366
## factor(stateid)20 373.72612 295.25289 1.266 0.205872
## factor(stateid)21 280.14216 296.78615 0.944 0.345428
## factor(stateid)22 -221.64406 301.12950 -0.736 0.461869
## factor(stateid)23 1001.31115 297.69555 3.364 0.000797 ***
## factor(stateid)24 791.84348 295.25289 2.682 0.007435 **
## factor(stateid)25 312.02174 295.25289 1.057 0.290849
## factor(stateid)26 1015.97833 295.25289 3.441 0.000602 ***
## factor(stateid)27 100.09134 295.25289 0.339 0.734676
## factor(stateid)28 91.08333 301.66021 0.302 0.762758
## factor(stateid)29 350.15650 295.25289 1.186 0.235909
## factor(stateid)30 998.15163 301.12950 3.315 0.000949 ***
## factor(stateid)31 -358.76953 295.25289 -1.215 0.224591
## factor(stateid)32 1376.55896 297.69555 4.624 4.23e-06 ***
## factor(stateid)33 703.03947 295.50308 2.379 0.017532 *
## factor(stateid)34 941.25656 295.25289 3.188 0.001475 **
## factor(stateid)35 -272.19999 295.25289 -0.922 0.356781
## factor(stateid)36 2102.08266 295.25289 7.120 2.01e-12 ***
## factor(stateid)37 -43.95841 297.69555 -0.148 0.882638
## factor(stateid)38 422.37334 301.12950 1.403 0.161023
## factor(stateid)39 921.12179 295.25289 3.120 0.001859 **
## factor(stateid)40 -120.59321 297.69555 -0.405 0.685495
## factor(stateid)41 1174.35722 301.66021 3.893 0.000105 ***
## factor(stateid)42 269.31275 301.98929 0.892 0.372707
## factor(stateid)44 917.35657 295.25289 3.107 0.001941 **
## factor(stateid)45 -459.94916 296.78615 -1.550 0.121499
## factor(stateid)46 385.63425 301.12950 1.281 0.200608
## factor(stateid)47 -789.50041 298.65178 -2.644 0.008327 **
## factor(stateid)48 221.38129 296.78615 0.746 0.455878
## factor(stateid)49 564.35287 301.66021 1.871 0.061648 .
## factor(stateid)50 820.00036 295.50308 2.775 0.005619 **
## factor(stateid)51 530.23287 297.69555 1.781 0.075181 .
## factor(stateid)53 675.99163 295.50308 2.288 0.022359 *
## factor(stateid)54 258.29534 301.98929 0.855 0.392573
## factor(stateid)55 166.67394 295.25289 0.565 0.572526
## factor(stateid)56 1026.94308 298.65178 3.439 0.000608 ***
## factor(year)78 9.92921 15.08834 0.658 0.510636
## factor(year)79 43.68195 15.62995 2.795 0.005289 **
## factor(year)80 64.59351 16.49314 3.916 9.57e-05 ***
## factor(year)81 59.38939 17.63076 3.369 0.000783 ***
## factor(year)82 31.16124 19.01026 1.639 0.101476
## factor(year)83 -8.88995 20.55501 -0.432 0.665470
## factor(year)84 -19.07643 22.24226 -0.858 0.391273
## factor(year)85 -16.51977 24.04203 -0.687 0.492159
## factor(year)86 2.65353 25.97974 0.102 0.918666
## factor(year)87 -17.65306 27.96811 -0.631 0.528057
## factor(year)88 -0.09298 30.01533 -0.003 0.997529
## factor(year)89 11.36956 32.07880 0.354 0.723091
## factor(year)90 58.16981 34.27817 1.697 0.089995 .
## factor(year)91 72.16221 36.52046 1.976 0.048423 *
## factor(year)92 74.43747 38.75609 1.921 0.055045 .
## factor(year)93 72.44707 40.93231 1.770 0.077030 .
## factor(year)94 43.31353 43.12731 1.004 0.315457
## factor(year)95 20.66425 45.50501 0.454 0.649844
## factor(year)96 -25.50318 47.95749 -0.532 0.594986
## factor(year)97 -56.12843 50.33579 -1.115 0.265072
## factor(year)98 -98.02079 52.57333 -1.864 0.062536 .
## factor(year)99 -139.29746 54.82070 -2.541 0.011198 *
## factor(stateid)1:year 14.75115 3.38905 4.353 1.48e-05 ***
## factor(stateid)2:year 14.26443 3.34566 4.264 2.19e-05 ***
## factor(stateid)4:year 8.03478 3.34566 2.402 0.016499 *
## factor(stateid)5:year 15.41036 3.34671 4.605 4.64e-06 ***
## factor(stateid)6:year 7.67377 3.38905 2.264 0.023760 *
## factor(stateid)8:year -1.64342 3.38905 -0.485 0.627834
## factor(stateid)9:year 5.78267 3.38905 1.706 0.088252 .
## factor(stateid)10:year 18.27437 3.38905 5.392 8.60e-08 ***
## factor(stateid)11:year 35.84956 3.38905 10.578 < 2e-16 ***
## factor(stateid)12:year 15.45213 3.35515 4.605 4.62e-06 ***
## factor(stateid)13:year 11.43319 3.35427 3.409 0.000678 ***
## factor(stateid)15:year 3.49492 3.38905 1.031 0.302666
## factor(stateid)16:year 4.08591 3.35264 1.219 0.223227
## factor(stateid)17:year 13.28267 3.38905 3.919 9.46e-05 ***
## factor(stateid)18:year 13.19235 3.38905 3.893 0.000105 ***
## factor(stateid)19:year 11.22456 3.38905 3.312 0.000958 ***
## factor(stateid)20:year 8.61261 3.38905 2.541 0.011187 *
## factor(stateid)21:year 9.02489 3.35050 2.694 0.007181 **
## factor(stateid)22:year 19.76404 3.35050 5.899 4.93e-09 ***
## factor(stateid)23:year -1.23953 3.34566 -0.370 0.711093
## factor(stateid)24:year 9.11043 3.38905 2.688 0.007298 **
## factor(stateid)25:year 11.87071 3.38905 3.503 0.000480 ***
## factor(stateid)26:year 4.76320 3.38905 1.405 0.160178
## factor(stateid)27:year 10.42160 3.38905 3.075 0.002159 **
## factor(stateid)28:year 11.40339 3.35264 3.401 0.000696 ***
## factor(stateid)29:year 11.05026 3.38905 3.261 0.001148 **
## factor(stateid)30:year -0.85819 3.35050 -0.256 0.797895
## factor(stateid)31:year 15.90263 3.38905 4.692 3.06e-06 ***
## factor(stateid)32:year 1.34109 3.34671 0.401 0.688709
## factor(stateid)33:year 1.88079 3.38905 0.555 0.579040
## factor(stateid)34:year 3.99423 3.38905 1.179 0.238837
## factor(stateid)35:year 19.95451 3.38905 5.888 5.26e-09 ***
## factor(stateid)36:year -4.78225 3.38905 -1.411 0.158514
## factor(stateid)37:year 14.88516 3.34671 4.448 9.60e-06 ***
## factor(stateid)38:year 4.36594 3.35264 1.302 0.193119
## factor(stateid)39:year 3.00292 3.38905 0.886 0.375784
## factor(stateid)40:year 15.36045 3.34671 4.590 4.98e-06 ***
## factor(stateid)41:year 0.69361 3.35264 0.207 0.836139
## factor(stateid)42:year 9.69435 3.35427 2.890 0.003930 **
## factor(stateid)44:year 2.18148 3.38905 0.644 0.519920
## factor(stateid)45:year 22.72558 3.35050 6.783 1.97e-11 ***
## factor(stateid)46:year 5.79885 3.35264 1.730 0.083989 .
## factor(stateid)47:year 23.97302 3.34566 7.165 1.46e-12 ***
## factor(stateid)48:year 12.85127 3.35050 3.836 0.000133 ***
## factor(stateid)49:year 5.20255 3.35427 1.551 0.121198
## factor(stateid)50:year 0.57852 3.38905 0.171 0.864491
## factor(stateid)51:year 6.04840 3.34671 1.807 0.071007 .
## factor(stateid)53:year 5.78899 3.38905 1.708 0.087905 .
## factor(stateid)54:year 7.60710 3.35427 2.268 0.023539 *
## factor(stateid)55:year 9.07427 3.38905 2.678 0.007533 **
## factor(stateid)56:year NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 75.26 on 1049 degrees of freedom
## Multiple R-squared: 0.9546, Adjusted R-squared: 0.9493
## F-statistic: 179.5 on 123 and 1049 DF, p-value: < 2.2e-16Column #5: vio_it = −253.3828 − 1.5958shall_it − 105.2594density_it + 8.4545avginc_it + 0.2345incarc_it + 31.6939pm1029_it + \(\hat{\alpha}\)_i +\(\hat{\lambda}\)_t + \(\hat{\gamma}\)_it + \(\epsilon\)_it.
#Column 5
regfesymulti<-lm(vio~shall+density+avginc+incarc_rate+pm1029+factor(stateid) +factor(year),data=mydata)
summary(regfesymulti)##
## Call:
## lm(formula = vio ~ shall + density + avginc + incarc_rate + pm1029 +
## factor(stateid) + factor(year), data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -656.73 -41.63 -0.67 40.47 655.11
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -253.38285 128.91439 -1.966 0.049607 *
## shall -1.59575 10.35422 -0.154 0.877547
## density -105.25936 38.73320 -2.718 0.006681 **
## avginc 8.45455 3.76599 2.245 0.024969 *
## incarc_rate 0.23448 0.05089 4.608 4.55e-06 ***
## pm1029 31.69391 6.74425 4.699 2.94e-06 ***
## factor(stateid)2 -82.99671 36.57359 -2.269 0.023444 *
## factor(stateid)4 26.10318 25.83076 1.011 0.312457
## factor(stateid)5 -86.31919 25.88512 -3.335 0.000883 ***
## factor(stateid)6 282.61679 30.41738 9.291 < 2e-16 ***
## factor(stateid)8 -92.42287 29.34543 -3.149 0.001680 **
## factor(stateid)9 -80.57591 44.68742 -1.803 0.071647 .
## factor(stateid)10 5.01747 31.44162 0.160 0.873241
## factor(stateid)11 2305.54247 405.85057 5.681 1.72e-08 ***
## factor(stateid)12 493.27290 32.57434 15.143 < 2e-16 ***
## factor(stateid)13 8.50786 26.32850 0.323 0.746649
## factor(stateid)15 -313.51700 30.50496 -10.278 < 2e-16 ***
## factor(stateid)16 -287.09979 26.94842 -10.654 < 2e-16 ***
## factor(stateid)17 278.31713 29.92820 9.299 < 2e-16 ***
## factor(stateid)18 -137.45330 28.67874 -4.793 1.87e-06 ***
## factor(stateid)19 -275.50082 27.92462 -9.866 < 2e-16 ***
## factor(stateid)20 -165.56016 27.37818 -6.047 2.02e-09 ***
## factor(stateid)21 -204.73057 25.64506 -7.983 3.58e-15 ***
## factor(stateid)22 179.10087 26.09434 6.864 1.12e-11 ***
## factor(stateid)23 -345.28740 30.00731 -11.507 < 2e-16 ***
## factor(stateid)24 309.04783 35.70689 8.655 < 2e-16 ***
## factor(stateid)25 141.82329 39.51054 3.590 0.000346 ***
## factor(stateid)26 124.26996 27.42273 4.532 6.50e-06 ***
## factor(stateid)27 -255.71185 30.92724 -8.268 3.91e-16 ***
## factor(stateid)28 -209.10929 26.29041 -7.954 4.48e-15 ***
## factor(stateid)29 41.61305 26.73147 1.557 0.119829
## factor(stateid)30 -338.57481 27.48231 -12.320 < 2e-16 ***
## factor(stateid)31 -231.47270 28.41451 -8.146 1.02e-15 ***
## factor(stateid)32 146.59859 29.62867 4.948 8.68e-07 ***
## factor(stateid)33 -388.20674 33.41878 -11.616 < 2e-16 ***
## factor(stateid)34 103.89685 50.87420 2.042 0.041368 *
## factor(stateid)35 194.51017 26.85298 7.244 8.23e-13 ***
## factor(stateid)36 411.40783 34.61098 11.887 < 2e-16 ***
## factor(stateid)37 -42.10407 25.68967 -1.639 0.101511
## factor(stateid)38 -472.24790 30.02116 -15.731 < 2e-16 ***
## factor(stateid)39 -89.36273 27.79460 -3.215 0.001342 **
## factor(stateid)40 -83.41108 25.39150 -3.285 0.001052 **
## factor(stateid)41 -28.14007 29.04991 -0.969 0.332919
## factor(stateid)42 -109.88422 30.65655 -3.584 0.000353 ***
## factor(stateid)44 -68.31700 40.02088 -1.707 0.088099 .
## factor(stateid)45 205.37778 26.01662 7.894 7.06e-15 ***
## factor(stateid)46 -382.28467 27.61317 -13.844 < 2e-16 ***
## factor(stateid)47 52.30056 26.05104 2.008 0.044929 *
## factor(stateid)48 0.46509 26.64474 0.017 0.986077
## factor(stateid)49 -308.02221 31.08534 -9.909 < 2e-16 ***
## factor(stateid)50 -388.38960 30.04099 -12.929 < 2e-16 ***
## factor(stateid)51 -258.40510 28.38027 -9.105 < 2e-16 ***
## factor(stateid)53 -100.83843 31.82162 -3.169 0.001573 **
## factor(stateid)54 -292.10268 28.32075 -10.314 < 2e-16 ***
## factor(stateid)55 -314.13547 27.75559 -11.318 < 2e-16 ***
## factor(stateid)56 -294.18885 28.21541 -10.427 < 2e-16 ***
## factor(year)78 18.84328 16.99116 1.109 0.267671
## factor(year)79 64.77400 17.07492 3.794 0.000157 ***
## factor(year)80 100.88516 17.12598 5.891 5.11e-09 ***
## factor(year)81 108.48391 17.35159 6.252 5.79e-10 ***
## factor(year)82 94.92329 17.85657 5.316 1.29e-07 ***
## factor(year)83 67.56475 18.70311 3.612 0.000317 ***
## factor(year)84 69.42013 20.10747 3.452 0.000577 ***
## factor(year)85 86.62470 21.59842 4.011 6.46e-05 ***
## factor(year)86 120.39456 23.42973 5.139 3.28e-07 ***
## factor(year)87 114.71451 25.24275 4.544 6.12e-06 ***
## factor(year)88 145.49820 27.19883 5.349 1.07e-07 ***
## factor(year)89 168.94232 29.03464 5.819 7.78e-09 ***
## factor(year)90 227.68784 30.64504 7.430 2.18e-13 ***
## factor(year)91 256.69345 31.96020 8.032 2.47e-15 ***
## factor(year)92 268.09274 33.62394 7.973 3.86e-15 ***
## factor(year)93 277.31653 34.71166 7.989 3.42e-15 ***
## factor(year)94 256.19677 36.09610 7.098 2.28e-12 ***
## factor(year)95 239.32627 37.43897 6.392 2.41e-10 ***
## factor(year)96 199.23630 38.72331 5.145 3.17e-07 ***
## factor(year)97 173.20331 39.95580 4.335 1.59e-05 ***
## factor(year)98 132.11441 41.38705 3.192 0.001452 **
## factor(year)99 94.35142 42.45962 2.222 0.026477 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 85.09 on 1095 degrees of freedom
## Multiple R-squared: 0.9395, Adjusted R-squared: 0.9352
## F-statistic: 220.7 on 77 and 1095 DF, p-value: < 2.2e-16#Stargazer Table
stargazer(regpols, regfes, regfesy,regfesyt, regfesymulti, type = "text", omit = c("year", "stateid"), no.space = TRUE, align = TRUE)##
## =========================================================================================================================================================
## Dependent variable:
## -------------------------------------------------------------------------------------------------------------------------------------
## vio
## (1) (2) (3) (4) (5)
## ---------------------------------------------------------------------------------------------------------------------------------------------------------
## shall -161.187*** 57.024*** -2.207 2.226 -1.596
## (22.275) (10.349) (10.388) (12.157) (10.354)
## density -105.259***
## (38.733)
## avginc 8.455**
## (3.766)
## incarc_rate 0.234***
## (0.051)
## pm1029 31.694***
## (6.744)
## Constant 542.238*** 558.174*** 447.562*** -747.874*** -253.383**
## (10.980) (22.642) (22.478) (280.542) (128.914)
## ---------------------------------------------------------------------------------------------------------------------------------------------------------
## Observations 1,173 1,173 1,173 1,173 1,173
## R2 0.043 0.899 0.932 0.955 0.939
## Adjusted R2 0.042 0.894 0.928 0.949 0.935
## Residual Std. Error 327.184 (df = 1171) 108.589 (df = 1121) 89.842 (df = 1099) 75.259 (df = 1049) 85.090 (df = 1095)
## F Statistic 52.364*** (df = 1; 1171) 195.790*** (df = 51; 1121) 207.202*** (df = 73; 1099) 179.457*** (df = 123; 1049) 220.687*** (df = 77; 1095)
## =========================================================================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01#(b) Write down the regression equation as well as the R commands to obtain each column of the table on p. 28.
mydatap<-pdata.frame(mydata,c("stateid","year"))Column #1 : vio_it = 542.2377 − 161.1868shall_it + \(\epsilon\)_it.
pregpols<-plm(vio~shall,model="pooling",data=mydatap)
rvpols<-vcovHC(pregpols,method="arellano",cluster="group")
coeftest(pregpols,vcov=rvpols)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 542.238 50.155 10.8113 <2e-16 ***
## shall -161.187 67.006 -2.4056 0.0163 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Column #2 : vio_it = 52.024shall_it + \(\hat{\alpha}\)_i +\(\hat{\lambda}\)_t +u_it.
pregfes <- plm(vio~shall,model="within", data=mydatap)
rvfes<-vcovHC(pregfes,method="arellano", cluster="group")
coeftest(pregfes,vcov=rvfes)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## shall 57.024 17.083 3.3381 0.0008712 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Column #3 : vio_it = -2.207shall_it + \(\hat{\alpha}\)_i +\(\hat{\lambda}\)_t +u_it.
pregfesy<-plm(vio~shall,effect="twoway",model="within",data=mydatap)
rvfesy<-vcovHC(pregfesy,,method="arellano",cluster="group")
coeftest(pregfesy,vcov=rvfesy)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## shall -2.2071 21.8838 -0.1009 0.9197Column #4 : vio_it = -1.596shall_it - 105.259density_it + 8.555avginc_it +0.234incarc_rate+ 31.694_pm109 + \(\hat{\alpha}\)_i +\(\hat{\lambda}\)_t +u_it.
pregfesymulti<-plm(vio~shall+density+avginc+incarc_rate+pm1029, effect="twoway",model="within", data=mydatap)
rvfesymulti<-vcovHC(pregfesymulti,method="arellano",cluster="group")
coeftest(pregfesymulti,vcov=rvfesymulti)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## shall -1.59575 20.65190 -0.0773 0.93842
## density -105.25936 68.86385 -1.5285 0.12667
## avginc 8.45455 8.92215 0.9476 0.34355
## incarc_rate 0.23448 0.11610 2.0196 0.04367 *
## pm1029 31.69391 15.65655 2.0243 0.04318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Stargazer for Pooled Data
stargazer(rvpols,rvfes, rvfesy, rvfesymulti,title="pooled regression results",no.space = TRUE, align = TRUE)##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Jun 03, 2022 - 04:56:52
## % Requires LaTeX packages: dcolumn
## \begin{table}[!htbp] \centering
## \caption{pooled regression results}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} D{.}{.}{-3} D{.}{.}{-3} D{.}{.}{-3} }
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{} & \multicolumn{1}{c}{(Intercept)} & \multicolumn{1}{c}{shall} \\
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{(Intercept)} & 2,515.505 & -2,044.921 \\
## \multicolumn{1}{c}{shall} & -2,044.921 & 4,489.760 \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}
##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Jun 03, 2022 - 04:56:52
## % Requires LaTeX packages: dcolumn
## \begin{table}[!htbp] \centering
## \caption{pooled regression results}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} D{.}{.}{-3} D{.}{.}{-3} }
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{} & \multicolumn{1}{c}{shall} \\
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{shall} & 291.821 \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}
##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Jun 03, 2022 - 04:56:52
## % Requires LaTeX packages: dcolumn
## \begin{table}[!htbp] \centering
## \caption{pooled regression results}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} D{.}{.}{-3} D{.}{.}{-3} }
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{} & \multicolumn{1}{c}{shall} \\
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{shall} & 478.902 \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}
##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Jun 03, 2022 - 04:56:52
## % Requires LaTeX packages: dcolumn
## \begin{table}[!htbp] \centering
## \caption{pooled regression results}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} D{.}{.}{-3} D{.}{.}{-3} D{.}{.}{-3} D{.}{.}{-3} D{.}{.}{-3} D{.}{.}{-3} }
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{} & \multicolumn{1}{c}{shall} & \multicolumn{1}{c}{density} & \multicolumn{1}{c}{avginc} & \multicolumn{1}{c}{incarc\_rate} & \multicolumn{1}{c}{pm1029} \\
## \hline \\[-1.8ex]
## \multicolumn{1}{c}{shall} & 426.501 & -6.583 & 11.013 & 0.070 & -22.468 \\
## \multicolumn{1}{c}{density} & -6.583 & 4,742.230 & 252.740 & 7.569 & -71.047 \\
## \multicolumn{1}{c}{avginc} & 11.013 & 252.740 & 79.605 & 0.249 & 22.168 \\
## \multicolumn{1}{c}{incarc\_rate} & 0.070 & 7.569 & 0.249 & 0.013 & 0.231 \\
## \multicolumn{1}{c}{pm1029} & -22.468 & -71.047 & 22.168 & 0.231 & 245.128 \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}#c) Why are the standard errors different between the two tables? Which command leads to this difference? Which standard errors should we use in practice and why? The results are more accurate in the second table (pooled regression table) as a result of the difference in these standard errors. The command used for robust standard errors is “vcovHC()”.
#d) Do you think that the data suggests that “shall” carry laws have a (positive or negative) effect on violent crime rates? Explain your answer and perform any statistical tests to support your answer. Since the data we have is panel data, our best regression model is “rvfesymulti” where we have controlled for most variables. inspite of this, the coefficent we get is -1.596, which indicates a negative correlation between shall gun laws and crime rate.
However, in order to test whether our data is statistically significant, we carry out t-test at a 5% significance level which reveals that the results are not statistically significant as -0.0773<1.96, hence we cannot deduce a causal relationship.
##II. Model Selection in the Sales and Advertising Example. Using the “Advertising” data set which we used extensively in our class, write an R program that can perform the best subset selection as well as LASSO:
#Load Data
load("/cloud/project/Advertising.RData")
ads_data<-mydata#a) Perform best subset selection using (1) Akaike information criterion (AIC), (2) Bayesian Schwarz information criterion (BIC), and (3) leave-one-out cross-validation (CV). Below are the steps you need to perform for best subset selection:
regnull = lm(Sales ~ 1, data=ads_data)
regn = lm(Sales ~ Newspaper, data=ads_data)
regt = lm(Sales ~ TV, data=ads_data)
regr = lm(Sales ~ Radio, data=ads_data)
regrn = lm(Sales ~ Newspaper + Radio, data=ads_data)
regrt = lm(Sales ~ Radio + TV, data=ads_data)
regnt = lm(Sales ~ Newspaper + TV, data=ads_data)
regall = lm(Sales ~ Newspaper + TV + Radio, data=ads_data)
CV(regnull)## CV AIC AICc BIC AdjR2
## 27.35865 663.80151 663.86242 670.39814 0.00000CV(regn)## CV AIC AICc BIC AdjR2
## 26.27078080 655.09593833 655.21838730 664.99089042 0.04733317CV(regt)## CV AIC AICc BIC AdjR2
## 10.7410876 476.5159143 476.6383632 486.4108664 0.6099148CV(regr)## CV AIC AICc BIC AdjR2
## 18.4856639 585.0983672 585.2208162 594.9933193 0.3286589CV(regrn)## CV AIC AICc BIC AdjR2
## 18.7544100 586.8968402 587.1019684 600.0901097 0.3259306CV(regrt)## CV AIC AICc BIC AdjR2
## 2.9106758 212.8186854 213.0238136 226.0119549 0.8961505CV(regnt)## CV AIC AICc BIC AdjR2
## 9.8975987 460.2027523 460.4078805 473.3960218 0.6422399CV(regall)## CV AIC AICc BIC AdjR2
## 2.9468998 214.7868226 215.0961010 231.2784094 0.8956373Based on our findings we find that the best subset is regrt.
#B) Perform the LASSO method to select the variables to include in the model to replicate the LASSO results in the Week 9 Lecture Notes.
X = model.matrix(Sales ~ ., ads_data)
y = ads_data$Sales
lassoreg = cv.glmnet(X, y, alpha = 1)
summary(lassoreg)## Length Class Mode
## lambda 58 -none- numeric
## cvm 58 -none- numeric
## cvsd 58 -none- numeric
## cvup 58 -none- numeric
## cvlo 58 -none- numeric
## nzero 58 -none- numeric
## call 4 -none- call
## name 1 -none- character
## glmnet.fit 12 elnet list
## lambda.min 1 -none- numeric
## lambda.1se 1 -none- numeric
## index 2 -none- numeric#C)Compare the results from the best subset selection method using the different criteria and the LASSO method.
predict(lassoreg, type = "coefficients")## 6 x 1 sparse Matrix of class "dgCMatrix"
## lambda.1se
## (Intercept) 4.56000275
## (Intercept) .
## X .
## TV 0.03993424
## Radio 0.15433575
## Newspaper .##III. Empirical Exercise: S&P500. Using the Stock P rice Data and the Stock P rice P rogram provided to you, perform the following tasks. Notes on the data: SP 500 is the index itself, SP 500L is its lag; SP 500D is its difference, SP 500D1 is the lag of the difference; SP 500R is the return on the S&P500, SP 500RL is its lag.
#Load Data
load("/cloud/project/Stock_Price_Data.RData")
stock_data<-mydata#a) Perform three OLS regressions (1) SP 500 on its lag SP 500L, (2) SP 500D on its lag SP 500D1, (3) SP 500R on its lag SP 500RL. Report the regression coefficients and the R^2’s. (answered under each plots)
regsp<-lm(SP500~SP500L, stock_data)
summary(regsp)##
## Call:
## lm(formula = SP500 ~ SP500L, data = stock_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.048 -6.883 0.687 8.207 103.480
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2848466 1.3807548 0.931 0.352
## SP500L 0.9992939 0.0009278 1077.078 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.21 on 2515 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9978, Adjusted R-squared: 0.9978
## F-statistic: 1.16e+06 on 1 and 2515 DF, p-value: < 2.2e-16coeftest(regsp, vcov = NeweyWest(regsp,lag=1))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2848466 1.5040266 0.8543 0.393
## SP500L 0.9992939 0.0010178 981.8438 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1stock_data$SP500t<-ts(stock_data$SP500)
plot(stock_data$SP500t,ylab="S&P500")
Coefficient = 0.999 R^2 (adjusted) =0.9978
regsd<-lm(SP500D~SP500D1,stock_data)
summary(regsd)##
## Call:
## lm(formula = SP500D ~ SP500D1, data = stock_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -106.602 -6.998 0.946 7.933 103.012
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.28126 0.32227 0.873 0.383
## SP500D1 -0.07821 0.01989 -3.932 8.65e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.16 on 2514 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.006112, Adjusted R-squared: 0.005717
## F-statistic: 15.46 on 1 and 2514 DF, p-value: 8.654e-05coeftest(regsd,vcov=NeweyWest(regsd,lag=1))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.281265 0.321849 0.8739 0.382254
## SP500D1 -0.078206 0.028715 -2.7235 0.006503 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1stock_data$SP500Dt<-ts(stock_data$SP500D)
plot(stock_data$SP500Dt,ylab="Changes in S&P500")
Coefficient = -0.07821 R^2 (adjusted) = 0.005717
regsr<-lm(SP500R~SP500RL,stock_data)
summary(regsr)##
## Call:
## lm(formula = SP500R ~ SP500RL, data = stock_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.090973 -0.004755 0.000472 0.005594 0.115095
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.451e-03 1.121e-03 1.295 0.195
## SP500RL -8.292e-07 7.531e-07 -1.101 0.271
##
## Residual standard error: 0.01316 on 2515 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.0004819, Adjusted R-squared: 8.446e-05
## F-statistic: 1.213 on 1 and 2515 DF, p-value: 0.2709coeftest(regsr,vcov=NeweyWest(regsr,lag=1))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.4512e-03 1.3649e-03 1.0632 0.2878
## SP500RL -8.2923e-07 8.4590e-07 -0.9803 0.3270stock_data$SP500Rt<-ts(stock_data$SP500R)
plot(stock_data$SP500Rt,ylab="Returns on S&P500")
Coefficient= 1.451e-03 R^2(adjusted)= 8.446e-05
#b) Which of the regressions in (a) may be spurious? Why? The most likely regression that is spurious is the first regression because both the coefficient and the R^2 is 1. This may indicate that there is no real relations but rather it is simply the 2 variables following a very close trend.
#c) In finance theory, it is well established that stock returns are slightly negatively correlated with their lags, does any of the regressions in (a) support this theory? Refer to the appropriate regression and explain in words what it means. Third regression is the closest to this theory. The coefficient is negative but very close to 0.