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#Chapter 7
#1.)
library(wooldridge)
data.frame("sleep75")
## X.sleep75.
## 1 sleep75
data.frame(sleep75)
## age black case clerical construc educ earns74 gdhlth inlf leis1 leis2 leis3
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## 2 31 0 2 0.000000 0.000000 14 9500 1 1 2140 2140 2140
## 3 44 0 3 0.000000 0.000000 17 42500 1 1 4595 4505 4227
## 4 30 0 4 0.000000 0.000000 12 42500 1 1 3211 3211 3211
## 5 64 0 5 0.000000 0.000000 14 2500 1 1 4052 4007 4007
## 6 41 0 6 0.000000 0.000000 12 0 1 1 4812 4797 4797
## 7 35 0 7 0.000000 0.000000 12 8250 1 1 4787 4157 4157
## 8 47 0 8 0.000000 0.000000 13 0 1 1 3544 3469 3439
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## 10 30 0 10 0.000000 0.000000 15 11750 1 1 4211 4061 4061
## 11 43 0 11 0.000000 0.000000 8 21250 1 1 2090 1677 1677
## 12 23 0 12 0.000000 0.000000 16 1000 1 1 6415 6355 6230
## 13 24 0 13 0.000000 0.000000 16 1000 1 1 3844 3844 3794
## 14 48 0 14 0.000000 0.000000 5 18750 1 1 4379 4379 4379
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## 18 37 0 18 0.000000 0.000000 14 13750 1 1 3489 3489 3489
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## smsa lhrwage lothinc male marr prot rlxall selfe sleep slpnaps south
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## 6 0 2.957511 10.657280 1 1 1 4078 0 4063 4078 0
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## 8 1 2.708717 10.657280 1 1 1 3033 1 2928 3003 0
## 9 0 1.465567 0.000000 1 1 0 3606 0 3368 3368 0
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## 13 1 0.207014 7.313887 1 1 0 3848 0 3798 3798 0
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## 18 0 1.376244 0.000000 1 1 1 2580 1 2580 2580 0
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## 20 1 2.698000 0.000000 1 1 0 3165 0 3090 3090 0
## 21 1 3.569814 0.000000 1 0 0 2760 1 2760 2760 0
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## 30 0 1.241269 6.908755 1 1 1 3292 1 3238 3292 0
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## 40 1 1.348073 0.000000 1 0 1 2838 0 2200 2838 0
## 41 1 1.684545 0.000000 1 1 1 3073 0 2885 3073 0
## 42 0 2.041220 10.075380 1 1 1 3606 0 3345 3495 0
## 43 0 0.770108 7.313887 0 0 0 2978 1 2765 2978 0
## 44 0 1.805005 10.075380 1 1 1 4141 1 3928 3953 1
## 45 0 1.752672 8.922792 1 1 1 3406 0 2833 3406 0
## 46 0 1.752672 8.888895 1 1 1 3750 0 3750 3750 0
## 47 0 1.752672 8.922792 1 1 1 3328 0 3328 3328 1
## 48 0 2.004179 8.517393 1 1 1 3903 0 3795 3848 1
## 49 0 1.465567 9.528867 1 1 1 3513 0 3363 3513 1
## 50 0 1.512927 0.000000 1 1 1 2280 0 2280 2280 0
## 51 0 1.193922 8.229777 1 1 0 4289 0 4151 4176 0
## 52 1 1.556037 0.000000 1 0 0 3266 0 3266 3266 0
## 53 0 1.220830 8.517393 1 1 1 3570 0 3570 3570 0
## 54 1 1.994700 10.221980 1 1 1 2900 0 2885 2885 0
## 55 1 1.147403 7.601402 1 0 0 2879 0 2879 2879 0
## 56 0 0.048790 0.000000 0 0 0 2790 1 2790 2790 0
## 57 0 2.128232 9.159152 1 1 1 2799 0 2799 2799 1
## 58 0 1.697449 8.922792 1 1 1 3211 0 3173 3211 1
## 59 0 1.697449 0.000000 1 1 1 3308 0 3308 3308 0
## 60 0 2.128232 0.000000 1 1 1 3305 1 3305 3305 0
## 61 1 1.029619 0.000000 0 0 0 3649 0 2975 3646 0
## 62 0 1.453953 9.528867 1 1 1 3533 0 3316 3466 0
## 63 0 1.115142 8.612685 1 1 1 3271 0 3226 3226 0
## 64 0 0.891998 8.888895 0 1 1 3635 0 3635 3635 1
## 65 0 1.644805 9.528867 1 1 1 3683 0 3233 3683 1
## 66 0 2.078191 10.221980 1 1 1 3498 0 3348 3348 0
## 67 1 1.791759 8.922792 0 0 1 2630 1 2630 2630 1
## 68 1 1.172482 0.000000 0 0 0 2918 0 2858 2858 0
## 69 1 1.172482 9.472781 0 1 1 3271 0 3203 3271 0
## 70 0 1.791759 0.000000 1 0 1 3551 0 3451 3551 0
## 71 1 1.752672 0.000000 1 1 1 3008 0 3008 3008 0
## 72 0 1.018847 0.000000 1 1 1 2889 0 2821 2851 1
## 73 1 1.711995 0.000000 1 1 1 3718 0 3525 3680 0
## 74 0 2.117460 10.075380 1 1 1 3210 0 3150 3210 1
## 75 0 1.018847 8.612685 0 1 1 3113 0 3113 3113 0
## 76 0 1.711995 9.159152 0 1 1 2816 0 2816 2816 1
## 77 0 1.711995 9.695910 1 1 1 3105 0 3105 3105 0
## 78 0 1.711995 0.000000 1 1 1 3635 1 3605 3605 1
## 79 0 2.060514 7.824446 1 0 1 3611 0 3611 3611 1
## 80 1 2.060514 0.000000 1 1 0 3128 0 3128 3128 1
## 81 1 2.060514 9.528867 1 1 0 3276 0 3213 3213 1
## 82 0 0.932164 0.000000 1 1 0 6110 0 3860 6110 0
## 83 0 0.239017 7.601402 0 1 1 4623 0 4275 4388 1
## 84 1 2.030776 7.824446 1 1 1 3701 0 3076 3701 0
## 85 0 2.000128 0.000000 1 1 1 4313 0 4313 4313 0
## 86 1 1.530395 9.472781 1 1 1 2930 0 2885 2885 0
## 87 0 2.783158 9.210441 1 0 1 3173 0 3165 3165 1
## 88 0 0.837247 0.000000 1 1 1 3674 0 3105 3555 0
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## 91 1 1.530395 7.824446 1 1 1 3445 0 3415 3415 0
## 92 0 2.446686 10.389030 1 1 1 3533 0 3508 3508 0
## 93 1 2.119864 0.000000 1 0 1 2933 0 2788 2908 0
## 94 0 1.607436 0.000000 1 0 0 3405 0 3180 3385 0
## 95 0 1.583094 9.210441 1 1 1 3123 0 3123 3123 0
## 96 0 1.867176 0.000000 1 1 1 3673 0 3388 3613 0
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## 101 0 1.662030 9.282754 1 1 1 3278 0 3218 3278 0
## 102 0 1.308333 0.000000 1 1 0 3065 0 3045 3045 0
## 103 1 1.308333 9.371694 1 1 1 3808 0 3433 3808 0
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## 105 0 0.329304 0.000000 1 1 1 3058 1 2970 2970 1
## 106 1 -0.040822 9.964159 0 1 1 3508 0 3475 3475 0
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## 108 0 0.364643 0.000000 0 1 1 3023 0 2910 2940 0
## 109 0 0.955511 0.000000 1 1 1 3577 0 3570 3577 1
## 110 1 1.832582 0.000000 1 1 0 3345 0 3060 3345 0
## 111 0 1.752672 8.517393 1 1 1 3720 0 3495 3660 0
## 112 1 1.752672 0.000000 0 0 0 2970 0 2970 2970 0
## 113 1 1.752672 9.328213 1 1 0 3423 0 3008 3423 0
## 114 1 1.570697 10.266430 0 1 1 3563 0 3428 3428 0
## 115 1 1.570697 9.528867 1 1 1 3288 0 3288 3288 0
## 116 0 2.263844 7.824446 1 1 1 2400 0 2400 2400 0
## 117 0 2.263844 10.075380 1 1 1 3173 0 3070 3100 0
## 118 0 1.465567 8.922792 0 1 1 2250 0 2250 2250 0
## 119 0 2.158715 9.491828 1 1 1 3666 0 3323 3628 0
## 120 0 1.408545 8.657129 1 0 1 3023 0 3023 3023 0
## 121 0 3.480624 7.824446 1 1 0 3918 1 3505 3505 0
## 122 0 1.686399 0.000000 1 1 0 3533 0 3503 3503 0
## 123 0 1.283708 8.160804 1 1 1 3520 0 3370 3370 1
## 124 1 1.976855 0.000000 1 1 1 3420 0 3120 3120 0
## 125 1 1.976855 9.528867 1 1 1 3308 1 3308 3308 0
## 126 0 1.214913 9.159152 0 1 1 3421 0 3398 3421 0
## 127 0 1.908060 0.000000 1 1 1 3431 0 3333 3393 0
## 128 0 1.264127 7.313887 0 0 1 2923 0 2728 2923 1
## 129 0 1.061257 7.601402 1 1 0 3256 0 3256 3256 0
## 130 0 0.506818 9.528867 0 1 0 3545 0 3250 3545 0
## 131 1 2.334084 0.000000 1 1 0 2915 0 2915 2915 0
## 132 1 1.235471 7.824446 1 1 0 4292 0 4170 4290 1
## 133 1 2.547881 10.657280 1 1 1 3030 0 3030 3030 0
## 134 0 1.541159 0.000000 0 0 1 3668 0 3668 3668 1
## 135 1 1.774952 10.484330 1 1 0 2303 0 2303 2303 0
## 136 1 0.900161 7.824446 0 1 1 3688 0 3618 3688 0
## 137 0 1.391282 7.824446 1 1 1 3466 0 3316 3466 0
## 138 0 -0.673345 9.453365 0 1 0 3989 1 3601 3676 0
## 139 0 0.058269 9.371694 0 1 0 2503 1 2413 2413 0
## 140 0 0.717840 0.000000 1 1 1 2801 0 2771 2771 1
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## 142 0 1.036737 6.908755 0 1 0 3808 0 3808 3808 0
## 143 0 1.278152 8.160804 1 1 1 3363 1 3363 3363 0
## 144 1 1.278152 9.235130 1 1 1 3675 0 3675 3675 0
## 145 0 1.472472 7.601402 1 1 1 3270 0 3120 3195 0
## 146 1 2.165619 9.528867 0 1 0 3561 0 3536 3536 1
## 147 0 1.635106 9.839003 1 1 1 3253 0 3253 3253 0
## 148 1 1.635106 0.000000 1 0 0 2945 0 2885 2945 0
## 149 0 1.635106 9.964159 1 1 1 2598 0 2560 2560 0
## 150 1 1.897620 0.000000 1 1 1 3007 0 2985 3007 0
## 151 1 1.897620 9.528867 0 1 0 3095 0 3095 3095 0
## 152 0 1.834180 8.922792 1 1 0 2985 0 2985 2985 0
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## 154 0 2.105353 9.839003 1 1 1 3383 0 2838 3383 0
## 155 1 2.423917 8.517393 1 1 1 3465 0 3375 3375 0
## 156 1 2.041220 8.922792 1 1 0 3393 0 3355 3355 0
## 157 1 1.818077 0.000000 1 1 0 3905 0 3743 3865 0
## 158 1 2.041220 8.517393 1 1 0 2741 0 2701 2741 0
## 159 1 1.124930 9.865318 0 1 1 3016 0 2943 3003 0
## 160 1 1.348073 9.132487 1 1 0 3463 0 3463 3463 0
## 161 0 1.530395 0.000000 1 0 1 2843 0 2723 2843 1
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## 167 1 2.261763 0.000000 1 1 1 3111 0 2991 3111 0
## 168 1 1.275363 8.853808 0 1 1 3225 0 3215 3215 0
## 169 1 1.731656 9.528867 0 1 1 3851 0 3611 3761 0
## 170 0 1.731656 9.491828 1 1 0 3580 0 3305 3455 0
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## 179 0 1.300192 8.853808 1 1 0 3065 0 3065 3065 0
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## 181 1 1.798404 0.000000 1 1 1 4435 0 3090 4353 0
## 182 0 1.574847 0.000000 1 0 1 2888 0 2798 2888 1
## 183 0 1.169381 0.000000 1 1 1 3610 0 3610 3610 1
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## 185 1 1.776646 8.354910 1 1 0 3881 0 3656 3881 0
## 186 1 2.086914 0.000000 1 1 1 3348 1 3348 3348 0
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## 191 0 1.376244 0.000000 1 0 1 3541 0 3203 3541 1
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model <- lm(sleep ~ totwrk + educ + age + agesq + male , data = sleep75)
summary(model)
##
## Call:
## lm(formula = sleep ~ totwrk + educ + age + agesq + male, data = sleep75)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2378.00 -243.29 6.74 259.24 1350.19
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3840.83197 235.10870 16.336 <2e-16 ***
## totwrk -0.16342 0.01813 -9.013 <2e-16 ***
## educ -11.71332 5.86689 -1.997 0.0463 *
## age -8.69668 11.20746 -0.776 0.4380
## agesq 0.12844 0.13390 0.959 0.3378
## male 87.75243 34.32616 2.556 0.0108 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 417.7 on 700 degrees of freedom
## Multiple R-squared: 0.1228, Adjusted R-squared: 0.1165
## F-statistic: 19.59 on 5 and 700 DF, p-value: < 2.2e-16
# (i) All other factors being equal, is there evidence that men sleep more than women? How strong is the evidence?
#p value is equal to 87.75/34.33=2.56. That means this value is significant according to the table. We can interpret that men sleep 87.75 minutes more than women.
# (ii) Is there a statistically significant tradeoff between working and sleeping? What is the estimated tradeoff?
#t significant=0.163/0.018=9.05. it is significant statistically
#When working time increased by one minute, sleeping time will be decreased by 0.163 which is equal to 9.78 minutes.
# (iii) What other regression do you need to run to test the null hypothesis that, holding other factors fixed, age has no effect on sleeping?
#We just have to exclude age variable.
model <- lm(sleep ~ totwrk + educ + male , data = sleep75)
summary(model)
##
## Call:
## lm(formula = sleep ~ totwrk + educ + male, data = sleep75)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2380.27 -239.15 6.74 257.31 1370.63
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3747.51727 81.00609 46.262 < 2e-16 ***
## totwrk -0.16734 0.01794 -9.329 < 2e-16 ***
## educ -13.88479 5.65757 -2.454 0.01436 *
## male 90.96919 34.27441 2.654 0.00813 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 418 on 702 degrees of freedom
## Multiple R-squared: 0.1193, Adjusted R-squared: 0.1155
## F-statistic: 31.69 on 3 and 702 DF, p-value: < 2.2e-16
#Rsq hasn't quite changed so age has no effect on sleeping time.
#3.)
library(wooldridge)
data.frame("gpa2")
## X.gpa2.
## 1 gpa2
data.frame(gpa2)
## sat tothrs colgpa athlete verbmath hsize hsrank hsperc female white
## 1 920 43 2.04 1 0.48387 0.10 4 40.0000000 1 0
## 2 1170 18 4.00 0 0.82813 9.40 191 20.3191490 0 1
## 3 810 14 1.78 1 0.88372 1.19 42 35.2941170 0 1
## 4 940 40 2.42 0 0.80769 5.71 252 44.1330986 0 1
## 5 1180 18 2.61 0 0.73529 2.14 86 40.1869164 0 1
## 6 980 114 3.03 0 0.81481 2.68 41 15.2985077 1 1
## 7 880 78 1.84 0 0.76000 3.11 161 51.7684898 0 0
## 8 980 55 3.05 0 0.88462 2.68 101 37.6865654 0 1
## 9 1240 18 3.00 0 0.69863 3.67 161 43.8692093 0 1
## 10 1230 17 2.00 0 0.86364 0.10 3 30.0000000 0 1
## 11 1140 78 2.98 0 0.93220 3.34 95 28.4431133 1 1
## 12 1150 43 2.93 0 0.85484 3.59 13 3.6211698 1 1
## 13 1080 17 2.00 1 0.80000 3.18 31 9.7484274 0 1
## 14 990 64 2.21 0 0.67797 1.92 51 26.5625000 1 1
## 15 1000 45 3.33 0 0.78571 3.69 29 7.8590784 1 1
## 16 1050 14 1.07 0 0.77966 2.66 134 50.3759384 1 1
## 17 1160 41 2.29 0 0.87097 1.45 99 68.2758636 1 1
## 18 1190 13 3.15 0 1.12500 1.76 74 42.0454559 0 1
## 19 1030 110 2.65 0 1.10204 3.86 81 20.9844551 1 1
## 20 960 106 2.41 1 1.00000 3.83 66 17.2323761 0 1
## 21 840 104 2.39 0 0.64706 1.07 7 6.5420561 0 1
## 22 920 115 2.64 0 1.00000 2.17 65 29.9539165 1 1
## 23 840 96 2.18 0 0.86667 2.34 141 60.2564087 1 1
## 24 1000 50 2.84 0 0.78571 4.63 133 28.7257023 0 1
## 25 1150 100 2.84 0 0.79688 5.95 301 50.5882339 1 1
## 26 1040 112 2.93 0 0.96226 0.91 30 32.9670334 0 1
## 27 970 17 2.29 0 0.79630 4.36 41 9.4036694 1 1
## 28 1200 39 2.38 0 0.90476 8.12 209 25.7389164 1 1
## 29 1090 118 3.92 0 0.75806 0.60 2 3.3333333 1 1
## 30 1340 46 2.23 0 0.83562 3.76 130 34.5744667 0 1
## 31 740 12 1.33 0 1.31250 5.32 390 73.3082733 1 1
## 32 880 85 2.81 0 0.76000 3.80 71 18.6842098 0 1
## 33 820 42 2.09 1 0.90698 2.28 155 67.9824524 0 1
## 34 1060 43 2.25 0 0.85965 5.51 248 45.0090752 0 1
## 35 730 50 1.90 1 0.78049 4.82 273 56.6390038 0 0
## 36 820 16 3.00 0 0.86364 3.90 102 26.1538467 1 1
## 37 780 71 2.40 1 0.69565 0.78 17 21.7948723 0 1
## 38 1040 78 2.16 0 1.03922 4.92 92 18.6991863 0 1
## 39 870 13 2.07 0 1.17500 1.86 86 46.2365608 1 1
## 40 940 19 2.21 0 1.29268 1.85 41 22.1621628 0 1
## 41 980 47 2.00 1 0.92157 1.52 45 29.6052628 0 0
## 42 1020 103 2.91 0 0.96154 0.10 2 20.0000000 1 1
## 43 1180 105 3.00 1 0.87302 6.37 255 40.0313988 0 1
## 44 1100 72 2.72 0 1.11538 0.12 2 16.6666660 0 1
## 45 1030 18 3.55 0 1.10204 2.52 27 10.7142859 0 1
## 46 960 16 3.25 0 1.04255 0.10 5 50.0000000 1 1
## 47 910 15 2.86 0 1.45946 1.27 28 22.0472450 0 1
## 48 1060 42 2.04 0 0.96296 0.13 1 7.6923075 0 1
## 49 880 14 1.92 0 1.37838 0.03 1 33.3333321 1 1
## 50 1010 17 3.58 0 0.94231 0.28 2 7.1428571 1 1
## 51 700 38 2.39 1 1.00000 0.32 22 68.7500000 0 1
## 52 930 15 3.46 0 0.86000 3.72 67 18.0107536 1 1
## 53 900 18 3.16 0 0.91489 2.54 69 27.1653538 0 1
## 54 1090 29 1.03 0 0.91228 2.02 121 59.9009895 0 1
## 55 1120 79 3.00 0 1.24000 4.70 78 16.5957451 1 0
## 56 960 15 2.33 1 0.77778 4.47 320 71.5883636 0 0
## 57 890 37 2.45 1 0.78000 1.24 50 40.3225822 0 1
## 58 1240 47 3.65 0 0.79710 5.37 31 5.7728119 0 1
## 59 1090 113 3.61 0 0.84746 3.64 50 13.7362633 1 1
## 60 820 47 3.25 0 1.10256 6.34 68 10.7255516 1 1
## 61 940 16 3.81 0 0.77358 3.42 53 15.4970760 0 1
## 62 820 40 2.25 1 1.10256 5.71 344 60.2451820 0 0
## 63 970 39 2.41 1 0.67241 5.66 83 14.6643114 0 1
## 64 790 17 2.82 1 1.07895 5.97 72 12.0603018 0 1
## 65 1080 13 2.30 0 1.11765 0.10 7 70.0000000 1 1
## 66 850 48 3.27 0 0.80851 3.10 54 17.4193554 1 1
## 67 850 15 2.66 1 0.80851 0.73 5 6.8493152 1 1
## 68 820 95 2.26 1 0.70833 1.31 98 74.8091583 0 1
## 69 1120 12 2.33 1 0.67164 4.88 20 4.0983605 0 1
## 70 880 43 2.37 1 1.09524 4.07 70 17.1990166 1 1
## 71 1540 85 4.00 0 0.97436 2.30 1 0.4347826 0 1
## 72 780 86 3.81 0 1.00000 3.47 38 10.9510088 0 1
## 73 1280 55 3.87 0 1.03175 2.03 3 1.4778326 1 1
## 74 1260 13 4.00 0 0.75000 2.17 5 2.3041475 1 1
## 75 830 83 1.95 1 0.84444 2.00 84 42.0000000 0 0
## 76 980 16 2.43 0 0.68966 0.92 28 30.4347820 0 1
## 77 500 14 1.21 1 1.27273 4.57 329 71.9912491 0 1
## 78 1040 15 3.00 0 0.96226 3.61 31 8.5872574 0 1
## 79 930 12 1.75 0 0.82353 3.25 26 8.0000000 1 0
## 80 570 79 1.73 1 0.96552 3.24 187 57.7160492 0 0
## 81 820 13 1.84 0 0.82222 3.03 147 48.5148506 1 1
## 82 1310 16 2.25 0 0.95522 4.67 122 26.1241970 0 1
## 83 770 15 2.13 0 0.79070 1.00 30 30.0000000 1 0
## 84 1180 18 3.77 0 0.87302 4.80 48 10.0000000 0 1
## 85 1310 53 3.22 0 0.92647 3.20 30 9.3750000 0 1
## 86 1150 63 2.17 0 1.12963 3.02 64 21.1920528 0 1
## 87 1130 113 2.77 0 0.91525 1.66 33 19.8795185 0 0
## 88 1110 122 3.36 0 1.09434 2.04 9 4.4117646 1 1
## 89 1210 16 3.62 0 1.01667 2.93 14 4.7781572 0 1
## 90 1090 20 3.70 0 1.01852 1.87 6 3.2085562 1 1
## 91 1040 54 2.00 0 0.82456 3.55 82 23.0985909 1 1
## 92 1340 81 3.69 0 1.03030 1.11 15 13.5135136 1 1
## 93 900 76 1.75 0 0.91489 0.86 16 18.6046505 0 1
## 94 650 52 2.19 1 0.80556 2.06 57 27.6699028 0 1
## 95 1190 77 3.40 0 0.67606 4.24 26 6.1320753 1 1
## 96 990 16 1.43 0 0.73684 2.51 39 15.5378485 1 1
## 97 1160 50 2.78 0 0.73134 3.72 79 21.2365589 1 1
## 98 1140 71 2.61 1 0.58333 2.41 24 9.9585066 0 1
## 99 1180 87 3.09 1 1.18519 4.69 36 7.6759062 0 1
## 100 1120 49 2.83 0 0.83607 0.10 1 10.0000000 1 1
## 101 1010 15 1.93 0 0.77193 3.19 157 49.2163010 1 1
## 102 1160 113 2.88 0 0.96610 4.02 15 3.7313433 0 1
## 103 1200 16 3.31 0 1.10526 4.32 209 48.3796310 1 1
## 104 720 16 1.93 1 0.94595 4.30 230 53.4883728 1 0
## 105 1190 36 2.41 0 0.91935 2.61 97 37.1647491 0 1
## 106 970 14 2.92 0 0.76364 3.41 116 34.0175972 1 1
## 107 1210 17 3.52 0 0.95161 5.11 1 0.1956947 1 1
## 108 930 49 2.93 0 0.72222 2.00 65 32.5000000 0 1
## 109 1000 74 2.28 0 0.85185 2.36 75 31.7796612 0 1
## 110 970 42 1.95 0 0.76364 4.33 130 30.0230942 0 1
## 111 960 45 3.02 1 0.88235 0.10 3 30.0000000 1 1
## 112 980 47 3.25 0 1.27907 0.10 4 40.0000000 0 1
## 113 960 118 3.32 0 0.92000 2.26 96 42.4778748 0 1
## 114 970 79 2.03 1 0.73214 0.10 3 30.0000000 0 1
## 115 960 79 2.34 0 1.00000 0.74 7 9.4594593 1 1
## 116 1160 96 3.41 0 0.93333 2.12 19 8.9622641 0 1
## 117 1080 80 2.56 0 0.68750 2.12 100 47.1698112 0 1
## 118 990 14 4.00 0 0.80000 3.05 3 0.9836066 1 1
## 119 1130 18 1.33 0 0.79365 2.35 91 38.7234039 1 1
## 120 1060 12 2.25 0 0.85965 2.35 66 28.0851059 0 1
## 121 1060 15 2.60 0 0.89286 2.35 44 18.7234039 1 1
## 122 1120 73 2.63 0 0.77778 2.95 15 5.0847459 0 1
## 123 1030 17 2.58 0 0.63492 2.78 59 21.2230225 0 1
## 124 1070 48 3.04 0 0.78333 3.15 99 31.4285717 0 1
## 125 910 13 2.76 0 0.75000 3.72 85 22.8494625 0 1
## 126 1100 108 1.95 0 1.00000 3.73 188 50.4021454 0 1
## 127 1000 106 2.92 0 0.78571 3.73 127 34.0482559 0 1
## 128 1000 17 3.41 0 0.75439 3.71 99 26.6846371 0 1
## 129 970 46 2.73 0 0.67241 4.10 113 27.5609760 1 1
## 130 1070 35 2.54 0 0.55072 6.00 62 10.3333330 0 1
## 131 950 15 3.06 0 0.66667 2.85 24 8.4210529 0 1
## 132 1140 16 1.93 0 0.86885 2.17 34 15.6682024 1 1
## 133 1060 17 3.23 0 0.89286 1.56 27 17.3076916 0 1
## 134 940 50 2.54 1 0.70909 2.51 45 17.9282875 0 1
## 135 960 48 2.22 0 0.71429 1.00 39 39.0000000 0 1
## 136 890 104 1.99 0 0.93478 2.10 38 18.0952377 0 1
## 137 1120 41 1.75 0 0.89831 3.28 152 46.3414650 1 1
## 138 1150 14 3.14 0 0.82540 0.10 4 40.0000000 0 1
## 139 1270 107 3.24 0 0.78873 0.10 4 40.0000000 0 1
## 140 1100 18 2.00 0 0.83333 0.10 4 40.0000000 1 1
## 141 1150 14 2.50 0 0.94915 0.10 5 50.0000000 0 1
## 142 1090 15 1.60 0 0.91228 1.50 79 52.6666679 0 1
## 143 1220 110 3.05 0 0.84848 0.10 5 50.0000000 1 1
## 144 1070 102 2.41 0 0.75410 0.10 5 50.0000000 0 1
## 145 1030 15 2.73 0 1.01961 1.36 4 2.9411764 1 1
## 146 980 49 2.93 0 0.63333 3.20 17 5.3125000 0 1
## 147 930 44 2.50 0 0.82353 2.71 40 14.7601480 1 1
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## 1081 1010 13 1.69 0 1.10417 5.10 154 30.1960793 0 1
## 1082 960 12 3.16 0 1.23256 5.10 43 8.4313726 0 1
## 1083 930 48 2.93 0 0.82353 5.05 75 14.8514853 1 1
## 1084 1130 75 2.48 0 0.85246 4.92 66 13.4146338 0 1
## 1085 950 14 2.28 0 0.86275 5.10 90 17.6470585 1 1
## 1086 1160 44 2.75 0 1.03509 5.05 33 6.5346537 1 1
## 1087 830 111 3.20 0 1.12821 4.44 96 21.6216221 1 1
## 1088 1160 16 3.31 0 0.81250 5.10 55 10.7843142 1 1
## 1089 950 17 3.41 0 0.75926 4.40 13 2.9545455 0 1
## 1090 980 74 2.37 1 0.88462 2.60 86 33.0769234 0 1
## 1091 880 17 3.05 1 0.76000 1.77 12 6.7796612 0 1
## 1092 1090 13 3.30 0 0.78689 0.56 30 53.5714302 0 1
## 1093 940 68 3.07 0 0.91837 0.10 3 30.0000000 0 1
## 1094 1120 42 2.45 0 0.86667 0.10 5 50.0000000 0 1
## 1095 930 48 2.60 0 0.69091 4.00 135 33.7500000 0 1
## 1096 970 43 3.09 0 0.97959 0.10 4 40.0000000 0 1
## 1097 930 15 1.86 0 0.66071 0.10 4 40.0000000 1 1
## 1098 1170 41 2.97 0 0.98305 0.10 2 20.0000000 1 1
## 1099 1220 18 3.38 0 0.93651 3.13 8 2.5559106 0 1
## 1100 1140 17 3.82 0 0.80952 2.21 3 1.3574661 1 1
## 1101 880 16 1.68 0 0.87234 4.55 89 19.5604401 1 1
## 1102 1130 94 1.91 0 0.79365 1.59 51 32.0754700 0 1
## 1103 880 16 1.50 0 0.79592 1.42 27 19.0140839 1 1
## 1104 1030 108 3.05 0 1.06000 1.59 7 4.4025159 1 1
## 1105 1010 13 2.00 0 1.06122 1.42 31 21.8309860 0 1
## 1106 1120 17 3.52 0 0.93103 2.81 5 1.7793595 0 1
## 1107 810 84 2.78 0 1.02500 2.38 12 5.0420170 1 1
## 1108 1160 49 3.61 0 0.96610 2.78 4 1.4388490 0 1
## 1109 1110 14 2.78 0 0.98214 2.60 63 24.2307701 1 1
## 1110 1370 73 3.23 0 0.82667 2.62 13 4.9618320 0 1
## 1111 950 114 2.62 0 0.75926 2.47 26 10.5263157 1 1
## 1112 960 92 3.03 1 0.60000 2.65 42 15.8490562 0 1
## 1113 1310 15 3.46 0 1.04688 1.68 6 3.5714285 1 1
## 1114 1030 14 0.85 0 0.77586 2.73 59 21.6117210 0 1
## 1115 1160 42 2.02 0 0.84127 3.89 36 9.2544985 0 1
## 1116 1180 15 3.06 0 0.87302 2.46 44 17.8861790 0 1
## 1117 1080 17 1.17 0 1.03774 4.04 63 15.5940590 0 1
## 1118 950 13 2.84 0 0.90000 1.59 18 11.3207550 0 1
## 1119 1170 14 3.28 0 0.74627 1.71 4 2.3391812 0 1
## 1120 790 79 2.59 0 1.07895 4.02 64 15.9203978 1 1
## 1121 940 73 2.42 0 0.84314 6.00 281 46.8333321 0 1
## 1122 1090 38 1.92 0 0.73016 6.50 71 10.9230766 0 1
## 1123 1280 101 3.39 0 0.93939 6.00 54 9.0000000 1 1
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## 1125 1090 11 2.54 0 1.13725 7.20 269 37.3611107 1 1
## 1126 1360 108 3.97 0 0.97101 4.59 1 0.2178649 1 1
## 1127 1320 119 3.21 0 0.80822 4.59 17 3.7037036 0 1
## 1128 910 15 3.06 0 0.85714 4.84 133 27.4793396 0 1
## 1129 880 40 2.07 0 0.79592 1.70 31 18.2352943 0 1
## 1130 1110 50 2.94 0 0.70769 1.26 9 7.1428571 0 1
## 1131 990 72 2.20 0 0.73684 1.61 30 18.6335411 0 1
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## 1134 890 17 2.88 0 0.81633 1.83 22 12.0218582 0 1
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## 1138 970 17 2.23 0 0.94000 6.63 212 31.9758663 0 1
## 1139 1230 56 3.07 0 0.75714 6.75 35 5.1851850 1 1
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## 1141 1350 48 3.85 0 0.80000 6.75 7 1.0370370 0 1
## 1142 870 44 2.22 0 0.77551 6.75 259 38.3703690 0 1
## 1143 890 50 3.36 0 0.97778 6.75 59 8.7407408 1 1
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## 1148 940 46 2.69 0 0.88000 0.10 3 30.0000000 1 1
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## 1151 900 95 2.16 1 0.87500 1.99 52 26.1306534 0 1
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## 1153 1000 14 3.07 0 0.92308 0.72 6 8.3333330 1 1
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## 1159 1300 80 3.38 0 0.83099 2.65 4 1.5094340 0 1
## 1160 1360 18 2.83 0 1.00000 2.41 35 14.5228214 0 1
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## 1172 990 82 2.86 0 0.80000 3.62 20 5.5248618 1 1
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## 1217 910 84 3.52 0 0.82000 4.31 8 1.8561485 1 1
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## 1219 1020 13 1.30 0 1.12500 1.35 60 44.4444427 0 1
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## 1222 860 16 2.62 0 1.00000 1.96 35 17.8571434 0 1
## 1223 920 112 3.85 0 1.04444 2.30 20 8.6956520 0 1
## 1224 960 15 1.26 0 0.81132 1.09 52 47.7064209 1 1
## 1225 760 74 2.35 0 0.94872 1.73 47 27.1676292 1 1
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## 1228 1000 15 1.60 0 0.92308 2.96 64 21.6216221 1 1
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## 1231 1190 44 2.97 0 0.83077 3.03 22 7.2607260 1 1
## 1232 710 12 2.91 0 1.08824 1.69 16 9.4674559 1 1
## 1233 1080 105 2.40 0 0.68750 2.88 81 28.1250000 0 1
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## 1244 970 13 3.07 0 0.97959 1.90 37 19.4736843 0 1
## 1245 1130 17 2.35 0 0.82258 6.09 82 13.4646959 1 1
## 1246 910 80 2.45 0 1.11628 2.95 20 6.7796612 1 1
## 1247 1180 15 2.20 0 1.00000 7.37 165 22.3880596 1 1
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## 1285 890 18 1.44 0 1.22500 0.10 9 90.0000000 1 0
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## 1292 1080 46 2.04 0 1.16000 0.79 42 53.1645584 1 1
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## 1307 920 110 2.83 0 1.00000 5.06 140 27.6679840 1 1
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## 1310 1200 49 3.57 0 0.73913 6.41 36 5.6162248 0 1
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## 1312 1020 17 3.05 0 1.04000 1.90 32 16.8421059 1 1
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## 1329 920 124 3.46 0 0.95745 1.52 21 13.8157892 0 1
## 1330 1120 14 2.21 0 1.00000 0.96 52 54.1666679 0 1
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## 1345 720 121 2.59 0 1.00000 1.52 14 9.2105265 1 0
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## 1398 890 76 3.36 0 1.22500 2.80 18 6.4285712 1 1
## 1399 1070 13 1.92 0 1.18367 3.40 108 31.7647057 0 1
## 1400 850 123 2.57 0 0.70000 2.80 52 18.5714283 0 1
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## 1402 890 12 2.75 0 0.93478 2.80 87 31.0714283 1 1
## 1403 1080 12 3.16 0 0.80000 3.40 9 2.6470587 0 1
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## 1418 920 114 2.14 0 0.73585 2.80 31 11.0714283 1 1
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## 1441 960 17 2.05 0 1.00000 1.57 9 5.7324839 1 1
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## 1443 1190 78 2.73 0 0.83077 2.95 23 7.7966104 1 1
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## 1683 850 97 2.11 1 1.23684 2.03 112 55.1724129 0 0
## 1684 810 56 2.26 0 0.92857 2.17 75 34.5622101 0 1
## 1685 960 15 1.73 0 1.04255 2.11 64 30.3317528 1 1
## 1686 1060 91 2.35 0 1.16327 2.03 31 15.2709360 1 1
## 1687 900 55 3.05 0 0.87500 2.17 78 35.9447021 1 1
## 1688 950 118 2.88 0 0.82692 2.03 86 42.3645325 1 1
## 1689 970 48 2.79 0 1.02083 2.17 21 9.6774197 1 1
## 1690 980 114 2.66 0 0.84906 2.03 42 20.6896553 0 1
## 1691 900 51 3.17 0 0.95652 2.24 28 12.5000000 1 1
## 1692 940 18 2.77 0 1.00000 2.11 53 25.1184826 1 1
## 1693 970 14 2.14 0 0.90196 2.03 60 29.5566502 1 1
## 1694 1050 16 2.12 0 0.94444 2.11 43 20.3791466 0 1
## 1695 810 18 2.33 0 0.76087 1.68 36 21.4285717 1 1
## 1696 1090 97 2.25 0 0.67692 1.25 61 48.7999992 0 1
## 1697 1070 16 2.81 0 1.05769 1.68 19 11.3095236 1 1
## 1698 910 96 2.10 0 0.75000 1.25 59 47.2000008 0 1
## 1699 970 16 1.43 0 0.76364 1.68 73 43.4523811 0 1
## 1700 930 112 2.73 0 1.02174 1.25 22 17.6000004 1 1
## 1701 1050 16 1.68 0 0.84211 1.68 64 38.0952377 0 1
## 1702 1180 43 2.20 0 0.71014 1.49 12 8.0536909 0 1
## 1703 990 81 3.16 0 0.94118 1.25 14 11.1999998 0 1
## 1704 1080 16 2.56 0 0.86207 1.68 50 29.7619057 0 1
## 1705 920 12 2.58 1 1.42105 1.68 75 44.6428566 0 1
## 1706 890 75 2.56 0 0.64815 1.25 30 24.0000000 1 1
## 1707 1050 108 3.72 0 0.77966 1.25 2 1.6000000 1 1
## 1708 1210 129 2.48 0 0.83333 1.25 10 8.0000000 1 1
## 1709 970 16 1.50 0 0.79630 1.68 57 33.9285698 0 1
## 1710 920 77 2.40 0 0.91667 1.25 48 38.4000015 0 1
## 1711 1070 121 3.27 0 0.81356 1.25 33 26.3999996 0 1
## 1712 1100 109 2.46 0 1.03704 1.25 21 16.7999992 1 1
## 1713 1340 16 3.75 0 0.94203 1.68 1 0.5952381 0 1
## 1714 1030 102 2.40 0 1.01961 1.25 14 11.1999998 1 1
## 1715 1160 16 1.93 0 1.00000 0.05 3 60.0000000 1 1
## 1716 1160 82 3.54 0 0.93333 0.28 1 3.5714285 1 1
## 1717 1000 124 3.20 0 0.96078 0.27 15 55.5555573 1 1
## 1718 890 110 2.40 0 0.78000 0.27 18 66.6666641 1 1
## 1719 1000 78 2.56 0 1.04082 0.05 3 60.0000000 1 1
## 1720 1170 16 3.00 0 0.82813 1.86 53 28.4946232 0 1
## 1721 990 46 2.76 0 0.80000 1.55 59 38.0645180 0 1
## 1722 1000 109 3.66 0 0.78571 2.01 11 5.4726367 1 1
## 1723 1140 13 2.23 0 0.90000 1.86 117 62.9032249 0 1
## 1724 980 16 2.37 0 0.92157 1.86 75 40.3225822 1 1
## 1725 850 39 2.17 0 0.93182 1.55 82 52.9032249 0 1
## 1726 1040 45 2.62 0 0.96226 1.55 47 30.3225803 0 1
## 1727 1050 42 3.23 0 1.01923 1.55 37 23.8709679 0 1
## 1728 1040 104 2.54 0 1.21277 2.01 37 18.4079609 1 1
## 1729 1220 75 3.32 0 0.69444 1.58 9 5.6962028 1 1
## 1730 980 17 2.76 0 0.88462 1.86 69 37.0967751 0 1
## 1731 1130 113 3.72 0 1.05455 2.01 1 0.4975124 1 1
## 1732 920 17 2.35 0 0.76923 1.86 49 26.3440857 1 0
## 1733 1080 38 2.31 0 1.00000 2.01 99 49.2537308 0 1
## 1734 1170 102 3.64 0 1.08929 2.01 2 0.9950249 1 1
## 1735 830 85 2.88 0 0.97619 1.76 66 37.5000000 1 1
## 1736 1020 45 2.44 0 0.82143 1.55 56 36.1290321 1 1
## 1737 880 44 2.72 0 0.72549 1.55 26 16.7741928 1 1
## 1738 1340 16 3.87 0 0.94203 1.86 1 0.5376344 1 1
## 1739 960 15 1.66 0 1.04255 1.86 108 58.0645180 1 1
## 1740 1020 79 2.37 0 0.96154 1.58 20 12.6582279 1 1
## 1741 1100 111 2.47 0 0.89655 2.01 30 14.9253731 0 1
## 1742 1070 81 3.34 1 0.87719 1.58 28 17.7215195 1 1
## 1743 1060 112 3.00 0 0.89286 2.01 4 1.9900497 1 0
## 1744 1040 71 2.19 0 0.89091 1.58 47 29.7468357 1 1
## 1745 1160 81 3.22 0 1.03509 1.58 13 8.2278481 1 1
## 1746 1160 51 2.96 0 0.78462 1.55 19 12.2580643 1 0
## 1747 1230 15 4.00 0 0.80882 1.86 5 2.6881721 1 1
## 1748 970 121 2.48 0 0.90196 2.01 24 11.9402981 1 1
## 1749 1090 16 3.18 0 0.91228 1.86 24 12.9032259 1 1
## 1750 1080 113 2.03 0 1.00000 2.08 4 1.9230769 1 1
## 1751 900 72 2.26 0 0.52542 2.34 21 8.9743586 1 0
## 1752 790 106 1.89 0 0.64583 2.57 10 3.8910506 1 0
## 1753 950 13 1.23 0 0.97917 0.32 9 28.1250000 1 1
## 1754 1220 11 4.00 0 0.96774 0.32 2 6.2500000 0 1
## 1755 960 15 2.26 0 0.77778 0.32 20 62.5000000 0 1
## 1756 1220 43 3.23 0 1.00000 0.24 4 16.6666660 0 1
## 1757 1120 79 2.84 0 1.03636 2.80 11 3.9285715 0 1
## 1758 1020 79 2.54 0 0.92453 2.80 14 5.0000000 1 1
## 1759 1120 18 2.55 0 0.77778 2.28 33 14.4736843 0 1
## 1760 1160 77 3.02 0 1.10909 2.80 6 2.1428571 1 1
## 1761 880 15 2.40 0 0.72549 2.37 136 57.3839645 0 0
## 1762 1170 15 3.00 0 1.05263 2.28 14 6.1403508 1 1
## 1763 1010 101 2.26 0 1.06122 2.80 21 7.5000000 0 1
## 1764 1050 87 2.03 0 0.61538 2.80 27 9.6428576 1 1
## 1765 1100 73 3.16 0 0.92982 2.80 13 4.6428571 0 1
## 1766 920 87 3.00 0 0.95745 2.80 30 10.7142859 0 1
## 1767 1320 49 3.46 0 0.91304 2.05 2 0.9756098 0 1
## 1768 1000 51 2.86 0 0.78571 2.05 29 14.1463413 0 1
## 1769 790 40 2.02 0 0.83721 2.05 32 15.6097565 1 1
## 1770 1000 89 1.58 0 0.69492 2.80 54 19.2857151 1 1
## 1771 810 17 2.11 0 0.72340 2.28 102 44.7368431 1 1
## 1772 1230 48 3.43 0 0.95238 2.05 6 2.9268293 1 1
## 1773 950 30 2.53 0 0.90000 2.05 36 17.5609760 1 1
## 1774 820 46 3.06 0 0.82222 2.05 24 11.7073174 1 1
## 1775 990 119 3.36 0 0.86792 2.80 25 8.9285717 1 1
## 1776 1160 94 3.53 0 0.70588 3.28 13 3.9634147 0 1
## 1777 1120 85 2.35 0 0.93103 2.80 35 12.5000000 0 1
## 1778 1110 51 3.21 0 0.88136 2.05 13 6.3414636 0 1
## 1779 1020 16 2.37 0 1.00000 2.28 19 8.3333330 1 1
## 1780 1100 80 3.37 0 1.00000 2.10 9 4.2857141 1 1
## 1781 1210 52 2.80 0 0.80597 2.48 13 5.2419353 0 1
## 1782 1290 17 3.82 0 0.92537 2.18 13 5.9633026 0 1
## 1783 990 43 1.62 0 1.06250 2.48 84 33.8709679 0 1
## 1784 1030 110 3.17 0 0.74576 2.06 49 23.7864075 1 1
## 1785 1110 87 2.89 0 1.01818 2.10 26 12.3809528 1 1
## 1786 1100 121 2.09 0 1.07547 2.06 29 14.0776701 0 1
## 1787 930 88 2.55 0 0.78846 2.10 25 11.9047623 1 0
## 1788 1090 16 2.12 0 0.81667 2.18 45 20.6422024 0 1
## 1789 1080 105 2.51 0 0.89474 2.06 27 13.1067963 0 1
## 1790 950 51 1.96 0 0.93878 2.50 43 17.2000008 1 0
## 1791 1100 16 3.31 0 1.03704 2.18 35 16.0550461 0 1
## 1792 800 15 3.00 0 0.90476 2.18 17 7.7981653 0 1
## 1793 920 13 1.38 0 1.13953 2.18 102 46.7889900 0 1
## 1794 1040 128 2.40 0 1.16667 2.06 15 7.2815533 1 1
## 1795 1120 11 2.54 0 1.07407 2.18 95 43.5779800 0 1
## 1796 1160 45 2.53 0 0.93333 2.48 16 6.4516129 0 1
## 1797 1140 112 3.82 0 0.80952 2.06 7 3.3980582 1 1
## 1798 800 91 2.07 0 1.05128 2.06 69 33.4951439 1 1
## 1799 1030 17 2.88 0 0.83929 2.18 54 24.7706413 0 1
## 1800 1080 53 3.83 0 0.71429 2.48 45 18.1451607 0 0
## 1801 1240 18 3.11 0 0.87879 2.18 40 18.3486233 0 1
## 1802 1150 18 2.77 0 1.05357 0.05 2 40.0000000 0 1
## 1803 950 42 2.19 0 0.93878 0.05 4 80.0000000 1 1
## 1804 1300 112 2.53 0 0.91176 0.05 2 40.0000000 0 1
## 1805 1340 44 3.93 0 0.91429 0.72 4 5.5555553 0 1
## 1806 1130 80 2.13 0 0.85246 0.05 4 80.0000000 0 1
## 1807 1140 17 3.23 0 0.93220 0.05 4 80.0000000 0 1
## 1808 960 38 2.28 0 0.68421 0.05 4 80.0000000 1 1
## 1809 1280 14 2.78 0 0.96923 0.05 2 40.0000000 0 1
## 1810 1080 42 1.64 0 0.86207 2.30 43 18.6956520 0 1
## 1811 950 45 2.62 0 0.69643 2.30 34 14.7826090 0 0
## 1812 1130 44 2.75 0 1.01786 2.30 25 10.8695650 1 1
## 1813 900 16 3.00 0 0.95652 2.29 38 16.5938873 1 1
## 1814 1080 17 1.70 0 1.03774 2.29 18 7.8602619 0 0
## 1815 890 15 0.80 0 1.06977 2.29 58 25.3275108 0 1
## 1816 900 43 1.76 0 0.87500 2.30 59 25.6521740 0 0
## 1817 1010 18 2.66 0 1.10417 2.29 29 12.6637554 1 1
## 1818 1240 52 2.53 0 0.90769 2.30 9 3.9130435 0 1
## 1819 990 14 2.71 0 1.15217 2.30 15 6.5217390 1 1
## 1820 1160 83 1.89 0 0.93333 1.68 21 12.5000000 0 1
## 1821 1000 96 2.55 0 1.08333 1.68 16 9.5238094 1 1
## 1822 1060 35 2.82 0 1.03846 0.18 6 33.3333321 0 1
## 1823 1090 49 1.95 0 0.57971 0.18 9 50.0000000 0 0
## 1824 930 45 1.73 0 1.06667 1.58 30 18.9873409 0 0
## 1825 970 49 2.53 0 0.97959 1.58 7 4.4303799 1 0
## 1826 830 13 1.30 0 0.76596 1.50 17 11.3333330 1 1
## 1827 1210 50 3.02 0 0.86154 1.58 2 1.2658228 0 0
## 1828 730 66 2.98 0 0.78049 1.96 9 4.5918369 1 1
## 1829 1230 100 3.64 0 0.86364 1.77 6 3.3898306 0 1
## 1830 1070 82 3.17 0 0.98148 1.96 2 1.0204082 0 1
## 1831 860 74 2.56 0 0.59259 1.96 22 11.2244902 1 1
## 1832 1020 105 2.30 0 0.92453 1.77 23 12.9943504 0 1
## 1833 1130 17 3.05 0 0.85246 2.02 4 1.9801980 0 1
## 1834 940 43 2.16 0 0.84314 1.72 24 13.9534883 1 1
## 1835 1030 16 2.75 0 0.80702 1.89 3 1.5873016 1 1
## 1836 590 88 1.53 1 0.78788 2.02 109 53.9603958 0 0
## 1837 1030 111 3.87 0 0.90741 1.94 3 1.5463917 0 1
## 1838 920 15 2.20 0 1.00000 1.93 28 14.5077724 1 1
## 1839 990 111 2.63 0 1.06250 1.17 12 10.2564106 0 1
## 1840 700 13 3.30 1 0.89189 1.33 54 40.6015053 1 1
## 1841 1000 14 2.07 0 0.96078 1.48 3 2.0270271 1 1
## 1842 1040 13 0.92 0 0.79310 1.48 9 6.0810809 0 1
## 1843 790 99 2.82 0 0.92683 1.17 7 5.9829059 0 1
## 1844 1110 13 1.15 0 0.68182 1.48 32 21.6216221 0 1
## 1845 1130 50 3.14 0 0.94828 2.51 3 1.1952192 1 1
## 1846 1180 15 3.80 0 1.03448 3.18 1 0.3144654 1 1
## 1847 930 17 2.58 0 0.78846 3.29 10 3.0395136 0 1
## 1848 850 81 2.80 0 0.77083 3.20 12 3.7500000 1 1
## 1849 1020 110 2.60 0 0.88889 2.74 7 2.5547445 1 1
## 1850 1010 48 3.02 0 0.94231 2.51 13 5.1792827 0 1
## 1851 1130 96 3.22 0 1.01786 2.74 5 1.8248175 0 1
## 1852 1350 42 1.61 0 0.82432 2.51 11 4.3824701 0 1
## 1853 1200 46 3.00 0 0.84615 2.51 4 1.5936255 1 1
## 1854 820 112 2.74 0 0.78261 2.74 34 12.4087591 0 1
## 1855 1010 16 2.31 0 0.98039 3.18 59 18.5534592 0 1
## 1856 910 43 2.11 0 0.75000 1.08 9 8.3333330 0 1
## 1857 870 76 2.77 0 1.41667 1.10 3 2.7272727 1 1
## 1858 1130 17 3.29 0 0.79365 2.29 16 6.9868994 0 1
## 1859 1060 17 2.11 0 0.82759 2.29 19 8.2969437 0 1
## 1860 930 18 2.66 1 0.97872 2.29 38 16.5938873 0 0
## 1861 1050 32 2.59 0 0.98113 0.10 1 10.0000000 0 1
## 1862 1090 18 3.22 0 0.91228 2.29 10 4.3668122 0 1
## 1863 1050 123 2.38 0 0.87500 2.34 1 0.4273504 1 0
## 1864 1000 42 3.47 0 1.00000 0.10 2 20.0000000 0 1
## 1865 1080 15 3.26 0 0.96364 2.29 29 12.6637554 1 1
## 1866 810 84 1.98 0 1.13158 2.14 10 4.6728973 1 1
## 1867 1290 15 3.73 0 0.98462 2.32 14 6.0344830 1 1
## 1868 1150 16 2.75 0 1.30000 0.38 1 2.6315789 0 0
## 1869 810 39 1.64 0 0.92857 0.35 1 2.8571429 1 0
## 1870 1000 43 2.74 0 1.08333 1.80 5 2.7777777 0 1
## 1871 940 137 2.92 0 0.77358 2.06 37 17.9611645 1 1
## 1872 940 107 2.27 0 0.77358 2.06 34 16.5048542 0 1
## 1873 1250 111 2.85 0 1.15517 2.06 11 5.3398056 1 1
## 1874 1040 42 1.88 0 0.65079 1.80 45 25.0000000 0 1
## 1875 830 83 2.49 0 0.84444 1.93 42 21.7616577 0 1
## 1876 940 41 2.68 0 0.77358 1.80 21 11.6666670 0 1
## 1877 910 80 2.53 0 1.02222 1.97 19 9.6446705 0 1
## 1878 1150 79 2.08 0 0.98276 1.79 20 11.1731844 0 1
## 1879 1200 16 2.62 0 1.18182 2.06 22 10.6796112 0 1
## 1880 990 13 0.30 0 0.76786 2.06 64 31.0679607 0 1
## 1881 790 46 2.78 0 0.71739 1.80 52 28.8888893 0 1
## 1882 740 74 2.81 0 0.80488 1.79 44 24.5810051 0 1
## 1883 1290 16 3.62 0 0.92537 2.06 4 1.9417475 0 1
## 1884 1090 14 2.85 0 0.75806 2.06 30 14.5631065 0 1
## 1885 1260 76 2.10 0 0.77465 1.79 10 5.5865922 0 1
## 1886 1170 17 3.64 0 0.88710 2.06 5 2.4271846 1 1
## 1887 910 13 1.53 0 1.11628 1.75 35 20.0000000 1 1
## 1888 1040 16 3.18 0 0.89091 0.83 23 27.7108440 0 1
## 1889 940 47 3.00 0 0.95833 0.82 15 18.2926826 1 1
## 1890 1000 85 3.35 0 0.85185 0.69 8 11.5942030 0 1
## 1891 810 82 2.45 0 1.02500 0.69 59 85.5072479 1 1
## 1892 840 115 2.86 0 0.95349 0.82 19 23.1707325 1 1
## 1893 910 66 2.60 0 0.89583 0.69 33 47.8260880 1 1
## 1894 980 15 3.13 0 0.84906 0.83 15 18.0722885 1 1
## 1895 1020 91 2.78 0 1.12500 0.69 19 27.5362320 1 1
## 1896 780 74 2.01 0 0.95000 2.35 36 15.3191490 0 0
## 1897 990 83 2.60 0 0.80000 2.35 31 13.1914892 0 1
## 1898 1060 16 2.12 0 0.70968 1.80 15 8.3333330 1 1
## 1899 910 45 1.86 0 0.89583 2.05 24 11.7073174 1 0
## 1900 1010 13 0.46 0 0.77193 1.80 44 24.4444447 0 1
## 1901 810 126 2.15 0 1.13158 2.14 25 11.6822433 1 0
## 1902 920 57 1.92 0 1.04444 4.50 27 6.0000000 1 0
## 1903 1050 14 2.92 0 1.05882 4.65 96 20.6451607 0 1
## 1904 820 52 2.38 0 1.00000 4.50 127 28.2222214 0 1
## 1905 1080 43 1.97 0 0.74194 4.50 191 42.4444427 0 1
## 1906 1160 12 3.50 0 0.96610 4.65 48 10.3225803 1 1
## 1907 1000 16 2.75 0 0.66667 4.65 67 14.4086018 1 1
## 1908 1030 111 2.62 0 0.74576 3.83 37 9.6605740 0 1
## 1909 1000 123 2.34 0 1.17391 3.83 110 28.7206268 0 1
## 1910 1020 43 3.34 0 1.21739 4.50 147 32.6666679 0 1
## 1911 900 13 1.53 0 0.87500 4.65 195 41.9354820 1 1
## 1912 940 39 1.87 0 1.00000 4.50 104 23.1111107 1 1
## 1913 1180 24 3.33 0 0.87302 4.50 44 9.7777777 0 1
## 1914 1130 124 3.41 0 0.91525 3.83 42 10.9660578 0 1
## 1915 920 41 3.21 0 0.67273 4.50 111 24.6666660 0 1
## 1916 1220 13 4.00 1 0.74286 4.65 8 1.7204301 0 0
## 1917 1000 19 3.68 0 0.81818 4.65 62 13.3333330 1 1
## 1918 990 10 2.30 0 1.25000 4.65 183 39.3548393 0 1
## 1919 950 80 2.93 0 0.93878 4.42 80 18.0995483 1 0
## 1920 1080 45 2.73 0 0.96364 4.50 62 13.7777777 0 1
## 1921 1110 13 1.76 0 1.26531 4.65 308 66.2365570 0 1
## 1922 970 45 3.11 0 0.73214 4.50 73 16.2222214 1 1
## 1923 1020 63 2.04 0 0.75862 3.90 63 16.1538467 1 1
## 1924 1060 115 3.25 0 1.07843 3.83 59 15.4046993 1 1
## 1925 860 17 1.35 0 0.82979 4.65 52 11.1827955 0 1
## 1926 970 79 2.13 0 0.79630 3.90 117 30.0000000 0 1
## 1927 1000 17 2.88 0 0.72414 4.65 86 18.4946232 0 1
## 1928 1100 17 2.11 0 1.15686 4.65 133 28.6021500 1 1
## 1929 1210 18 2.72 0 0.83333 4.65 26 5.5913978 0 0
## 1930 1090 14 3.14 0 0.57971 4.65 115 24.7311821 0 1
## 1931 880 13 1.84 0 0.83333 4.65 141 30.3225803 1 1
## 1932 970 110 2.60 0 1.10870 3.83 54 14.0992165 0 1
## 1933 1050 45 3.11 0 0.90909 4.50 56 12.4444447 0 0
## 1934 1050 15 2.53 0 1.33333 4.65 231 49.6774178 1 1
## 1935 1060 78 2.05 0 0.68254 3.90 157 40.2564087 0 1
## 1936 910 54 2.01 0 0.93617 3.90 118 30.2564106 0 1
## 1937 830 46 2.80 0 1.12821 4.50 97 21.5555553 1 1
## 1938 1110 63 3.01 0 0.88136 3.90 30 7.6923075 1 1
## 1939 1210 17 3.29 0 0.77941 4.65 12 2.5806451 1 1
## 1940 990 42 2.40 0 0.90385 4.50 87 19.3333340 1 1
## 1941 1200 123 3.09 0 0.76471 3.83 8 2.0887728 0 1
## 1942 940 46 2.71 0 0.95833 4.50 133 29.5555553 1 1
## 1943 1000 119 2.07 0 0.81818 3.83 148 38.6422958 0 1
## 1944 1160 85 3.07 0 0.81250 2.41 53 21.9917011 0 1
## 1945 930 18 3.00 0 0.97872 2.66 53 19.9248123 0 1
## 1946 1210 15 1.80 0 0.92063 2.66 35 13.1578951 0 1
## 1947 960 13 1.46 0 0.88235 2.66 69 25.9398499 0 1
## 1948 1100 52 2.88 0 1.07547 2.40 12 5.0000000 0 1
## 1949 950 68 2.20 0 1.02128 2.41 66 27.3858929 0 1
## 1950 1100 17 3.41 0 0.83333 2.66 24 9.0225563 1 1
## 1951 1050 110 3.72 0 0.81034 2.26 3 1.3274336 1 1
## 1952 960 47 2.06 0 1.04255 2.40 55 22.9166660 1 0
## 1953 1220 34 2.76 0 0.84848 3.00 1 0.3333333 0 0
## 1954 980 47 2.74 0 0.88462 3.00 2 0.6666667 0 0
## 1955 900 55 2.21 0 0.91489 3.00 30 10.0000000 0 0
## 1956 1010 15 2.26 0 0.94231 2.70 7 2.5925925 0 0
## 1957 1180 103 2.15 0 0.59459 0.53 25 47.1698112 0 1
## 1958 960 44 2.06 0 0.88235 0.59 21 35.5932198 1 1
## 1959 1140 44 2.18 0 0.93220 0.59 20 33.8983040 0 1
## 1960 880 73 2.24 0 0.95556 0.81 71 87.6543198 0 1
## 1961 990 115 3.23 0 0.76786 0.83 23 27.7108440 1 1
## 1962 840 79 2.35 0 0.75000 0.81 59 72.8395081 0 1
## 1963 1000 85 2.51 0 0.81818 0.83 57 68.6746979 0 1
## 1964 1150 48 3.54 0 0.91667 0.70 20 28.5714283 1 1
## 1965 1010 68 3.04 0 1.02000 0.81 26 32.0987663 0 1
## 1966 1080 17 1.70 0 0.77049 0.73 19 26.0273972 1 1
## 1967 1320 77 3.01 0 0.91304 0.81 19 23.4567909 0 1
## 1968 910 80 3.32 0 0.71698 0.81 22 27.1604939 1 1
## 1969 1170 73 2.89 0 1.38776 0.81 16 19.7530861 1 1
## 1970 1090 105 2.72 0 0.67692 0.83 8 9.6385546 1 1
## 1971 1040 118 2.62 0 0.76271 0.84 42 50.0000000 1 1
## 1972 950 49 2.71 0 0.97917 0.70 24 34.2857132 0 1
## 1973 1050 17 2.47 0 0.87500 0.73 27 36.9863014 0 1
## 1974 960 69 2.11 0 0.81132 0.81 56 69.1358032 0 1
## 1975 1000 72 2.23 0 0.63934 0.81 34 41.9753075 1 1
## 1976 820 72 2.62 0 1.00000 0.81 42 51.8518524 1 1
## 1977 1220 50 2.46 0 0.93651 0.70 42 60.0000000 0 1
## 1978 1350 109 2.95 0 0.92857 4.00 36 9.0000000 1 1
## 1979 1110 13 2.61 0 0.81967 4.00 73 18.2500000 1 1
## 1980 1280 82 3.70 0 0.77778 4.00 8 2.0000000 0 1
## 1981 940 119 2.92 0 1.13636 4.00 54 13.5000000 1 1
## 1982 990 102 2.00 0 1.10638 4.00 120 30.0000000 0 1
## 1983 1140 127 2.44 0 0.80952 4.00 31 7.7500000 0 1
## 1984 980 61 2.44 0 0.84906 4.00 134 33.5000000 0 0
## 1985 870 16 1.75 0 0.97727 4.00 168 42.0000000 0 1
## 1986 1080 10 1.90 0 1.00000 4.00 46 11.5000000 1 1
## 1987 1170 45 3.35 0 0.64789 3.50 36 10.2857141 1 1
## 1988 1220 13 3.07 0 0.90625 4.00 150 37.5000000 0 1
## 1989 1130 17 2.11 0 0.73846 4.00 71 17.7500000 0 1
## 1990 880 83 1.77 0 0.57143 4.00 67 16.7500000 0 0
## 1991 1000 71 2.18 0 0.88679 4.00 94 23.5000000 0 1
## 1992 1110 13 2.00 0 0.88136 4.00 48 12.0000000 0 1
## 1993 1190 13 2.23 0 0.85938 4.00 130 32.5000000 0 1
## 1994 1090 110 3.75 0 0.94643 4.00 13 3.2500000 1 1
## 1995 1170 101 2.35 0 0.85714 4.00 27 6.7500000 0 1
## 1996 1130 14 2.42 0 0.82258 4.00 80 20.0000000 0 1
## 1997 1050 73 2.73 0 0.98113 4.00 32 8.0000000 1 1
## 1998 950 18 2.94 0 1.02128 4.00 25 6.2500000 1 0
## 1999 1210 73 2.16 0 0.98361 4.00 119 29.7500000 0 1
## 2000 950 13 0.84 0 1.02128 4.00 112 28.0000000 0 0
## 2001 990 77 2.10 0 0.86792 1.61 7 4.3478260 1 0
## 2002 1250 74 3.40 0 0.81159 1.61 1 0.6211180 0 1
## 2003 840 16 1.18 0 0.90909 2.30 5 2.1739130 0 0
## 2004 860 77 1.94 0 0.59259 1.61 32 19.8757763 0 0
## 2005 840 19 2.36 0 0.95349 2.30 8 3.4782608 1 0
## 2006 960 16 2.43 0 0.92000 3.86 10 2.5906737 0 1
## 2007 920 13 2.46 0 1.13953 3.86 54 13.9896374 0 1
## 2008 1010 106 2.78 0 0.98039 3.50 13 3.7142856 1 1
## 2009 850 46 2.02 0 0.88889 3.50 86 24.5714283 1 1
## 2010 1100 16 3.25 0 0.77419 3.86 12 3.1088083 0 1
## 2011 960 14 2.28 0 0.81132 3.86 45 11.6580315 0 1
## 2012 950 10 2.00 0 0.79245 3.86 31 8.0310879 1 1
## 2013 950 16 2.56 0 0.75926 3.86 25 6.4766841 1 1
## 2014 840 118 2.80 0 1.15385 3.50 27 7.7142859 0 0
## 2015 860 111 2.19 0 1.04762 3.50 22 6.2857141 1 1
## 2016 800 64 2.54 0 0.90476 2.96 17 5.7432432 1 1
## 2017 1060 47 2.23 0 0.79661 3.50 19 5.4285712 0 1
## 2018 980 76 2.55 0 0.84906 2.96 43 14.5270271 0 1
## 2019 770 17 1.35 1 0.71111 3.86 223 57.7720222 0 0
## 2020 1010 13 3.76 0 0.87037 3.86 12 3.1088083 1 1
## 2021 1100 53 1.71 0 0.92982 3.50 16 4.5714288 0 1
## 2022 1060 117 1.82 0 0.96296 0.82 3 3.6585367 1 0
## 2023 1060 49 2.53 0 1.16327 1.12 15 13.3928576 0 1
## 2024 1100 18 1.66 0 0.86441 1.15 44 38.2608681 0 1
## 2025 1140 17 3.82 0 0.72727 1.15 1 0.8695652 0 1
## 2026 810 49 2.20 0 0.84091 0.84 1 1.1904762 1 0
## 2027 880 97 2.44 0 0.72549 0.94 1 1.0638298 0 0
## 2028 920 125 2.52 0 1.04444 2.92 33 11.3013697 1 1
## 2029 1000 44 2.25 0 0.81818 2.71 5 1.8450185 1 0
## 2030 1040 48 3.00 0 0.73333 2.71 7 2.5830259 0 0
## 2031 1020 16 4.00 0 0.92453 0.68 5 7.3529410 1 1
## 2032 1180 16 2.00 0 0.96667 5.39 128 23.7476807 0 1
## 2033 850 79 3.27 0 1.12500 0.72 26 36.1111107 1 1
## 2034 910 13 3.23 0 1.27500 0.75 38 50.6666679 1 1
## 2035 990 78 2.41 0 0.70690 0.72 3 4.1666665 0 1
## 2036 890 12 2.75 1 1.02273 0.69 63 91.3043442 0 1
## 2037 990 122 2.94 0 1.06250 0.52 2 3.8461537 1 1
## 2038 900 16 1.81 0 1.04545 0.78 6 7.6923075 1 0
## 2039 700 40 2.22 0 0.84211 0.90 2 2.2222223 0 0
## 2040 1000 77 2.29 0 1.38095 1.57 11 7.0063696 1 1
## 2041 910 10 1.60 0 0.89583 1.77 55 31.0734463 0 1
## 2042 1080 84 3.11 0 1.07692 1.57 5 3.1847134 0 1
## 2043 840 116 2.08 0 0.90909 0.94 1 1.0638298 0 0
## 2044 1010 12 1.66 0 0.90566 0.12 6 50.0000000 0 1
## 2045 1100 84 2.77 0 0.86441 2.23 10 4.4843049 1 1
## 2046 1110 44 3.38 0 0.65672 2.67 7 2.6217229 0 1
## 2047 960 36 2.38 0 0.77778 2.67 20 7.4906368 0 1
## 2048 830 15 2.73 0 0.76596 2.50 23 9.1999998 1 1
## 2049 1100 118 3.70 0 1.03704 2.44 8 3.2786884 1 1
## 2050 910 39 1.46 0 0.89583 2.67 33 12.3595505 0 0
## 2051 1030 16 2.81 0 0.90741 0.77 4 5.1948051 0 1
## 2052 1130 13 2.84 0 0.88333 0.75 8 10.6666670 1 1
## 2053 1150 121 3.23 0 0.76923 0.80 3 3.7500000 0 1
## 2054 1100 48 2.31 0 0.71875 0.57 5 8.7719297 0 1
## 2055 1170 82 2.58 0 0.95000 0.72 2 2.7777777 1 1
## 2056 920 108 3.31 0 0.73585 2.50 19 7.5999999 0 1
## 2057 1000 50 3.00 0 1.38095 2.44 34 13.9344263 1 1
## 2058 1240 17 1.94 0 0.82353 2.04 20 9.8039217 0 1
## 2059 1030 118 3.45 0 1.39535 2.50 21 8.3999996 1 1
## 2060 1080 41 2.29 0 0.80000 2.44 18 7.3770490 0 1
## 2061 990 48 3.18 0 0.73684 2.44 27 11.0655737 1 1
## 2062 1290 50 3.02 0 0.79167 2.44 26 10.6557379 0 0
## 2063 880 17 2.70 0 0.95556 2.77 85 30.6859207 1 1
## 2064 1150 40 2.77 0 1.09091 2.44 6 2.4590163 0 1
## 2065 1240 16 3.25 0 1.13793 2.04 5 2.4509804 1 1
## 2066 1000 108 2.61 0 1.12766 2.50 26 10.3999996 0 1
## 2067 990 14 2.14 1 0.98000 2.04 31 15.1960783 1 0
## 2068 1130 84 3.47 0 0.79365 2.57 18 7.0038910 0 1
## 2069 1110 18 3.38 0 0.76190 2.04 9 4.4117646 0 1
## 2070 980 43 2.18 0 0.71930 2.44 15 6.1475410 1 1
## 2071 950 53 3.77 0 1.26190 2.44 19 7.7868853 1 1
## 2072 1200 17 2.82 0 0.96721 2.68 6 2.2388060 1 1
## 2073 950 49 2.08 0 0.86275 2.68 43 16.0447769 0 1
## 2074 1020 117 2.69 0 0.88889 2.72 15 5.5147057 0 1
## 2075 850 13 2.00 0 0.80851 2.68 59 22.0149250 0 1
## 2076 1010 66 1.77 0 0.74138 2.75 82 29.8181820 0 1
## 2077 1260 113 3.29 0 1.13559 2.72 4 1.4705882 1 1
## 2078 870 43 2.06 0 0.97727 2.68 15 5.5970149 1 0
## 2079 970 77 2.45 0 1.36585 2.72 49 18.0147057 0 1
## 2080 870 42 2.61 0 0.93333 2.68 13 4.8507462 0 1
## 2081 1130 53 3.18 0 0.82258 2.68 4 1.4925373 1 1
## 2082 860 44 2.84 0 1.15000 3.03 114 37.6237640 0 1
## 2083 950 13 0.76 0 0.93878 2.68 26 9.7014923 1 1
## 2084 890 51 2.17 0 0.78000 2.68 30 11.1940298 0 1
## 2085 1050 117 3.50 0 0.81034 2.72 2 0.7352941 0 1
## 2086 940 17 1.52 0 0.67857 2.68 71 26.4925365 0 1
## 2087 950 17 2.76 0 0.97917 2.68 16 5.9701490 0 1
## 2088 1020 113 2.13 0 0.75862 2.72 139 51.1029396 0 1
## 2089 1180 17 3.41 0 0.78788 2.68 12 4.4776120 0 1
## 2090 690 16 1.75 0 0.91667 3.15 160 50.7936516 1 1
## 2091 770 78 2.88 0 0.92500 2.75 60 21.8181820 1 1
## 2092 1030 48 3.62 0 0.60938 2.68 14 5.2238808 0 1
## 2093 1020 106 2.30 0 1.12500 2.72 40 14.7058821 0 1
## 2094 1120 38 1.92 0 1.00000 2.68 18 6.7164178 0 1
## 2095 730 15 1.53 0 1.02778 3.09 75 24.2718449 0 1
## 2096 780 101 2.24 0 0.95000 3.14 30 9.5541401 1 1
## 2097 890 120 2.65 0 0.71154 2.72 31 11.3970585 1 1
## 2098 930 17 2.17 0 0.97872 2.68 67 25.0000000 0 1
## 2099 1060 77 2.09 0 0.79661 2.75 31 11.2727270 1 1
## 2100 840 15 1.53 0 0.86667 2.68 105 39.1791039 1 1
## 2101 1090 12 1.50 0 0.73016 2.68 69 25.7462692 0 1
## 2102 800 115 2.48 0 1.05128 2.72 54 19.8529415 1 1
## 2103 1140 107 2.23 0 1.11111 2.72 22 8.0882349 0 1
## 2104 830 111 2.60 0 0.72917 2.72 37 13.6029415 1 1
## 2105 880 74 2.33 0 1.25641 3.03 13 4.2904291 1 1
## 2106 1460 17 2.94 0 0.94667 3.57 2 0.5602241 0 1
## 2107 1030 47 3.17 0 0.87273 2.95 32 10.8474579 0 1
## 2108 970 47 1.87 0 0.86538 2.68 37 13.8059702 1 1
## 2109 900 85 2.95 0 1.25000 3.01 9 2.9900331 1 1
## 2110 1010 15 1.93 0 0.98039 0.12 2 16.6666660 1 1
## 2111 1040 83 2.77 0 1.03922 0.11 2 18.1818180 1 1
## 2112 870 17 3.47 0 0.85106 0.10 6 60.0000000 0 1
## 2113 910 46 2.32 0 0.71698 0.11 2 18.1818180 0 1
## 2114 720 18 2.44 0 0.80000 2.08 50 24.0384617 0 1
## 2115 1000 13 1.92 0 1.00000 2.08 38 18.2692299 1 0
## 2116 1180 70 3.78 0 0.71014 1.85 2 1.0810810 0 1
## 2117 960 51 1.92 0 0.74545 2.05 65 31.7073174 0 1
## 2118 860 13 2.38 0 0.75510 2.08 59 28.3653851 0 0
## 2119 1060 16 3.25 0 0.89286 2.08 10 4.8076925 0 1
## 2120 1120 15 2.73 0 0.86667 2.08 4 1.9230769 1 1
## 2121 820 40 1.67 0 1.00000 2.05 36 17.5609760 1 1
## 2122 880 13 2.38 0 0.91304 2.08 6 2.8846154 1 0
## 2123 1060 17 2.82 0 0.92727 2.08 12 5.7692308 0 1
## 2124 940 73 2.13 0 0.95833 1.85 26 14.0540543 1 0
## 2125 940 17 3.58 0 0.70909 0.85 1 1.1764706 1 0
## 2126 740 41 1.41 0 0.76190 1.26 4 3.1746032 1 0
## 2127 990 11 2.63 0 0.94118 0.37 16 43.2432442 0 1
## 2128 1180 115 3.66 0 0.78788 0.25 2 8.0000000 1 1
## 2129 950 73 3.06 0 0.82692 0.27 8 29.6296291 0 1
## 2130 950 119 2.26 0 0.86275 0.25 14 56.0000000 0 1
## 2131 970 78 3.67 0 0.90196 0.27 5 18.5185184 1 1
## 2132 1130 18 3.61 0 0.94828 2.89 3 1.0380623 0 1
## 2133 1280 18 3.22 0 0.77778 2.89 11 3.8062284 0 1
## 2134 970 15 2.86 0 0.97959 2.89 50 17.3010387 0 1
## 2135 830 41 2.02 1 0.80435 2.45 73 29.7959175 0 1
## 2136 1000 101 2.71 0 1.12766 2.63 46 17.4904938 1 1
## 2137 870 46 2.82 0 0.97727 2.52 25 9.9206352 1 1
## 2138 1020 88 2.28 0 0.82143 3.05 19 6.2295084 0 1
## 2139 1190 15 4.00 0 1.08772 2.89 7 2.4221454 0 1
## 2140 900 46 3.13 0 0.87500 3.05 18 5.9016395 1 1
## 2141 1100 45 2.46 0 0.96429 2.52 22 8.7301588 0 1
## 2142 780 20 1.95 0 1.22857 2.89 87 30.1038055 0 1
## 2143 870 42 2.47 0 0.93333 2.52 40 15.8730154 1 1
## 2144 1130 52 1.71 0 0.68657 2.62 90 34.3511467 0 1
## 2145 1020 15 2.00 0 0.92453 2.75 96 34.9090919 0 1
## 2146 990 81 2.69 0 0.76786 2.50 25 10.0000000 0 1
## 2147 1030 32 3.46 0 0.71667 2.28 3 1.3157895 1 0
## 2148 970 117 2.47 0 0.79630 2.52 12 4.7619047 1 1
## 2149 1170 76 2.51 0 0.91803 2.50 34 13.6000004 0 1
## 2150 1060 111 2.85 0 0.70968 2.52 19 7.5396824 0 1
## 2151 1120 110 2.58 0 1.00000 2.52 15 5.9523811 0 1
## 2152 820 14 1.85 0 0.82222 2.75 78 28.3636360 1 1
## 2153 860 13 2.38 0 0.95455 2.75 49 17.8181820 1 1
## 2154 980 47 2.78 0 0.88462 2.28 12 5.2631578 1 1
## 2155 1100 81 3.54 0 0.83333 2.50 6 2.4000001 0 1
## 2156 1140 90 3.73 0 0.72727 2.50 9 3.5999999 0 1
## 2157 950 15 1.86 0 0.82692 2.75 23 8.3636360 1 1
## 2158 1040 100 2.23 0 0.79310 2.52 7 2.7777777 1 1
## 2159 820 16 2.25 0 1.00000 2.75 45 16.3636360 1 1
## 2160 1060 47 3.51 0 0.73770 2.28 6 2.6315789 1 1
## 2161 880 16 2.56 0 0.72549 2.75 83 30.1818180 1 1
## 2162 1340 109 3.44 0 1.06154 2.52 1 0.3968254 1 1
## 2163 1060 43 2.18 0 0.73770 2.28 58 25.4385967 0 1
## 2164 1050 39 2.74 0 0.84211 2.28 26 11.4035091 0 1
## 2165 1080 16 3.31 0 0.86207 2.75 21 7.6363635 0 1
## 2166 990 43 2.18 0 0.86792 2.28 36 15.7894735 0 1
## 2167 920 15 2.80 0 0.80392 2.75 39 14.1818180 1 1
## 2168 1050 42 2.21 0 0.90909 2.28 84 36.8421059 0 1
## 2169 720 102 2.08 0 0.71429 2.46 13 5.2845531 1 0
## 2170 770 75 2.22 0 0.75000 2.57 26 10.1167316 0 0
## 2171 1190 17 2.41 0 0.80303 1.96 6 3.0612245 0 0
## 2172 870 124 2.58 0 0.70588 1.50 34 22.6666660 0 1
## 2173 1140 82 3.79 0 0.72727 1.86 7 3.7634408 0 1
## 2174 1040 15 3.06 0 0.92593 2.38 11 4.6218486 1 1
## 2175 1050 15 2.46 0 0.81034 2.38 31 13.0252104 0 1
## 2176 1320 17 4.00 0 0.91304 2.38 1 0.4201681 0 1
## 2177 850 47 2.63 0 0.80851 1.89 28 14.8148146 1 1
## 2178 950 103 2.53 1 0.69643 1.48 18 12.1621618 0 1
## 2179 1100 116 3.16 0 0.66667 1.48 46 31.0810814 0 1
## 2180 1290 15 4.00 0 0.69737 2.38 6 2.5210085 0 1
## 2181 960 113 2.95 0 0.71429 1.48 4 2.7027028 1 1
## 2182 1050 13 1.76 0 0.90909 2.38 41 17.2268906 0 1
## 2183 890 44 2.86 0 0.74510 1.89 39 20.6349201 1 1
## 2184 1020 78 1.97 0 1.04000 1.78 35 19.6629219 0 1
## 2185 1110 74 2.21 0 1.01818 1.78 12 6.7415729 0 1
## 2186 960 19 2.21 0 1.00000 2.38 38 15.9663868 1 1
## 2187 930 14 2.71 0 0.69091 2.38 98 41.1764717 0 1
## 2188 1190 46 2.82 0 0.98333 1.89 7 3.7037036 1 1
## 2189 980 13 2.76 1 0.88462 2.38 46 19.3277302 0 1
## 2190 1230 17 4.00 0 0.80882 2.38 5 2.1008403 0 1
## 2191 940 17 2.52 0 0.84314 2.38 36 15.1260500 0 1
## 2192 1040 43 3.16 0 0.76271 1.89 63 33.3333321 0 1
## 2193 960 75 3.32 0 0.88235 1.50 8 5.3333335 0 1
## 2194 1060 108 2.36 0 1.00000 1.50 35 23.3333340 0 1
## 2195 1280 17 3.47 0 0.70667 2.38 17 7.1428571 0 1
## 2196 1340 17 4.00 0 0.86111 2.38 8 3.3613446 0 1
## 2197 1050 85 1.77 0 0.94444 1.78 34 19.1011238 0 1
## 2198 1100 47 2.31 0 0.80328 1.89 24 12.6984129 0 1
## 2199 980 15 3.73 0 1.04167 2.38 10 4.2016807 1 1
## 2200 1130 49 2.91 0 0.79365 1.89 10 5.2910051 0 1
## 2201 1140 83 2.62 0 0.86885 0.63 3 4.7619047 1 1
## 2202 1000 11 2.36 0 1.17391 0.23 9 39.1304359 0 1
## 2203 1060 17 1.05 0 1.12000 0.23 7 30.4347820 0 1
## 2204 1190 73 3.56 0 0.77612 4.94 9 1.8218623 0 1
## 2205 1090 47 2.72 0 0.94643 3.96 18 4.5454545 1 1
## 2206 640 95 1.92 1 0.82857 5.34 165 30.8988762 0 0
## 2207 880 78 2.20 0 0.60000 4.01 27 6.7331672 1 1
## 2208 1020 42 1.92 0 0.70000 3.96 33 8.3333330 0 0
## 2209 1010 43 1.53 0 0.83636 3.96 37 9.3434343 1 0
## 2210 1410 68 3.72 0 0.98592 4.09 5 1.2224939 0 1
## 2211 820 60 2.36 0 0.86364 4.34 59 13.5944700 1 1
## 2212 880 15 0.53 0 0.83333 4.13 53 12.8329296 0 1
## 2213 1010 13 2.61 0 1.06122 4.13 49 11.8644066 1 1
## 2214 1240 92 2.57 0 0.93750 4.09 25 6.1124697 0 0
## 2215 890 18 1.61 0 1.17073 4.13 94 22.7602901 1 1
## 2216 960 20 1.60 0 0.77778 4.13 123 29.7820816 0 1
## 2217 1140 48 3.04 0 1.15094 3.96 9 2.2727273 1 1
## 2218 900 90 3.06 0 0.91489 4.01 77 19.2019958 1 1
## 2219 950 113 3.55 0 0.72727 4.09 14 3.4229829 1 1
## 2220 910 104 3.61 0 0.93617 4.09 45 11.0024452 1 1
## 2221 1150 79 2.94 0 0.82540 4.09 16 3.9119804 1 0
## 2222 1030 18 2.11 0 0.87273 4.13 52 12.5907993 0 1
## 2223 1070 17 2.00 0 0.72581 4.13 36 8.7167072 0 1
## 2224 850 14 1.28 0 0.88889 4.13 183 44.3099289 0 1
## 2225 960 99 1.92 0 0.71429 4.09 40 9.7799511 0 1
## 2226 1030 45 3.93 0 0.63492 3.96 4 1.0101010 1 0
## 2227 1030 17 2.58 0 0.80702 4.13 24 5.8111382 1 1
## 2228 1040 52 3.28 0 1.00000 3.96 26 6.5656567 1 1
## 2229 1110 48 3.29 0 1.05556 3.96 5 1.2626263 1 1
## 2230 950 75 2.50 0 0.69643 4.01 14 3.4912717 1 1
## 2231 960 90 3.06 0 0.92000 4.01 40 9.9750624 0 1
## 2232 900 107 2.79 0 0.69811 4.09 66 16.1369190 0 1
## 2233 950 73 2.28 0 0.69643 4.94 83 16.8016186 0 1
## 2234 1040 64 2.73 0 0.85714 4.01 22 5.4862843 1 1
## 2235 1020 50 2.54 0 0.72881 3.96 10 2.5252526 0 1
## 2236 910 17 1.23 0 1.45946 4.13 44 10.6537533 1 1
## 2237 890 16 1.62 0 0.78000 0.79 1 1.2658228 1 0
## 2238 1200 50 3.38 0 0.73913 2.75 10 3.6363637 0 1
## 2239 780 14 1.92 0 0.85714 3.20 38 11.8750000 1 1
## 2240 950 17 2.88 0 0.75926 3.20 9 2.8125000 1 1
## 2241 950 17 2.94 0 0.82692 2.76 3 1.0869565 1 0
## 2242 730 65 2.52 0 0.65909 2.76 35 12.6811590 0 0
## 2243 880 13 2.61 0 1.20000 3.20 14 4.3750000 1 1
## 2244 1280 81 3.32 0 0.75342 2.76 3 1.0869565 0 1
## 2245 1100 71 2.46 0 0.86441 3.80 98 25.7894745 0 1
## 2246 890 70 2.47 0 0.85417 1.06 14 13.2075472 0 1
## 2247 1110 46 1.95 0 1.05556 1.02 14 13.7254906 1 0
## 2248 1130 65 3.33 0 0.82258 1.03 4 3.8834951 0 1
## 2249 920 75 3.36 0 0.70370 1.03 11 10.6796112 0 1
## 2250 1120 17 3.17 0 0.69697 3.05 18 5.9016395 0 0
## 2251 1070 44 2.38 0 0.75410 2.70 41 15.1851854 0 1
## 2252 1180 13 2.30 0 0.78788 2.70 3 1.1111112 0 0
## 2253 1140 84 3.10 0 0.80952 3.25 10 3.0769231 0 0
## 2254 870 41 2.48 0 1.63636 2.70 44 16.2962971 1 1
## 2255 1210 88 2.94 0 0.95161 3.25 13 4.0000000 0 1
## 2256 1090 72 3.04 0 0.62687 3.50 27 7.7142859 0 1
## 2257 990 75 2.78 0 0.80000 3.25 8 2.4615386 0 0
## 2258 1110 51 2.74 0 0.88136 3.68 16 4.3478260 1 0
## 2259 940 115 2.37 0 1.08889 2.61 40 15.3256702 1 1
## 2260 1150 45 3.64 0 0.71642 3.68 6 1.6304348 0 1
## 2261 1000 17 3.17 0 0.81818 3.58 11 3.0726256 0 1
## 2262 980 83 2.85 0 0.81481 2.61 7 2.6819923 0 1
## 2263 930 14 2.64 0 1.02174 3.58 42 11.7318439 1 0
## 2264 1150 17 2.94 0 0.88525 3.58 3 0.8379889 0 0
## 2265 860 13 2.07 0 0.86957 3.58 108 30.1675968 1 1
## 2266 910 15 2.33 0 0.85714 0.90 15 16.6666660 0 1
## 2267 960 14 0.64 0 1.00000 0.91 20 21.9780216 0 1
## 2268 900 13 0.92 0 0.87500 1.98 66 33.3333321 1 1
## 2269 1250 113 3.23 0 1.15517 2.26 4 1.7699115 1 1
## 2270 1180 50 3.26 0 0.81538 2.19 8 3.6529679 0 1
## 2271 860 84 2.07 0 1.15000 2.23 26 11.6591930 0 1
## 2272 1050 33 4.00 0 0.94444 2.19 2 0.9132420 1 1
## 2273 1010 17 3.00 0 0.83636 1.98 10 5.0505052 0 1
## 2274 1190 15 2.33 0 0.72464 1.98 3 1.5151515 1 1
## 2275 1020 40 2.77 0 0.82143 2.19 14 6.3926940 0 1
## 2276 1290 49 2.93 0 0.76712 2.19 6 2.7397261 0 1
## 2277 910 118 2.38 0 0.78431 2.26 69 30.5309734 1 1
## 2278 1210 17 3.82 0 0.77941 1.98 1 0.5050505 0 1
## 2279 990 100 2.43 0 0.59677 2.26 57 25.2212391 0 1
## 2280 970 107 2.07 0 0.70175 2.26 58 25.6637173 0 1
## 2281 940 112 2.25 0 1.23810 2.26 35 15.4867258 1 1
## 2282 1310 47 3.93 0 0.81944 2.19 4 1.8264840 0 1
## 2283 1000 16 2.18 0 0.81818 1.98 24 12.1212120 1 1
## 2284 1060 45 2.33 0 0.68254 2.19 18 8.2191782 1 1
## 2285 1000 81 2.03 0 0.85185 2.23 77 34.5291481 0 1
## 2286 1010 119 3.35 0 0.62903 2.26 12 5.3097343 1 1
## 2287 950 79 2.69 0 0.75926 2.23 21 9.4170408 1 1
## 2288 1080 46 2.97 0 0.83051 1.12 35 31.2500000 0 1
## 2289 920 51 1.74 0 0.80392 1.95 27 13.8461542 1 0
## 2290 1220 15 2.46 0 0.82090 2.00 9 4.5000000 0 1
## 2291 1040 122 3.14 0 0.79310 1.92 7 3.6458333 1 1
## 2292 880 81 2.49 0 0.76000 1.77 3 1.6949153 1 1
## 2293 850 118 1.92 0 0.57407 1.92 16 8.3333330 0 1
## 2294 910 80 2.76 0 0.89583 1.77 18 10.1694918 0 0
## 2295 1170 59 2.61 1 1.05263 2.30 13 5.6521740 0 1
## 2296 1150 15 3.06 0 0.79688 2.00 2 1.0000000 1 0
## 2297 990 16 2.12 0 0.80000 2.00 23 11.5000000 0 1
## 2298 1000 11 2.72 0 0.85185 2.00 9 4.5000000 1 1
## 2299 1050 132 2.89 0 0.87500 0.10 1 10.0000000 1 1
## 2300 1160 15 1.73 0 0.90164 0.10 6 60.0000000 0 1
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## 2302 1030 11 2.72 0 0.94340 0.10 7 70.0000000 0 1
## 2303 820 47 1.91 0 1.05000 2.09 49 23.4449768 1 1
## 2304 1140 136 2.18 0 0.80952 2.40 32 13.3333330 1 1
## 2305 1140 16 4.00 0 0.86885 2.19 11 5.0228310 1 1
## 2306 980 100 3.16 0 1.04167 2.20 56 25.4545460 1 1
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## 2308 1010 114 3.14 0 0.90566 2.40 12 5.0000000 1 1
## 2309 1080 85 3.50 0 1.00000 2.20 11 5.0000000 1 1
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## 2311 1020 48 3.08 0 0.70000 2.09 20 9.5693779 1 1
## 2312 880 44 2.54 0 0.41935 2.09 58 27.7511959 1 1
## 2313 970 17 3.23 0 0.90196 2.19 12 5.4794521 0 1
## 2314 830 79 2.69 0 0.84444 2.20 17 7.7272725 1 1
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## 2316 980 76 2.67 0 1.04167 2.20 47 21.3636360 1 1
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## 2321 1090 88 2.25 0 0.94643 2.40 62 25.8333340 0 1
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## 2323 1150 64 3.01 0 0.66667 2.20 61 27.7272720 0 1
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## 2341 990 60 2.81 0 1.15217 2.11 53 25.1184826 1 1
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## 2343 880 11 1.36 0 1.00000 1.91 53 27.7486916 0 1
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## 2345 850 120 2.67 0 0.84783 1.20 26 21.6666660 0 1
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## 2349 990 37 2.62 0 0.90385 0.36 18 50.0000000 0 1
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## 2359 1100 88 2.65 0 0.92982 1.21 8 6.6115704 1 1
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## 2375 960 16 1.81 0 1.00000 3.24 125 38.5802460 0 1
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## 2382 1080 11 3.27 0 0.80000 3.24 16 4.9382715 1 1
## 2383 1020 15 2.33 0 1.00000 3.24 236 72.8395081 0 1
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## 2385 900 104 2.51 0 0.91489 2.76 106 38.4057961 1 1
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## 2387 1150 18 3.16 0 1.01754 3.23 18 5.5727553 1 1
## 2388 1270 16 2.00 0 1.08197 3.24 142 43.8271599 0 1
## 2389 1090 13 1.15 0 0.94643 3.24 149 45.9876556 0 1
## 2390 1050 16 0.87 0 0.77966 3.24 80 24.6913586 0 1
## 2391 1170 45 3.91 0 0.91803 2.38 5 2.1008403 1 1
## 2392 1050 11 2.63 0 0.98113 3.24 111 34.2592583 1 1
## 2393 1080 49 3.32 0 0.92857 2.38 44 18.4873943 1 1
## 2394 1140 119 2.90 0 0.96552 2.76 20 7.2463770 0 1
## 2395 1010 13 2.76 0 1.10417 2.36 77 32.6271172 1 1
## 2396 1110 14 3.57 0 0.85000 3.22 5 1.5527951 0 1
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## 2398 1290 17 3.82 0 1.01563 3.24 6 1.8518518 0 1
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## 2405 910 119 3.33 0 1.21951 0.10 1 10.0000000 1 1
## 2406 1130 17 2.41 0 0.76563 0.12 3 25.0000000 0 1
## 2407 1020 59 2.62 0 0.61905 0.11 4 36.3636360 0 1
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## 2409 900 42 1.88 0 0.95652 5.56 88 15.8273382 1 1
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## 2419 1020 15 1.20 0 0.70000 5.26 78 14.8288975 1 1
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## 2432 790 15 2.60 0 0.92683 5.56 176 31.6546764 0 1
## 2433 1130 116 3.11 0 1.05455 5.39 32 5.9369202 0 1
## 2434 1080 110 2.37 1 0.56522 5.39 152 28.2003708 0 1
## 2435 1140 13 2.46 0 0.78125 5.26 76 14.4486694 0 1
## 2436 970 87 2.29 0 0.73214 5.39 171 31.7254181 0 1
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## 2439 930 95 2.06 0 0.86000 5.39 109 20.2226353 0 1
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## 2441 1220 56 2.64 0 0.96774 5.03 59 11.7296219 0 1
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## 2445 1140 14 0.28 0 0.72727 5.26 140 26.6159687 0 1
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## 2448 840 124 2.62 0 0.82609 5.39 124 23.0055656 1 1
## 2449 1000 51 2.13 0 0.81818 5.56 37 6.6546764 0 1
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## 2452 750 119 2.49 0 1.08333 5.39 70 12.9870129 1 1
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## 2466 960 87 2.91 0 1.00000 1.92 18 9.3750000 0 1
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## 2468 1080 13 3.53 0 0.80000 1.96 36 18.3673477 1 1
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## 2480 830 40 2.05 0 0.84444 2.38 70 29.4117641 0 1
## 2481 1100 15 4.00 0 1.03704 2.37 17 7.1729956 1 1
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## 2483 1010 15 3.60 0 0.98039 2.37 21 8.8607597 1 1
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## 2487 1080 79 2.94 0 0.80000 2.51 18 7.1713147 1 1
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## 2490 1060 47 2.91 0 1.00000 2.38 38 15.9663868 1 1
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## 2494 880 15 3.20 0 1.00000 2.37 66 27.8481007 1 1
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## 2499 1090 77 2.22 0 1.05660 2.04 88 43.1372566 1 1
## 2500 960 45 2.44 0 1.00000 2.38 54 22.6890755 1 1
## 2501 930 18 3.22 0 0.93750 2.37 58 24.4725742 1 1
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## 2503 1300 67 2.23 0 1.00000 2.51 61 24.3027897 0 1
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## 2526 1060 16 1.25 0 0.73770 0.60 6 10.0000000 0 0
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## 2528 990 78 2.44 0 0.73684 3.38 20 5.9171596 1 1
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## 2904 1010 97 3.57 0 0.77193 2.77 34 12.2743683 1 1
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## 2906 1080 14 2.71 0 1.03774 3.02 68 22.5165558 1 1
## 2907 1090 80 3.66 0 0.94643 2.77 8 2.8880866 1 1
## 2908 1170 14 1.92 0 0.72059 3.00 85 28.3333340 0 1
## 2909 1040 13 1.46 0 0.82456 3.00 185 61.6666679 0 1
## 2910 830 10 1.70 0 1.18421 3.00 97 32.3333321 1 0
## 2911 1090 17 3.35 0 0.57971 0.66 2 3.0303030 0 1
## 2912 790 83 2.28 0 0.88095 0.62 12 19.3548393 0 1
## 2913 820 17 3.82 0 0.95238 0.62 7 11.2903223 1 1
## 2914 760 10 1.80 0 0.94872 0.05 1 20.0000000 0 1
## 2915 750 15 1.93 0 0.78571 0.20 6 30.0000000 0 1
## 2916 930 15 0.46 0 0.97872 0.20 7 35.0000000 0 1
## 2917 880 45 2.04 0 0.87234 3.45 3 0.8695652 0 1
## 2918 900 43 2.90 0 0.95652 0.12 1 8.3333330 1 1
## 2919 780 15 1.60 0 0.73333 0.20 3 15.0000000 0 1
## 2920 880 120 3.41 0 1.31579 1.35 6 4.4444447 1 1
## 2921 770 49 1.85 0 0.60417 1.02 1 0.9803922 1 0
## 2922 780 13 2.23 0 0.65957 1.05 9 8.5714283 1 0
## 2923 780 15 1.60 0 0.73333 1.05 3 2.8571429 1 0
## 2924 940 14 2.64 0 1.00000 2.92 70 23.9726028 0 1
## 2925 1140 15 3.53 0 0.83871 2.79 4 1.4336917 1 1
## 2926 790 114 2.67 0 1.02564 2.33 20 8.5836906 1 1
## 2927 1120 10 2.30 0 0.96491 2.79 26 9.3189964 0 1
## 2928 750 48 2.10 0 1.08333 2.88 34 11.8055553 0 1
## 2929 1250 14 3.71 0 0.86567 2.79 6 2.1505377 0 1
## 2930 1020 13 3.30 0 0.96154 2.92 9 3.0821917 1 1
## 2931 1070 49 3.34 0 0.91071 2.88 2 0.6944444 1 1
## 2932 1190 15 3.73 0 0.91935 2.79 5 1.7921147 1 1
## 2933 1020 42 2.26 0 0.96154 2.88 9 3.1250000 1 1
## 2934 900 83 1.93 0 0.73077 2.33 23 9.8712444 0 1
## 2935 940 50 2.40 0 0.70909 2.88 20 6.9444447 0 1
## 2936 1010 100 2.96 0 1.10417 2.33 7 3.0042918 0 1
## 2937 1340 43 2.90 0 0.88732 0.16 5 31.2500000 0 1
## 2938 980 56 3.35 0 0.78182 0.18 4 22.2222214 0 1
## 2939 700 71 2.12 0 0.84211 0.18 5 27.7777786 0 1
## 2940 1150 75 3.80 0 0.94915 0.18 2 11.1111107 0 1
## 2941 730 103 3.18 0 1.14706 0.26 9 34.6153831 0 1
## 2942 880 18 2.27 0 1.20000 1.05 15 14.2857141 0 1
## 2943 740 40 2.82 0 0.72093 1.14 21 18.4210529 0 1
## 2944 880 49 1.44 0 0.91304 0.99 28 28.2828274 0 1
## 2945 930 15 1.53 0 0.72222 0.63 16 25.3968258 0 1
## 2946 880 76 2.76 0 1.37838 0.07 2 28.5714283 1 1
## 2947 1050 92 2.98 0 1.01923 0.39 3 7.6923075 1 1
## 2948 970 81 2.71 0 1.20455 0.41 4 9.7560978 1 1
## 2949 1310 72 2.98 0 0.95522 0.39 5 12.8205128 0 1
## 2950 910 44 2.45 0 0.56897 2.55 47 18.4313717 0 0
## 2951 990 83 2.39 0 1.10638 2.52 35 13.8888893 0 1
## 2952 1080 43 2.88 0 0.92857 2.55 71 27.8431377 0 1
## 2953 1060 13 1.38 0 0.96296 3.19 103 32.2884026 0 1
## 2954 830 42 2.23 0 0.97619 2.55 150 58.8235283 1 1
## 2955 1030 66 2.66 0 0.71667 2.52 103 40.8730164 0 1
## 2956 1130 49 2.89 0 0.76563 2.55 33 12.9411764 0 1
## 2957 1110 70 3.10 1 0.73438 2.52 19 7.5396824 0 1
## 2958 990 112 3.13 0 0.94118 2.35 11 4.6808510 1 1
## 2959 1000 111 3.16 0 0.96078 2.35 34 14.4680853 1 1
## 2960 880 106 3.09 0 1.09524 2.35 23 9.7872343 0 1
## 2961 1080 15 1.93 0 0.63636 3.19 142 44.5141068 1 1
## 2962 910 102 2.41 0 0.93617 2.35 37 15.7446804 1 1
## 2963 1400 75 3.80 1 0.94444 2.52 1 0.3968254 0 1
## 2964 1070 50 3.62 0 0.94545 2.55 44 17.2549019 0 1
## 2965 900 73 2.16 0 0.83673 2.52 81 32.1428566 1 1
## 2966 830 103 2.84 0 1.12821 3.01 153 50.8305664 0 1
## 2967 970 50 3.34 0 1.06383 2.52 7 2.7777777 0 1
## 2968 1170 15 3.20 0 0.85714 3.19 35 10.9717865 0 1
## 2969 1060 102 3.35 0 0.96296 2.35 21 8.9361706 1 1
## 2970 970 51 2.98 0 1.10870 2.55 35 13.7254906 1 1
## 2971 1270 73 3.45 0 1.04839 2.52 5 1.9841269 0 1
## 2972 1010 10 2.00 0 1.10417 3.19 81 25.3918495 0 1
## 2973 1050 121 2.68 0 1.05882 2.53 8 3.1620553 0 1
## 2974 1180 117 2.95 0 0.93443 2.35 41 17.4468079 0 1
## 2975 880 46 3.08 0 0.62963 2.55 98 38.4313736 1 1
## 2976 860 65 2.60 0 0.65385 2.52 84 33.3333321 0 1
## 2977 960 13 1.46 0 0.88235 1.58 10 6.3291140 0 0
## 2978 890 17 1.88 0 0.85417 1.58 9 5.6962028 0 1
## 2979 840 18 1.77 0 1.04878 1.58 111 70.2531662 0 1
## 2980 960 19 2.78 0 0.60000 0.20 7 35.0000000 0 1
## 2981 1040 45 2.55 0 0.67742 0.34 8 23.5294113 0 1
## 2982 870 52 1.75 0 1.02326 0.34 6 17.6470585 1 1
## 2983 820 17 1.94 0 0.90698 1.58 57 36.0759506 0 1
## 2984 1060 13 2.30 0 0.92727 0.31 19 61.2903214 0 1
## 2985 1120 90 3.87 0 1.03636 3.17 2 0.6309148 1 1
## 2986 1010 13 1.15 0 0.74138 2.12 63 29.7169819 0 1
## 2987 930 41 2.31 0 1.06667 2.11 38 18.0094795 0 1
## 2988 1050 17 3.58 0 0.77966 2.12 15 7.0754719 1 1
## 2989 910 14 2.35 0 0.78431 2.12 50 23.5849056 0 1
## 2990 1150 75 3.06 0 0.88525 2.09 24 11.4832535 0 1
## 2991 1200 15 3.60 0 0.79104 2.12 18 8.4905663 1 1
## 2992 970 16 2.56 0 0.79630 2.12 41 19.3396225 1 1
## 2993 930 19 2.73 0 0.75472 2.12 35 16.5094337 1 1
## 2994 1050 114 2.06 0 1.05882 2.00 34 17.0000000 0 0
## 2995 1250 17 3.00 0 0.95313 2.12 25 11.7924528 0 1
## 2996 1050 14 2.50 0 0.87500 2.12 35 16.5094337 1 1
## 2997 1160 79 1.64 0 0.75758 3.11 15 4.8231511 0 1
## 2998 1290 42 3.04 0 1.08065 3.45 36 10.4347830 0 1
## 2999 1010 44 1.81 0 0.87037 3.40 115 33.8235283 0 1
## 3000 920 52 2.44 0 1.04444 3.45 55 15.9420290 0 1
## 3001 1030 15 2.80 0 0.74576 3.65 34 9.3150682 0 1
## 3002 830 55 2.03 0 0.93023 3.35 172 51.3432846 0 1
## 3003 1170 29 2.48 0 0.88710 3.45 46 13.3333330 0 1
## 3004 860 50 1.92 0 0.62264 3.45 117 33.9130440 0 1
## 3005 870 54 3.27 0 0.93333 3.45 28 8.1159420 1 1
## 3006 1190 86 3.72 0 0.70000 3.17 4 1.2618296 0 1
## 3007 990 18 2.83 0 0.94118 3.65 20 5.4794521 0 1
## 3008 920 42 2.11 0 0.67273 1.81 27 14.9171267 1 1
## 3009 1230 52 3.92 0 1.05000 1.59 4 2.5157232 0 1
## 3010 940 17 2.41 0 0.80769 1.95 24 12.3076925 1 1
## 3011 910 17 3.23 0 0.71698 1.99 11 5.5276380 1 1
## 3012 950 55 2.10 0 0.79245 1.59 7 4.4025159 0 1
## 3013 1020 49 3.16 0 0.67213 1.59 14 8.8050318 0 1
## 3014 880 45 2.80 0 1.14634 1.59 33 20.7547169 1 1
## 3015 990 14 1.42 0 0.67797 2.05 71 34.6341476 0 1
## 3016 1110 43 2.62 0 0.76190 1.59 11 6.9182391 0 1
## 3017 1100 17 3.82 0 0.80328 1.95 3 1.5384616 1 1
## 3018 1190 107 3.33 0 0.72464 1.67 1 0.5988024 1 1
## 3019 860 13 1.15 0 0.59259 1.95 95 48.7179489 0 1
## 3020 880 89 2.53 0 0.62963 1.67 6 3.5928144 1 0
## 3021 830 18 1.94 0 0.84444 0.87 15 17.2413788 0 1
## 3022 1020 17 0.70 0 0.82143 0.87 8 9.1954021 0 1
## 3023 850 73 2.34 0 0.63462 1.12 6 5.3571429 1 1
## 3024 1290 35 3.31 0 0.74324 0.76 1 1.3157895 0 1
## 3025 740 18 2.61 0 0.80488 0.87 43 49.4252892 0 1
## 3026 1180 81 3.02 0 0.87302 1.01 2 1.9801980 1 1
## 3027 1110 16 4.00 0 0.85000 1.21 1 0.8264463 0 1
## 3028 910 84 2.38 0 0.97826 1.01 6 5.9405942 1 1
## 3029 770 114 2.92 0 0.79070 0.99 11 11.1111107 1 1
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## 3031 1050 90 2.21 0 0.98113 0.99 19 19.1919193 0 1
## 3032 1030 45 3.20 0 0.87273 0.93 2 2.1505377 0 1
## 3033 1000 41 2.09 0 0.96078 0.93 10 10.7526884 0 1
## 3034 1060 14 3.14 0 0.79661 3.32 44 13.2530117 0 1
## 3035 1020 14 2.42 0 0.75862 3.32 83 25.0000000 0 1
## 3036 1030 14 2.21 0 0.98077 3.32 94 28.3132534 0 1
## 3037 960 10 2.20 0 0.92000 3.32 76 22.8915653 0 1
## 3038 1120 11 2.90 0 0.86667 0.30 5 16.6666660 0 1
## 3039 1030 17 3.17 0 0.66129 3.32 14 4.2168674 1 1
## 3040 960 17 3.58 0 0.54839 3.50 30 8.5714283 0 1
## 3041 1430 47 2.42 0 0.93243 3.13 40 12.7795525 0 1
## 3042 1100 114 2.74 0 1.07547 3.22 25 7.7639751 1 1
## 3043 1070 12 2.50 0 0.69841 3.32 95 28.6144581 0 1
## 3044 990 16 1.93 0 0.86792 3.32 29 8.7349396 1 1
## 3045 1130 46 3.34 1 0.79365 3.13 10 3.1948881 0 1
## 3046 1170 12 1.83 0 0.88710 3.32 82 24.6987953 0 1
## 3047 1170 14 1.85 0 0.72059 3.50 105 30.0000000 0 1
## 3048 1040 116 2.60 0 0.73333 3.22 14 4.3478260 0 1
## 3049 1290 64 4.00 0 0.79167 2.70 2 0.7407407 0 1
## 3050 1250 83 2.63 0 0.86567 2.70 35 12.9629631 0 1
## 3051 1260 47 3.61 0 0.77465 3.13 8 2.5559106 0 1
## 3052 1040 32 3.21 0 0.85714 3.21 40 12.4610596 0 1
## 3053 910 38 1.94 0 0.93617 3.13 72 23.0031948 1 1
## 3054 1020 33 2.51 0 0.75862 3.13 20 6.3897762 1 1
## 3055 810 121 2.52 0 0.68750 3.22 63 19.5652180 1 1
## 3056 1010 116 2.67 0 0.83636 3.22 47 14.5962734 0 1
## 3057 990 112 2.83 0 0.83333 3.22 11 3.4161491 0 1
## 3058 1020 71 2.36 0 1.12500 2.70 29 10.7407408 1 1
## 3059 990 21 3.33 0 0.70690 3.13 16 5.1118212 0 1
## 3060 1210 41 2.73 0 0.89063 3.13 25 7.9872203 1 1
## 3061 890 45 1.62 0 0.89362 3.13 65 20.7667732 0 1
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## 3070 1170 88 3.29 0 0.85714 1.26 11 8.7301588 0 1
## 3071 1150 52 1.71 0 1.16981 1.33 19 14.2857141 1 1
## 3072 1210 119 3.16 0 1.05085 1.26 8 6.3492064 1 1
## 3073 1050 45 2.35 0 0.84211 1.33 39 29.3233089 0 1
## 3074 1040 15 2.40 0 1.00000 1.53 49 32.0261421 0 1
## 3075 1060 17 1.52 0 0.76667 1.42 30 21.1267605 0 1
## 3076 1060 123 2.78 0 0.79661 1.26 16 12.6984129 0 1
## 3077 830 14 2.28 0 0.93023 1.65 21 12.7272730 0 0
## 3078 810 72 3.00 0 1.07692 0.12 1 8.3333330 1 1
## 3079 800 96 2.21 0 0.70213 0.10 3 30.0000000 0 1
## 3080 960 15 2.33 0 1.04255 1.64 82 50.0000000 0 1
## 3081 820 90 1.86 0 0.78261 1.51 31 20.5298004 1 1
## 3082 940 12 1.66 0 0.84314 3.75 60 16.0000000 1 0
## 3083 1020 40 2.80 0 0.82143 4.03 23 5.7071962 0 1
## 3084 1070 14 2.42 0 0.81356 3.75 4 1.0666667 1 0
## 3085 1130 54 2.51 0 0.71212 4.03 13 3.2258065 0 0
## 3086 820 59 1.72 0 1.15789 4.30 25 5.8139534 0 0
## 3087 880 15 0.53 0 0.95556 3.75 89 23.7333336 0 0
## 3088 850 12 0.58 0 0.80851 3.75 56 14.9333334 1 0
## 3089 840 72 2.02 0 1.10000 4.30 106 24.6511631 0 1
## 3090 790 51 2.07 0 0.79545 1.22 63 51.6393433 1 1
## 3091 1110 63 2.47 0 0.91379 0.66 8 12.1212120 1 1
## 3092 1070 48 2.75 0 0.67188 1.21 17 14.0495872 0 1
## 3093 1020 37 2.43 0 1.08163 1.22 55 45.0819664 0 1
## 3094 1080 83 2.43 0 0.80000 0.66 43 65.1515121 0 1
## 3095 750 12 0.66 0 0.87500 0.66 50 75.7575760 0 1
## 3096 920 13 3.30 0 1.04444 1.08 19 17.5925922 1 1
## 3097 940 82 2.15 0 0.80769 0.66 37 56.0606079 0 1
## 3098 920 110 3.29 0 0.67273 0.74 5 6.7567568 1 1
## 3099 1030 45 2.75 0 0.71667 1.22 20 16.3934422 1 0
## 3100 810 74 3.00 0 1.02500 0.66 22 33.3333321 1 1
## 3101 1110 17 3.41 0 0.91379 1.08 4 3.7037036 0 1
## 3102 950 38 1.39 0 1.15909 1.22 96 78.6885223 0 1
## 3103 1260 12 3.75 0 0.96875 1.08 16 14.8148146 0 1
## 3104 870 118 2.84 0 0.81250 0.74 34 45.9459457 1 1
## 3105 1020 76 3.61 0 0.88889 0.66 14 21.2121220 1 1
## 3106 860 16 2.00 0 1.09756 1.08 22 20.3703709 1 1
## 3107 1150 76 2.86 0 0.74242 0.66 12 18.1818180 0 1
## 3108 860 72 2.70 1 0.79167 0.66 21 31.8181820 0 1
## 3109 820 40 1.65 0 0.86364 1.22 82 67.2131119 0 1
## 3110 890 94 2.77 0 0.93478 0.65 41 63.0769234 0 1
## 3111 1310 52 4.00 0 0.95522 1.22 1 0.8196721 0 1
## 3112 1400 83 3.96 0 0.97183 0.66 4 6.0606060 0 1
## 3113 880 45 2.35 0 1.04651 1.22 53 43.4426231 1 1
## 3114 990 15 2.66 0 1.02041 1.08 30 27.7777786 1 1
## 3115 1010 114 3.55 0 0.90566 0.74 1 1.3513514 1 1
## 3116 1080 46 3.67 0 0.89474 1.22 13 10.6557379 0 1
## 3117 1090 46 3.23 0 0.84746 1.22 37 30.3278694 1 1
## 3118 840 15 3.00 0 0.86667 1.08 48 44.4444427 0 1
## 3119 1160 49 2.00 0 0.81250 1.22 38 31.1475410 0 1
## 3120 960 14 2.85 0 1.28571 1.08 32 29.6296291 1 1
## 3121 1090 52 2.55 0 0.75806 1.22 24 19.6721306 0 0
## 3122 900 80 2.75 0 0.69811 0.43 5 11.6279068 1 1
## 3123 960 79 2.36 0 0.84615 0.43 10 23.2558136 1 1
## 3124 950 115 2.41 0 1.15909 0.52 19 36.5384598 1 1
## 3125 1010 65 1.89 0 0.90566 0.54 43 79.6296310 0 1
## 3126 910 79 2.69 0 1.02222 0.43 6 13.9534883 0 1
## 3127 730 101 2.42 0 1.08571 0.37 17 45.9459457 0 1
## 3128 1180 17 3.82 0 0.84375 2.75 8 2.9090910 0 1
## 3129 930 15 2.26 0 1.06667 2.95 50 16.9491520 0 1
## 3130 1210 53 3.49 0 0.80597 2.39 1 0.4184100 0 1
## 3131 1320 24 1.41 0 0.88571 2.31 63 27.2727280 0 1
## 3132 950 117 2.68 0 0.86275 2.33 14 6.0085835 1 1
## 3133 1040 81 2.02 0 0.89091 2.33 27 11.5879831 0 1
## 3134 1080 117 2.87 0 0.77049 2.33 23 9.8712444 0 1
## 3135 1270 111 3.28 0 1.11667 2.33 2 0.8583691 1 1
## 3136 910 113 2.02 0 0.82000 0.82 4 4.8780489 0 0
## 3137 1350 49 3.69 0 1.10938 0.84 1 1.1904762 0 1
## 3138 800 46 2.19 0 0.95122 0.84 2 2.3809524 1 0
## 3139 1110 17 3.17 0 0.88136 0.74 1 1.3513514 0 1
## 3140 1080 17 3.82 0 0.71429 0.74 2 2.7027028 1 1
## 3141 1230 12 3.00 0 0.86364 0.74 6 8.1081085 0 1
## 3142 1000 42 1.88 0 0.72414 0.62 4 6.4516129 0 1
## 3143 1000 118 2.60 0 0.92308 0.53 12 22.6415100 0 1
## 3144 1120 17 3.23 0 0.72308 1.80 8 4.4444447 0 1
## 3145 1080 19 3.15 0 0.83051 1.80 22 12.2222223 0 1
## 3146 890 98 1.93 0 0.67925 1.83 23 12.5683060 0 1
## 3147 830 13 2.38 0 0.80435 1.70 121 71.1764679 1 1
## 3148 940 122 2.69 0 0.91837 1.83 2 1.0928962 1 1
## 3149 870 52 1.57 0 0.70588 1.60 16 10.0000000 0 0
## 3150 790 13 1.69 0 0.83721 1.70 31 18.2352943 1 1
## 3151 920 15 1.60 0 1.09091 1.80 46 25.5555553 0 1
## 3152 1190 46 3.00 0 0.72464 1.60 3 1.8750000 0 1
## 3153 910 18 2.72 0 0.68519 1.80 37 20.5555553 0 1
## 3154 1070 50 1.96 0 0.98148 1.60 38 23.7500000 1 1
## 3155 860 14 2.57 0 1.09756 1.85 29 15.6756754 0 1
## 3156 880 18 2.83 0 1.04651 1.60 27 16.8750000 0 1
## 3157 990 96 1.81 0 0.83333 1.83 16 8.7431698 0 1
## 3158 1010 50 2.34 0 0.80357 1.57 25 15.9235668 0 1
## 3159 980 73 2.34 0 1.00000 1.55 8 5.1612902 1 1
## 3160 930 97 2.00 0 1.16279 1.55 29 18.7096767 1 1
## 3161 1060 48 2.95 0 0.73770 1.57 7 4.4585986 1 1
## 3162 1340 116 3.83 0 0.83562 1.55 1 0.6451613 0 1
## 3163 860 18 3.05 0 0.68627 1.56 54 34.6153831 0 1
## 3164 940 72 2.70 0 1.00000 1.55 9 5.8064518 1 1
## 3165 1120 78 2.84 0 0.83607 1.55 37 23.8709679 0 1
## 3166 1140 17 3.94 0 1.00000 1.56 1 0.6410257 1 1
## 3167 940 68 2.11 0 0.84314 1.55 18 11.6129036 0 1
## 3168 930 72 2.25 0 0.97872 1.40 39 27.8571434 1 1
## 3169 890 92 2.72 0 0.67925 1.68 21 12.5000000 0 1
## 3170 1150 59 3.27 0 1.01754 1.62 45 27.7777786 0 1
## 3171 1000 18 2.16 0 1.00000 1.56 29 18.5897427 0 1
## 3172 1040 49 2.89 0 0.89091 1.65 8 4.8484850 0 1
## 3173 700 68 2.36 0 0.70732 1.55 70 45.1612892 0 0
## 3174 920 18 2.66 0 0.70370 6.98 75 10.7449856 1 1
## 3175 1040 93 2.45 0 0.89091 1.55 12 7.7419353 1 1
## 3176 1040 15 2.93 0 0.67742 1.56 16 10.2564106 0 1
## 3177 1000 12 2.75 0 0.81818 2.84 35 12.3239441 0 1
## 3178 920 14 2.78 0 1.00000 2.63 107 40.6844101 1 1
## 3179 870 17 2.23 0 0.85106 2.34 45 19.2307701 1 1
## 3180 980 13 3.07 0 1.13043 2.73 40 14.6520147 0 1
## 3181 1090 12 2.50 0 0.87931 2.34 33 14.1025639 0 1
## 3182 1140 46 2.15 0 0.78125 2.87 39 13.5888500 0 1
## 3183 1050 45 1.95 0 0.72131 2.57 95 36.9649811 0 1
## 3184 810 51 2.31 0 0.80000 2.57 76 29.5719852 1 1
## 3185 1050 47 3.10 0 1.01923 2.57 30 11.6731520 1 1
## 3186 890 16 1.43 0 0.93478 2.34 88 37.6068382 0 1
## 3187 850 48 2.83 0 0.97674 2.57 46 17.8988323 1 1
## 3188 1100 17 3.64 0 0.80328 2.34 30 12.8205128 0 1
## 3189 980 111 2.58 0 0.88462 2.57 31 12.0622568 0 1
## 3190 920 16 1.87 0 0.80392 2.34 46 19.6581192 0 1
## 3191 970 38 2.26 0 0.83019 2.57 45 17.5097275 0 1
## 3192 890 48 2.66 0 0.74510 2.57 36 14.0077820 1 1
## 3193 1020 16 4.00 0 0.88889 2.34 1 0.4273504 1 1
## 3194 830 20 2.50 0 0.97619 2.57 122 47.4708176 1 1
## 3195 1020 14 0.64 0 0.92453 2.34 46 19.6581192 0 1
## 3196 1070 14 3.14 0 0.84483 2.34 36 15.3846149 0 1
## 3197 920 16 2.31 0 0.76923 2.34 44 18.8034191 1 1
## 3198 1030 17 1.64 0 1.14583 2.34 15 6.4102564 1 1
## 3199 880 125 3.37 0 0.91304 2.57 4 1.5564202 0 1
## 3200 1020 18 3.44 0 0.85455 2.34 7 2.9914529 1 1
## 3201 1130 17 0.94 0 0.98246 2.34 13 5.5555553 0 1
## 3202 970 17 2.29 0 0.97959 2.34 24 10.2564106 1 1
## 3203 1320 14 3.85 0 0.85915 2.34 3 1.2820513 0 1
## 3204 780 73 3.47 0 0.81395 2.57 6 2.3346303 0 1
## 3205 1130 14 0.00 0 1.01786 2.34 88 37.6068382 0 1
## 3206 820 19 2.31 0 1.05000 2.34 148 63.2478638 0 1
## 3207 1190 99 2.74 0 1.01695 2.57 11 4.2801557 0 1
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## 3885 710 15 1.86 1 0.86842 2.58 129 50.0000000 1 0
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## 3940 1060 86 3.40 0 1.16327 4.00 146 36.5000000 0 1
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## 3942 960 79 2.91 0 0.92000 0.10 2 20.0000000 0 1
## 3943 1120 95 2.43 0 0.72308 2.60 26 10.0000000 0 1
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## 3955 770 88 2.45 1 0.75000 3.96 197 49.7474747 1 0
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## 4075 880 76 2.31 0 0.95556 1.60 85 53.1250000 0 1
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## 4078 980 13 2.53 0 0.88462 5.37 220 40.9683418 1 1
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## 4110 1210 44 2.20 0 0.77941 0.10 3 30.0000000 0 1
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model <- lm(sat ~ hsize + hsizesq + female + black + I(female*black) , data = gpa2)
summary(model)
##
## Call:
## lm(formula = sat ~ hsize + hsizesq + female + black + I(female *
## black), data = gpa2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -570.45 -89.54 -5.24 85.41 479.13
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1028.0972 6.2902 163.445 < 2e-16 ***
## hsize 19.2971 3.8323 5.035 4.97e-07 ***
## hsizesq -2.1948 0.5272 -4.163 3.20e-05 ***
## female -45.0915 4.2911 -10.508 < 2e-16 ***
## black -169.8126 12.7131 -13.357 < 2e-16 ***
## I(female * black) 62.3064 18.1542 3.432 0.000605 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 133.4 on 4131 degrees of freedom
## Multiple R-squared: 0.08578, Adjusted R-squared: 0.08468
## F-statistic: 77.52 on 5 and 4131 DF, p-value: < 2.2e-16
# (i) Is there strong evidence that hsize2 should be included in the model? From this equation,what is the optimal high school size?
# From this equation we don’t have the information about SE to calculate the significance of the coeficientes so we can not be sure. However R square is very small so seems that the equation is not very good. To calculate the optimal size we need to take the first derivative 19.30hsize − 2.19hsize2 the result is 4.4
# (ii) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and non-black males?
# For that we just need to use white female (female =1, black = 0) − 45.09female +62.31female = 17.22. This is just a simple comparison between white male and female
# (iii) What is the estimated difference in SAT score between non-black males and black males?
# − 169.81black
# (iv) What is the estimated difference in SAT score between black females and non-black females?
# − 169.81black +62.31female · black = -107.5
#C1.
# (i) Add variables mothcoll and fathcoll to the equation
data.frame(gpa1)
## age soph junior senior senior5 male campus business engineer colGPA hsGPA
## 1 21 0 0 1 0 0 0 1 0 3.0 3.0
## 2 21 0 0 1 0 0 0 1 0 3.4 3.2
## 3 20 0 1 0 0 0 0 1 0 3.0 3.6
## 4 19 1 0 0 0 1 1 1 0 3.5 3.5
## 5 20 0 1 0 0 0 0 1 0 3.6 3.9
## 6 20 0 0 1 0 1 1 1 0 3.0 3.4
## 7 22 0 0 0 1 0 0 1 0 2.7 3.5
## 8 22 0 0 0 1 0 0 0 0 2.7 3.0
## 9 22 0 0 0 1 0 0 0 0 2.7 3.0
## 10 19 1 0 0 0 0 0 1 0 3.8 4.0
## 11 21 0 0 1 0 1 0 1 0 2.8 3.0
## 12 22 0 0 0 1 0 1 1 0 2.9 3.1
## 13 21 0 0 1 0 0 1 1 0 3.0 3.5
## 14 20 0 1 0 0 1 1 1 0 2.9 3.8
## 15 20 0 1 0 0 1 0 1 0 3.3 3.7
## 16 22 0 0 1 0 1 0 1 0 2.6 3.0
## 17 19 1 0 0 0 1 0 0 1 2.5 3.5
## 18 22 0 0 1 0 1 0 1 0 2.5 3.0
## 19 20 0 1 0 0 1 0 1 0 2.4 3.0
## 20 21 0 0 1 0 1 0 1 0 3.6 3.5
## 21 20 0 1 0 0 0 0 1 0 2.6 3.5
## 22 22 0 0 1 0 1 0 0 1 2.7 3.0
## 23 20 0 1 0 0 0 0 1 0 2.9 3.6
## 24 21 0 0 1 0 0 1 0 0 3.0 4.0
## 25 20 0 1 0 0 1 0 1 0 3.3 3.6
## 26 20 0 1 0 0 0 0 1 0 3.1 3.3
## 27 20 0 1 0 0 0 0 1 0 3.0 3.6
## 28 20 0 1 0 0 0 0 0 0 3.2 3.1
## 29 20 0 1 0 0 0 0 1 0 3.0 3.4
## 30 20 0 1 0 0 0 0 1 0 3.4 3.7
## 31 21 0 1 0 0 1 0 1 0 2.9 3.7
## 32 21 0 0 1 0 0 0 1 0 3.5 3.3
## 33 22 0 0 1 0 1 0 1 0 3.7 3.3
## 34 20 0 0 1 0 0 0 1 0 3.5 3.5
## 35 21 0 0 1 0 1 0 1 0 2.8 3.2
## 36 21 0 0 1 0 0 1 1 0 2.5 3.3
## 37 21 0 0 1 0 0 0 1 0 3.1 3.4
## 38 20 0 1 0 0 1 0 1 0 3.5 3.5
## 39 20 0 1 0 0 0 0 1 0 3.4 3.4
## 40 21 0 0 1 0 0 0 1 0 3.5 3.7
## 41 21 0 0 1 0 1 0 1 0 2.6 2.5
## 42 21 0 0 1 0 1 0 1 0 2.8 3.7
## 43 21 0 0 1 0 0 0 1 0 2.6 3.0
## 44 20 0 1 0 0 1 0 1 0 3.5 3.0
## 45 22 0 0 0 1 0 0 1 0 4.0 4.0
## 46 20 0 1 0 0 0 0 1 0 3.8 3.8
## 47 19 0 1 0 0 1 0 1 0 2.8 3.0
## 48 21 0 0 1 0 0 0 1 0 3.5 3.7
## 49 21 0 0 1 0 0 0 1 0 3.0 3.4
## 50 21 0 0 1 0 1 0 1 0 2.6 2.4
## 51 21 0 1 0 0 0 0 1 0 3.0 3.8
## 52 22 0 0 0 1 0 0 0 0 3.7 4.0
## 53 19 0 1 0 0 0 0 1 0 3.0 3.5
## 54 20 0 1 0 0 1 0 1 0 2.9 3.4
## 55 20 0 0 1 0 1 1 0 1 2.6 3.6
## 56 22 0 0 0 1 1 0 1 0 3.0 3.2
## 57 21 0 0 1 0 1 0 1 0 3.3 3.8
## 58 22 0 1 0 0 1 0 1 0 2.7 3.3
## 59 21 0 0 1 0 1 0 0 0 3.0 3.4
## 60 21 0 1 0 0 0 0 1 0 3.2 3.0
## 61 20 0 1 0 0 1 0 1 0 2.7 3.6
## 62 21 0 0 1 0 0 1 1 0 3.6 3.9
## 63 21 0 0 1 0 0 0 1 0 2.4 3.0
## 64 21 0 0 1 0 0 0 1 0 2.9 3.0
## 65 21 0 0 1 0 0 1 0 0 3.3 3.3
## 66 20 0 1 0 0 1 0 1 0 3.5 3.3
## 67 21 0 0 1 0 1 0 0 0 3.0 3.2
## 68 21 0 0 1 0 1 0 1 0 3.0 3.4
## 69 21 0 0 1 0 0 0 0 1 2.8 3.7
## 70 21 0 0 1 0 1 1 0 0 2.9 3.4
## 71 22 0 0 1 0 1 0 0 1 3.8 3.9
## 72 20 0 1 0 0 0 0 1 0 2.5 3.6
## 73 21 0 1 0 0 1 0 1 0 3.0 4.0
## 74 20 0 1 0 0 0 0 1 0 3.2 3.6
## 75 21 0 0 1 0 1 1 1 0 2.2 3.0
## 76 30 0 0 1 0 1 0 0 0 3.4 2.8
## 77 22 0 1 0 0 1 1 1 0 2.9 3.2
## 78 22 0 0 1 0 1 0 1 0 3.7 2.9
## 79 20 0 1 0 0 1 1 1 0 2.9 2.9
## 80 23 0 0 0 1 1 1 0 0 2.8 3.6
## 81 22 0 0 0 1 1 0 0 0 3.2 3.4
## 82 21 0 0 1 0 0 0 1 0 3.4 3.6
## 83 22 0 0 0 1 0 0 0 0 3.0 3.2
## 84 22 0 0 1 0 0 0 1 0 2.5 3.2
## 85 21 0 0 1 0 0 0 1 0 3.5 3.2
## 86 21 0 0 1 0 1 0 1 0 3.1 3.7
## 87 21 0 0 1 0 1 0 1 0 2.8 2.9
## 88 21 0 0 1 0 0 0 1 0 2.9 3.3
## 89 21 0 0 1 0 1 1 1 0 2.9 3.1
## 90 19 0 1 0 0 0 0 1 0 3.4 3.5
## 91 20 0 1 0 0 1 1 1 0 3.4 3.5
## 92 22 0 0 1 0 1 0 1 0 3.6 3.7
## 93 26 0 0 1 0 0 0 1 0 3.2 3.0
## 94 20 0 1 0 0 0 0 0 0 3.2 3.8
## 95 21 0 0 1 0 0 0 1 0 2.8 3.3
## 96 20 0 1 0 0 0 0 0 0 3.1 3.6
## 97 20 0 1 0 0 1 1 1 0 2.8 3.2
## 98 21 0 0 1 0 1 0 1 0 3.4 3.6
## 99 21 0 0 1 0 1 0 0 0 2.7 3.5
## 100 20 0 1 0 0 0 0 1 0 3.0 3.7
## 101 21 0 0 1 0 1 0 1 0 2.5 2.7
## 102 25 0 0 1 0 1 0 0 0 2.5 3.1
## 103 21 0 0 1 0 0 0 1 0 2.7 3.4
## 104 20 0 1 0 0 1 0 1 0 3.6 3.3
## 105 20 0 1 0 0 0 0 1 0 2.9 3.4
## 106 21 0 0 1 0 0 0 1 0 2.8 3.5
## 107 22 0 0 1 0 1 0 0 0 3.9 3.9
## 108 20 0 1 0 0 1 0 1 0 2.8 3.5
## 109 21 0 0 1 0 0 0 1 0 3.9 4.0
## 110 21 0 1 0 0 1 0 1 0 3.2 2.9
## 111 22 0 0 1 0 1 0 1 0 3.3 3.3
## 112 20 0 1 0 0 1 0 1 0 3.3 3.5
## 113 21 0 0 1 0 0 1 1 0 3.2 3.5
## 114 22 0 0 0 1 1 1 0 0 3.1 3.1
## 115 20 0 1 0 0 1 0 1 0 3.0 3.1
## 116 20 0 1 0 0 1 0 1 0 3.4 3.7
## 117 20 0 1 0 0 1 0 1 0 3.1 3.3
## 118 21 0 0 1 0 0 0 1 0 3.2 3.7
## 119 20 0 0 1 0 1 0 1 0 3.3 3.0
## 120 21 0 0 1 0 0 0 0 0 3.0 3.8
## 121 21 0 0 1 0 0 0 1 0 2.8 3.5
## 122 21 0 0 1 0 1 0 0 0 2.8 3.6
## 123 20 0 1 0 0 1 0 1 0 2.7 3.5
## 124 21 0 0 1 0 0 1 0 0 2.6 3.0
## 125 19 0 1 0 0 1 0 1 0 2.9 3.8
## 126 20 0 1 0 0 0 0 1 0 3.0 3.5
## 127 22 0 0 0 1 0 0 1 0 3.0 3.6
## 128 22 0 0 1 0 0 0 0 0 2.9 3.8
## 129 20 0 1 0 0 0 0 1 0 3.3 3.6
## 130 21 0 0 1 0 0 0 1 0 2.7 3.3
## 131 20 0 1 0 0 1 0 1 0 3.0 3.2
## 132 20 0 0 1 0 1 0 1 0 2.9 3.3
## 133 20 0 1 0 0 1 1 1 0 3.8 3.6
## 134 20 0 1 0 0 1 1 1 0 2.9 3.8
## 135 22 0 0 1 0 1 0 1 0 3.0 3.3
## 136 21 0 0 1 0 1 0 1 0 3.2 3.2
## 137 22 0 0 0 1 0 0 1 0 3.0 3.3
## 138 21 0 0 1 0 1 0 1 0 2.3 3.6
## 139 20 0 1 0 0 0 0 1 0 2.8 3.4
## 140 20 0 1 0 0 1 1 1 0 3.4 3.7
## 141 21 0 0 1 0 1 0 0 0 2.8 3.3
## ACT job19 job20 drive bike walk voluntr PC greek car siblings bgfriend
## 1 21 0 1 1 0 0 0 0 0 1 1 0
## 2 24 0 1 1 0 0 0 0 0 1 0 1
## 3 26 1 0 0 0 1 0 0 0 1 1 0
## 4 27 1 0 0 0 1 0 0 0 0 1 0
## 5 28 0 1 0 1 0 0 0 0 1 1 1
## 6 25 0 0 0 0 1 0 0 0 1 1 0
## 7 25 0 0 0 1 0 0 0 1 1 1 0
## 8 22 1 0 1 0 0 0 1 0 0 1 1
## 9 21 1 0 1 0 0 0 0 0 1 1 1
## 10 27 1 0 0 0 1 0 1 0 0 1 0
## 11 19 1 0 0 0 1 0 0 0 1 1 1
## 12 22 0 1 0 0 1 1 0 0 1 1 1
## 13 23 1 0 0 0 1 0 1 0 1 1 1
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## 15 25 0 0 1 0 0 0 1 1 0 1 0
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## 100 24 1 0 0 1 0 0 1 0 1 1 0
## 101 25 0 0 0 1 0 0 1 0 1 1 0
## 102 23 0 0 1 0 0 0 0 0 1 1 1
## 103 22 0 0 0 1 0 1 0 0 1 1 1
## 104 24 0 0 0 0 1 0 1 0 0 1 0
## 105 23 1 0 0 0 1 0 1 0 1 1 0
## 106 26 0 0 0 0 1 1 1 1 1 1 1
## 107 26 1 0 0 1 0 0 1 0 1 1 0
## 108 22 0 0 0 1 0 0 0 0 1 1 1
## 109 26 1 0 0 0 1 1 1 0 1 1 0
## 110 28 1 0 0 1 0 1 0 1 1 1 1
## 111 24 0 0 0 1 0 0 0 1 1 1 1
## 112 24 0 0 0 1 0 0 0 0 0 1 0
## 113 23 1 0 0 0 1 0 0 0 0 1 1
## 114 16 0 1 0 0 1 1 1 0 1 1 1
## 115 21 1 0 0 0 1 0 1 1 0 1 0
## 116 30 1 0 1 0 0 0 0 1 1 1 0
## 117 23 1 0 0 1 0 0 0 1 0 1 1
## 118 23 1 0 0 0 1 1 0 0 0 1 0
## 119 23 1 0 0 0 1 0 1 0 1 1 1
## 120 22 1 0 1 0 0 0 0 0 1 1 1
## 121 22 0 0 0 1 0 0 0 1 0 1 0
## 122 25 1 0 1 0 0 0 0 1 1 1 1
## 123 27 1 0 0 1 0 0 0 0 1 1 0
## 124 19 0 1 0 0 1 1 0 0 1 0 1
## 125 23 1 0 1 0 0 0 0 0 0 1 0
## 126 26 1 0 0 0 1 0 0 0 0 1 1
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## 129 26 0 1 0 0 1 0 0 0 1 1 1
## 130 23 0 0 0 0 1 0 1 0 1 1 1
## 131 21 1 0 1 0 0 0 1 0 1 1 0
## 132 22 0 0 0 1 0 1 0 1 1 1 0
## 133 26 0 0 0 1 0 0 0 0 0 1 1
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## 136 19 0 0 0 0 1 0 0 1 0 1 1
## 137 23 0 1 0 0 1 1 0 0 1 1 1
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## 139 21 0 1 0 1 0 0 0 0 1 1 1
## 140 26 0 0 0 0 1 0 0 1 1 1 1
## 141 28 1 0 0 1 0 0 0 0 0 1 1
## clubs skipped alcohol gradMI fathcoll mothcoll
## 1 0 2.00 1.00 1 0 0
## 2 1 0.00 1.00 1 1 1
## 3 1 0.00 1.00 1 1 1
## 4 0 0.00 0.00 0 0 0
## 5 0 0.00 1.50 1 1 0
## 6 0 0.00 0.00 0 1 0
## 7 1 0.00 2.00 1 0 1
## 8 0 3.00 3.00 1 1 1
## 9 1 2.00 2.50 1 1 1
## 10 1 0.50 0.75 1 0 1
## 11 0 2.00 1.00 1 0 0
## 12 1 1.00 1.00 1 0 1
## 13 1 0.00 1.00 1 0 1
## 14 0 3.00 2.50 0 1 1
## 15 0 1.00 4.00 1 1 1
## 16 1 3.00 3.50 1 1 0
## 17 0 4.00 3.00 1 1 0
## 18 1 5.00 5.00 0 1 0
## 19 0 2.00 4.00 0 1 0
## 20 1 1.00 5.00 1 1 1
## 21 1 3.00 2.00 1 1 1
## 22 1 1.00 1.00 1 0 1
## 23 1 1.00 1.00 0 1 0
## 24 1 0.00 0.00 1 0 0
## 25 0 2.00 5.00 1 1 0
## 26 1 1.00 1.00 1 1 0
## 27 0 2.00 1.00 1 0 0
## 28 1 1.00 2.00 1 0 0
## 29 0 0.00 2.00 1 1 1
## 30 0 0.50 2.00 1 1 1
## 31 0 1.00 2.00 1 0 0
## 32 0 1.00 0.00 1 1 1
## 33 1 0.00 1.00 1 1 0
## 34 1 0.00 1.00 1 1 1
## 35 1 1.00 3.00 1 1 1
## 36 1 1.00 1.00 1 1 1
## 37 0 0.50 1.00 1 1 1
## 38 1 1.00 3.00 1 1 0
## 39 0 0.50 0.00 1 1 1
## 40 1 0.00 2.00 1 0 1
## 41 0 1.00 1.00 0 0 0
## 42 1 0.00 2.00 1 1 1
## 43 0 2.00 3.00 1 0 0
## 44 1 1.00 3.00 1 0 1
## 45 1 0.00 0.50 1 1 1
## 46 1 1.00 3.00 1 1 1
## 47 0 4.00 2.00 1 1 1
## 48 1 1.00 2.00 1 0 0
## 49 0 2.00 1.00 1 1 1
## 50 0 1.00 2.00 1 0 0
## 51 0 1.00 2.00 1 0 0
## 52 1 1.00 2.00 1 0 0
## 53 1 0.00 2.00 1 1 1
## 54 1 1.00 3.00 1 1 1
## 55 1 1.00 0.00 1 1 0
## 56 0 2.00 5.00 1 1 1
## 57 1 0.50 1.00 1 0 1
## 58 1 2.00 3.00 1 1 0
## 59 1 0.00 1.00 1 1 1
## 60 0 0.00 0.00 1 1 1
## 61 1 1.00 3.00 1 0 1
## 62 0 1.00 2.00 1 1 0
## 63 1 2.00 3.00 1 0 1
## 64 0 1.00 2.00 1 0 0
## 65 1 1.00 1.00 1 0 0
## 66 1 0.50 1.50 1 1 1
## 67 1 2.00 3.00 1 1 1
## 68 1 0.00 2.00 1 1 1
## 69 1 0.00 1.00 0 0 1
## 70 0 0.00 2.00 1 1 1
## 71 1 2.00 7.00 1 1 1
## 72 0 2.00 1.00 1 0 0
## 73 1 1.00 4.00 1 0 0
## 74 1 1.00 2.00 1 1 1
## 75 0 0.00 1.00 0 1 1
## 76 1 0.00 0.00 1 0 0
## 77 0 0.00 3.00 1 1 0
## 78 1 1.00 5.00 1 1 0
## 79 1 1.00 0.50 0 1 1
## 80 1 0.50 1.00 0 1 1
## 81 1 1.00 2.00 1 1 0
## 82 1 0.50 2.00 0 1 1
## 83 1 2.00 1.00 1 0 1
## 84 1 2.00 1.00 1 0 1
## 85 0 1.00 3.00 1 0 1
## 86 1 1.00 4.00 0 1 1
## 87 0 0.00 7.00 1 1 1
## 88 1 1.00 2.00 1 0 0
## 89 1 2.00 3.00 1 1 0
## 90 1 0.00 1.00 1 0 0
## 91 1 0.00 1.50 1 1 1
## 92 0 3.00 3.00 1 0 0
## 93 0 0.25 0.50 1 1 0
## 94 1 1.00 2.00 0 1 1
## 95 1 0.00 0.50 0 1 1
## 96 0 0.00 1.00 1 0 0
## 97 1 1.00 2.00 1 0 0
## 98 1 3.00 3.00 1 1 0
## 99 0 0.00 3.00 1 1 1
## 100 0 0.00 2.00 1 0 0
## 101 0 0.50 3.00 1 0 1
## 102 0 1.00 1.00 1 0 0
## 103 1 1.00 2.00 1 1 0
## 104 1 0.00 3.00 1 1 1
## 105 1 1.00 0.50 1 1 1
## 106 0 1.00 2.00 1 1 1
## 107 0 0.00 0.50 1 0 0
## 108 1 2.00 2.00 1 0 0
## 109 1 0.00 2.00 1 1 1
## 110 1 1.00 2.50 1 1 0
## 111 0 2.00 4.00 0 1 1
## 112 1 2.00 2.00 1 0 0
## 113 1 0.00 1.00 1 1 0
## 114 1 0.00 0.00 1 1 0
## 115 0 1.00 0.50 1 0 1
## 116 0 5.00 3.00 1 0 0
## 117 1 2.00 1.00 1 1 1
## 118 1 2.00 0.00 1 0 0
## 119 0 0.00 3.00 1 1 1
## 120 0 1.00 3.00 1 1 1
## 121 0 1.00 2.00 1 1 1
## 122 0 3.00 0.00 1 0 0
## 123 0 4.00 3.00 1 0 0
## 124 1 1.00 0.00 1 0 1
## 125 1 1.00 2.00 0 1 1
## 126 0 2.00 1.00 1 0 1
## 127 1 0.00 2.00 1 1 1
## 128 1 2.00 1.00 0 0 0
## 129 1 0.00 0.00 1 0 1
## 130 1 1.00 3.00 1 0 0
## 131 1 1.00 1.00 1 1 1
## 132 0 2.00 1.00 1 1 0
## 133 1 0.00 0.00 1 1 1
## 134 1 0.00 1.00 1 1 0
## 135 1 0.00 3.00 1 1 0
## 136 0 0.00 3.00 1 0 0
## 137 1 0.00 0.00 1 0 0
## 138 0 1.00 1.00 1 0 0
## 139 0 0.00 0.30 1 0 0
## 140 1 3.00 4.00 1 0 1
## 141 1 3.00 2.00 1 1 1
model <- lm(hsGPA ~ mothcoll + fathcoll, data = gpa1)
# Add mothcoll and fathcoll to the model
model_updated <- update(model, . ~ . + mothcoll + fathcoll)
# View the results
summary(model_updated)
##
## Call:
## lm(formula = hsGPA ~ mothcoll + fathcoll, data = gpa1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.99342 -0.20982 0.00926 0.20926 0.60658
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.393421 0.046719 72.635 <2e-16 ***
## mothcoll 0.019080 0.057555 0.332 0.741
## fathcoll -0.002679 0.058303 -0.046 0.963
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3221 on 138 degrees of freedom
## Multiple R-squared: 0.0008268, Adjusted R-squared: -0.01365
## F-statistic: 0.0571 on 2 and 138 DF, p-value: 0.9445
# (ii) Test for joint significance of mothcoll and fathcoll
# Calculate F-statistic manually
joint_test <- summary(model)$fstatistic
p_value_joint_test <- pf(joint_test[1], joint_test[2], joint_test[3], lower.tail = FALSE)
p_value_joint_test
## value
## 0.9445229
# (iii) Add hsGPA to the model and compare models
model_iii <- lm(PC ~ mothcoll + fathcoll + hsGPA, data = gpa1)
anova(model, model_iii)
## Warning in anova.lmlist(object, ...): models with response '"PC"' removed
## because response differs from model 1
## Analysis of Variance Table
##
## Response: hsGPA
## Df Sum Sq Mean Sq F value Pr(>F)
## mothcoll 1 0.0116 0.011629 0.1121 0.7383
## fathcoll 1 0.0002 0.000219 0.0021 0.9634
## Residuals 138 14.3175 0.103750
#C3.)
data.frame(wage2)
## wage hours IQ KWW educ exper tenure age married black south urban sibs
## 1 769 40 93 35 12 11 2 31 1 0 0 1 1
## 2 808 50 119 41 18 11 16 37 1 0 0 1 1
## 3 825 40 108 46 14 11 9 33 1 0 0 1 1
## 4 650 40 96 32 12 13 7 32 1 0 0 1 4
## 5 562 40 74 27 11 14 5 34 1 0 0 1 10
## 6 1400 40 116 43 16 14 2 35 1 1 0 1 1
## 7 600 40 91 24 10 13 0 30 0 0 0 1 1
## 8 1081 40 114 50 18 8 14 38 1 0 0 1 2
## 9 1154 45 111 37 15 13 1 36 1 0 0 0 2
## 10 1000 40 95 44 12 16 16 36 1 0 0 1 1
## 11 930 43 132 44 18 8 13 38 1 0 0 0 1
## 12 921 38 102 45 14 9 11 33 1 0 0 0 1
## 13 900 45 125 40 15 4 3 30 0 0 0 0 2
## 14 1318 38 119 24 16 7 2 28 1 0 0 1 3
## 15 1792 40 118 47 16 9 9 34 1 0 0 1 1
## 16 958 50 105 37 10 17 2 35 1 0 0 1 1
## 17 1360 45 109 39 15 6 9 36 1 0 0 1 3
## 18 850 40 72 36 11 19 10 38 1 0 0 1 2
## 19 830 44 105 29 14 4 7 29 1 0 0 1 3
## 20 471 44 101 34 12 13 7 31 1 0 0 1 3
## 21 1275 40 123 37 14 9 1 31 1 0 0 1 0
## 22 1615 50 113 49 16 10 4 36 1 0 0 1 2
## 23 873 65 95 36 12 14 3 38 1 0 0 1 5
## 24 2137 45 145 50 16 17 8 38 1 0 0 1 2
## 25 1053 38 114 35 16 12 7 32 1 0 0 1 0
## 26 1602 60 124 32 16 8 9 29 1 0 0 1 3
## 27 1188 40 93 40 13 16 5 35 1 0 0 1 2
## 28 800 40 115 39 18 11 1 35 1 0 1 1 0
## 29 1417 48 125 41 17 9 4 34 1 0 0 1 3
## 30 635 40 128 35 18 8 13 36 0 0 0 1 2
## 31 1000 40 103 40 12 17 2 34 1 0 0 1 1
## 32 1424 50 98 41 14 15 4 35 1 0 0 1 1
## 33 2668 75 108 41 13 12 2 32 1 0 1 1 1
## 34 666 75 129 40 18 8 12 38 1 0 0 0 2
## 35 1779 40 132 42 17 8 9 32 1 0 0 1 1
## 36 782 40 92 24 13 9 10 31 1 0 0 1 3
## 37 1572 35 108 39 14 7 5 28 1 1 0 1 1
## 38 1274 40 106 35 13 11 12 31 1 0 0 1 0
## 39 714 35 105 37 16 9 2 29 1 0 0 1 1
## 40 1081 40 123 46 18 11 7 36 1 0 0 0 1
## 41 692 40 108 48 12 21 11 38 1 0 0 1 3
## 42 1318 38 122 47 17 10 9 33 1 0 0 1 1
## 43 1239 45 109 44 12 16 4 38 1 0 0 1 3
## 44 1027 27 100 40 13 12 15 38 1 0 0 1 3
## 45 1748 55 125 50 18 12 12 34 1 0 0 1 1
## 46 981 40 122 41 14 9 15 35 0 0 0 1 3
## 47 770 40 105 34 17 7 11 30 1 0 0 1 3
## 48 1154 50 94 37 16 11 5 33 1 0 0 1 1
## 49 1155 40 102 36 12 16 5 34 1 0 0 1 1
## 50 808 60 109 47 13 14 12 38 1 0 0 1 2
## 51 1100 40 105 45 12 22 14 38 1 0 0 1 1
## 52 1154 40 134 46 18 10 10 37 1 0 1 1 2
## 53 1749 40 108 32 12 13 9 29 0 0 0 1 7
## 54 1000 50 104 36 16 11 8 30 1 0 0 1 1
## 55 462 40 112 35 12 11 1 29 1 0 0 1 8
## 56 769 55 120 49 18 8 12 32 0 0 0 1 1
## 57 875 50 124 40 16 9 3 31 0 0 0 0 2
## 58 1375 40 103 34 12 12 7 29 1 0 0 1 4
## 59 1452 45 115 45 17 1 7 30 1 0 0 1 3
## 60 800 40 96 33 12 17 12 35 1 0 0 1 1
## 61 1748 55 123 48 17 10 7 36 1 0 0 1 1
## 62 1151 40 98 34 12 12 12 29 1 0 0 1 3
## 63 840 50 96 34 12 18 13 35 1 0 0 1 2
## 64 978 45 89 47 12 17 2 38 1 0 0 1 0
## 65 963 40 109 43 12 15 15 37 0 0 0 0 5
## 66 619 42 93 20 12 10 10 28 0 0 0 1 8
## 67 442 60 82 32 12 12 0 33 1 0 0 1 2
## 68 600 40 120 45 15 12 1 38 1 0 0 0 3
## 69 1366 38 122 38 12 15 15 32 1 0 0 1 1
## 70 1643 48 117 48 18 8 2 33 1 0 0 1 2
## 71 1455 40 109 44 16 8 13 36 1 0 0 1 1
## 72 2310 40 114 55 18 12 7 38 1 0 0 1 2
## 73 1682 45 126 40 16 10 11 31 1 0 0 1 1
## 74 1235 40 82 45 12 10 2 33 1 0 0 1 1
## 75 855 45 119 45 16 11 4 32 1 0 0 1 3
## 76 1072 42 104 37 16 6 8 35 1 0 0 1 2
## 77 1040 40 115 49 15 8 15 35 1 0 0 1 3
## 78 1000 50 97 45 12 17 15 36 1 0 0 1 1
## 79 675 40 105 27 15 8 2 31 1 0 0 0 3
## 80 1100 37 100 32 12 14 1 30 1 0 0 1 1
## 81 996 50 114 41 12 5 14 31 1 0 0 1 2
## 82 732 40 73 28 10 17 5 36 1 0 0 1 5
## 83 1200 40 96 48 11 15 3 37 1 0 0 1 4
## 84 1694 30 113 30 15 9 8 29 0 0 0 1 3
## 85 686 55 106 38 10 15 3 36 1 0 1 1 4
## 86 754 40 104 37 13 9 5 32 1 0 0 1 1
## 87 857 35 80 39 10 14 15 33 1 0 0 1 2
## 88 832 50 104 30 13 4 2 30 1 0 0 1 1
## 89 579 44 122 36 13 8 1 30 1 0 0 0 4
## 90 672 61 96 38 12 13 3 34 1 0 0 1 2
## 91 2500 40 95 51 15 12 9 36 1 0 0 1 3
## 92 1076 45 105 24 12 5 8 31 0 0 0 1 1
## 93 750 40 94 18 12 16 3 37 1 1 0 1 7
## 94 1186 30 91 41 17 8 9 33 1 0 0 1 1
## 95 833 48 96 37 16 9 7 31 1 0 0 1 4
## 96 650 40 69 37 12 14 11 30 1 1 0 1 3
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## 98 1122 48 111 44 15 12 9 31 1 0 0 1 3
## 99 865 40 110 35 16 1 11 31 1 0 0 1 3
## 100 808 40 97 37 16 10 7 29 1 0 0 1 3
## 101 1299 60 125 44 18 6 12 35 0 0 0 1 1
## 102 903 40 91 39 12 6 12 36 1 0 0 1 5
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## 104 625 40 110 32 12 18 0 35 1 0 0 1 4
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## 109 1282 45 112 41 16 6 6 31 0 0 1 1 2
## 110 770 48 91 39 12 13 2 38 1 0 0 1 1
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## 115 654 50 111 51 13 5 16 38 1 0 0 1 3
## 116 601 48 111 30 12 15 3 33 1 0 0 1 0
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## 118 433 40 98 28 12 11 10 30 0 0 0 1 1
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## 142 480 40 59 28 10 11 5 34 0 0 0 1 0
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## 144 513 45 119 30 17 8 5 31 0 0 0 1 1
## 145 1105 40 93 36 11 17 16 37 0 0 0 1 2
## 146 1193 50 82 38 12 19 10 36 1 0 1 1 0
## 147 2771 50 134 45 18 6 7 34 1 0 0 1 4
## 148 779 40 84 29 12 9 6 30 1 0 0 1 0
## 149 950 60 98 36 11 13 6 31 1 0 0 1 2
## 150 1394 40 118 41 16 11 8 30 1 0 0 0 2
## 151 1495 45 113 50 17 13 9 33 1 0 0 1 3
## 152 650 40 100 18 12 4 3 28 1 0 0 1 6
## 153 670 40 93 27 13 9 5 29 1 0 0 1 2
## 154 1126 40 119 30 16 5 8 32 1 0 0 1 1
## 155 450 64 67 19 12 11 1 33 0 1 0 1 6
## 156 1028 40 111 28 12 19 12 37 1 1 1 1 3
## 157 2404 50 106 38 15 8 0 32 1 0 0 1 2
## 158 1899 40 127 49 18 9 14 36 0 0 0 1 0
## 159 757 40 113 35 16 10 9 33 1 0 0 1 2
## 160 1250 40 115 36 14 9 1 29 1 0 0 1 2
## 161 1162 48 102 40 16 8 11 31 1 0 0 1 3
## 162 1025 40 85 29 15 9 13 29 1 1 0 1 6
## 163 1100 50 117 51 16 11 12 32 1 0 0 0 0
## 164 714 35 125 34 16 7 5 28 1 0 0 1 4
## 165 1318 35 118 47 16 16 17 37 1 0 0 0 1
## 166 1411 45 121 40 18 14 3 38 1 0 0 1 3
## 167 2162 40 115 51 17 4 4 38 1 0 0 1 1
## 168 1273 55 120 44 14 11 16 36 1 0 0 0 1
## 169 1140 48 109 43 12 16 15 35 1 0 0 1 2
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## 173 750 40 106 32 14 9 9 29 1 0 0 1 1
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## 644 2 12 8 7.234177
## 645 1 12 16 7.338888
## 646 5 17 18 7.050990
## 647 4 8 4 6.869014
## 648 2 8 NA 6.582025
## 649 3 10 11 6.173786
## 650 2 17 12 6.694562
## 651 1 12 12 7.273787
## 652 1 12 NA 6.994850
## 653 1 12 NA 5.857933
## 654 1 7 NA 6.214608
## 655 2 16 14 6.933423
## 656 2 13 16 6.357842
## 657 2 12 12 7.195187
## 658 NA 10 NA 6.818924
## 659 1 11 10 7.007601
## 660 NA 9 3 6.813445
## 661 7 1 4 6.907755
## 662 6 3 4 7.056175
## 663 8 3 4 6.908755
## 664 4 NA NA 6.569481
## 665 1 12 12 6.834109
## 666 1 6 2 5.991465
## 667 3 12 12 7.123673
## 668 1 12 NA 6.970730
## 669 NA 12 12 5.998937
## 670 2 NA NA 6.845880
## 671 2 8 3 6.699501
## 672 NA 6 10 6.551080
## 673 NA NA NA 6.354370
## 674 6 12 12 6.109248
## 675 3 8 6 6.431331
## 676 4 8 6 6.089045
## 677 1 NA NA 6.437752
## 678 2 6 NA 6.587550
## 679 6 6 NA 6.214608
## 680 1 17 18 6.907755
## 681 1 8 7 5.973810
## 682 2 9 12 6.396930
## 683 1 6 NA 6.869014
## 684 1 10 8 6.869014
## 685 4 0 10 6.762730
## 686 1 16 14 7.050990
## 687 1 4 14 7.234177
## 688 2 NA NA 6.595780
## 689 3 8 8 6.762730
## 690 6 8 4 6.551080
## 691 NA 5 4 6.882438
## 692 3 12 12 7.170120
## 693 1 12 12 6.802395
## 694 5 8 8 6.720220
## 695 NA 12 NA 6.907755
## 696 1 16 12 6.717805
## 697 NA 12 NA 6.214608
## 698 2 12 12 7.051856
## 699 NA 12 12 6.856462
## 700 5 8 NA 6.551080
## 701 1 12 NA 7.444249
## 702 1 11 12 6.278522
## 703 1 12 12 7.602901
## 704 2 7 7 6.791222
## 705 2 12 12 8.032035
## 706 2 12 16 7.338888
## 707 NA NA NA 6.230482
## 708 1 16 16 7.210818
## 709 1 12 12 7.041412
## 710 1 10 10 6.869014
## 711 1 12 12 7.130899
## 712 1 8 8 6.897705
## 713 5 12 12 6.807935
## 714 5 0 2 6.830874
## 715 4 8 8 7.351800
## 716 1 12 8 7.179308
## 717 1 7 NA 6.827629
## 718 2 13 13 6.778785
## 719 1 12 10 6.684612
## 720 3 12 10 6.955593
## 721 4 12 10 6.309918
## 722 1 12 14 7.081708
## 723 1 12 12 6.368187
## 724 1 6 7 7.090077
## 725 2 14 17 6.680855
## 726 2 16 12 7.223296
## 727 NA 12 8 5.886104
## 728 2 12 12 7.146772
## 729 2 8 12 7.513164
## 730 3 12 7 6.812345
## 731 3 12 12 7.465083
## 732 5 12 12 6.253829
## 733 6 12 12 6.694562
## 734 3 12 NA 7.667158
## 735 1 8 8 6.539586
## 736 2 12 12 6.836259
## 737 2 12 8 6.699501
## 738 1 12 12 6.763885
## 739 5 12 12 7.273787
## 740 2 11 6 6.214608
## 741 1 12 13 7.232733
## 742 5 12 12 6.269096
## 743 3 12 NA 6.781058
## 744 1 14 17 6.933423
## 745 NA 12 10 7.100027
## 746 2 10 NA 7.390182
## 747 2 12 NA 7.519150
## 748 2 12 12 7.379008
## 749 2 8 14 6.907755
## 750 4 10 NA 6.602588
## 751 3 12 12 7.437795
## 752 2 12 8 7.437795
## 753 3 NA 12 6.932448
## 754 3 11 12 7.009409
## 755 4 12 12 6.437752
## 756 2 11 11 6.579251
## 757 2 12 12 6.751101
## 758 2 12 12 7.130899
## 759 2 18 15 7.029973
## 760 NA 13 13 6.802395
## 761 1 4 NA 7.562161
## 762 1 12 16 6.869014
## 763 NA NA NA 7.535830
## 764 3 11 8 7.360740
## 765 2 12 10 6.845880
## 766 2 12 12 6.802395
## 767 3 8 10 6.782192
## 768 1 12 12 7.444249
## 769 2 9 8 7.138867
## 770 1 10 8 6.621406
## 771 1 12 11 7.000334
## 772 6 12 NA 6.908755
## 773 1 12 9 7.050990
## 774 4 12 8 6.907755
## 775 NA 6 2 7.130899
## 776 1 8 8 6.753438
## 777 2 16 12 7.099202
## 778 NA 16 12 6.842683
## 779 NA 12 NA 6.806829
## 780 1 12 18 6.770790
## 781 3 NA 8 7.090077
## 782 1 6 8 7.139660
## 783 1 8 2 6.856462
## 784 6 10 11 4.744932
## 785 5 16 12 6.511745
## 786 2 16 16 6.988413
## 787 1 15 9 6.964136
## 788 6 7 8 6.684612
## 789 4 NA NA 5.910797
## 790 1 12 NA 7.562161
## 791 1 7 6 6.751101
## 792 1 12 12 6.761573
## 793 4 13 13 6.995766
## 794 NA 10 12 6.932448
## 795 2 17 NA 6.745236
## 796 2 12 12 6.511745
## 797 2 10 12 6.684612
## 798 3 10 12 6.955593
## 799 2 14 9 6.784457
## 800 3 12 8 6.684612
## 801 1 8 8 7.090077
## 802 6 12 12 6.498282
## 803 3 NA NA 7.013016
## 804 2 NA NA 6.745236
## 805 2 8 12 6.907755
## 806 NA 14 14 6.774224
## 807 2 12 12 7.091742
## 808 3 12 12 6.501290
## 809 1 12 7 6.827629
## 810 5 10 3 6.669498
## 811 9 NA 6 6.856462
## 812 4 NA NA 7.273787
## 813 5 6 0 6.763885
## 814 7 4 NA 6.437752
## 815 1 6 7 6.522093
## 816 2 12 8 6.541030
## 817 9 6 NA 6.774224
## 818 1 12 13 7.744137
## 819 3 10 6 7.086738
## 820 NA 2 8 6.551080
## 821 2 12 4 6.580639
## 822 3 12 8 7.313221
## 823 1 16 9 6.956545
## 824 1 NA NA 6.685861
## 825 NA NA NA 6.461468
## 826 2 12 12 7.088409
## 827 NA 16 13 5.966147
## 828 2 9 12 6.790097
## 829 1 12 9 6.981006
## 830 2 14 12 7.027315
## 831 1 12 9 6.620073
## 832 1 NA 12 6.751101
## 833 1 10 12 6.263398
## 834 2 10 12 7.006695
## 835 2 8 9 6.315358
## 836 1 10 10 6.684612
## 837 1 13 14 7.232733
## 838 1 14 12 6.052089
## 839 6 2 10 6.234411
## 840 2 3 4 5.913503
## 841 8 2 8 6.390241
## 842 2 NA 10 5.996452
## 843 1 9 10 6.035481
## 844 1 12 NA 7.032624
## 845 NA 9 10 6.523562
## 846 4 10 6 6.856462
## 847 1 5 6 6.396930
## 848 2 NA 5 6.493754
## 849 2 6 NA 6.829794
## 850 1 5 5 6.309918
## 851 4 3 7 6.406880
## 852 4 3 7 6.052089
## 853 3 8 18 5.828946
## 854 2 7 5 6.539586
## 855 2 8 12 6.354370
## 856 1 8 6 6.347389
## 857 2 0 5 6.705639
## 858 2 12 12 6.894670
## 859 5 9 NA 6.423247
## 860 1 14 10 6.933423
## 861 2 8 7 6.694562
## 862 2 15 15 6.694562
## 863 1 12 12 6.669498
## 864 1 12 9 6.745236
## 865 NA 3 2 6.802395
## 866 3 8 8 7.257003
## 867 3 NA NA 5.560682
## 868 1 5 5 6.495265
## 869 1 12 11 6.331502
## 870 NA 12 12 6.331502
## 871 7 NA NA 5.877736
## 872 1 12 10 6.916715
## 873 1 9 12 7.273787
## 874 7 10 11 6.478509
## 875 NA 3 NA 6.620073
## 876 1 10 NA 6.625392
## 877 3 NA NA 6.551080
## 878 NA 9 9 6.220590
## 879 2 12 9 6.842683
## 880 3 10 6 6.436151
## 881 1 10 6 6.620073
## 882 2 10 6 6.802395
## 883 NA 10 7 6.291569
## 884 10 4 10 6.464588
## 885 NA 12 NA 5.991465
## 886 3 12 10 6.802395
## 887 2 12 10 6.240276
## 888 8 9 8 6.795706
## 889 2 12 18 7.156177
## 890 3 12 18 6.184149
## 891 2 10 13 5.783825
## 892 1 7 7 6.645091
## 893 8 7 4 6.426488
## 894 7 7 3 6.946976
## 895 3 8 3 6.621406
## 896 1 7 7 5.940171
## 897 1 3 NA 5.703783
## 898 2 12 7 6.624065
## 899 3 11 12 6.970730
## 900 2 14 12 6.975414
## 901 1 14 18 7.360740
## 902 1 12 9 6.476973
## 903 2 10 10 6.551080
## 904 NA NA NA 6.202536
## 905 1 NA NA 6.791222
## 906 1 6 NA 6.253829
## 907 5 12 9 6.792345
## 908 3 12 NA 6.345636
## 909 1 11 9 7.275172
## 910 3 NA NA 6.175867
## 911 NA 12 7 6.214608
## 912 2 12 14 7.295056
## 913 4 10 12 6.688354
## 914 1 12 12 6.869014
## 915 1 11 NA 6.907755
## 916 1 12 12 6.396930
## 917 3 8 8 6.109248
## 918 3 10 6 6.444131
## 919 NA 8 NA 6.198479
## 920 1 12 13 7.353722
## 921 2 13 16 5.877736
## 922 NA 10 NA 6.866933
## 923 2 12 12 6.338594
## 924 2 12 8 6.175867
## 925 2 8 8 7.273787
## 926 7 7 8 6.469250
## 927 NA 9 NA 6.669498
## 928 3 12 NA 6.467699
## 929 3 7 7 6.167517
## 930 4 16 16 6.498282
## 931 1 11 NA 6.253829
## 932 7 8 6 7.091742
## 933 NA 7 NA 6.287858
## 934 1 NA 11 6.771935
## 935 1 NA NA 6.907755
## (i) Estimate the model
# Fit the regression model
model <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2)
# Print the regression results
summary(model)
##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16
## (ii) Add the variables exper and tenure? to the equation and show that they are jointly insignificant at even the 20% level.
# Extend the model with exper and tenure
extended_model <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban + exper + tenure, data = wage2)
# Test joint insignificance of exper and tenure
anova(model, extended_model)
## Analysis of Variance Table
##
## Model 1: log(wage) ~ educ + exper + tenure + married + black + south +
## urban
## Model 2: log(wage) ~ educ + exper + tenure + married + black + south +
## urban + exper + tenure
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 927 123.82
## 2 927 123.82 0 0
## (iii) Extend the original model to allow the return to education to depend on race and test whether the return to education does depend on race.
# Extend the original model to allow the return to education to depend on race
extended_model_race <- lm(log(wage) ~ educ * black + exper + tenure + married + south + urban, data = wage2)
# Test whether the return to education depends on race
summary(extended_model_race)
##
## Call:
## lm(formula = log(wage) ~ educ * black + exper + tenure + married +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.97782 -0.21832 0.00475 0.24136 1.23226
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.374817 0.114703 46.859 < 2e-16 ***
## educ 0.067115 0.006428 10.442 < 2e-16 ***
## black 0.094809 0.255399 0.371 0.710561
## exper 0.013826 0.003191 4.333 1.63e-05 ***
## tenure 0.011787 0.002453 4.805 1.80e-06 ***
## married 0.198908 0.039047 5.094 4.25e-07 ***
## south -0.089450 0.026277 -3.404 0.000692 ***
## urban 0.183852 0.026955 6.821 1.63e-11 ***
## educ:black -0.022624 0.020183 -1.121 0.262603
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3654 on 926 degrees of freedom
## Multiple R-squared: 0.2536, Adjusted R-squared: 0.2471
## F-statistic: 39.32 on 8 and 926 DF, p-value: < 2.2e-16
# (iv) What is the estimated wage differential between married blacks and married nonblacks?
wage2$educ <- ifelse(is.na(wage2$educ), mean(wage2$educ, na.rm = TRUE), wage2$educ)
# Fit the original model after handling missing values
model_original <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2)
# Print the regression results
summary(model_original)
##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16
# Allow wages to differ across four groups
model_groups <- lm(log(wage) ~ educ + exper + tenure + married * black + south + urban, data = wage2)
# Extract estimated wage differential between married blacks and married nonblacks
married_black_diff <- coef(model_groups)["marriedTRUE:blackTRUE"]
# Print the result
married_black_diff
## <NA>
## NA
#Chapter 8
#1
#Which of the following are consequences of heteroskedasticity?
# (i) The OLS estimators, b^ j, are inconsistent.
# (ii) The usual F statistic no longer has an F distribution.
# (iii) The OLS estimators are no longer BLUE.
# All three statements are consequences of heteroskedasticity. It is important to detect and address heteroskedasticity to obtain valid and efficient inference in regression analysis. Common remedies include using heteroskedasticity-robust standard errors or transforming the data to stabilize the variance.
#5
# (i) Comparison of usual and robust standard errors
# Assuming the provided standard errors are listed in parentheses (usual) and brackets (robust)
# Check the differences in standard errors using the model output
# (ii) Impact of education on estimated probability of smoking
# Calculate the change in estimated probability when education increases by four years
change_education <- -0.029 * 4 # Assuming 'educ' coefficient as -0.029
# (iii) Impact of age on probability of smoking
# Calculate the age at which another year decreases the probability of smoking
age_effect <- 0.020 / (2 * 0.00026) # Coefficient of 'age' / (2 * coefficient of 'age²')
# (iv) Interpretation of the 'restaurn' coefficient
# The coefficient on 'restaurn' represents the change in the probability of smoking for someone residing in a state with restaurant smoking restrictions compared to someone in a state without restrictions, holding other variables constant.
# (v) Predicted probability of smoking for person number 206
# Define the characteristics of person number 206
cigpric_206 <- 67.44
income_206 <- 6500
educ_206 <- 16
age_206 <- 77
restaurn_206 <- 0
white_206 <- 0
# Calculate the predicted probability of smoking for person number 206 using the provided model coefficients
predicted_smoking_206 <- 0.656 - 0.069 * log(cigpric_206) + 0.012 * log(income_206) - 0.029 * educ_206 + 0.020 * age_206 - 0.00026 * age_206^2 - 0.101 * restaurn_206 - 0.026 * white_206
# Display the results
cat("Change in estimated probability for a 4-year increase in education:", change_education, "\n")
## Change in estimated probability for a 4-year increase in education: -0.116
cat("Age at which another year reduces probability of smoking:", age_effect, "\n")
## Age at which another year reduces probability of smoking: 38.46154
cat("Predicted probability of smoking for person 206:", predicted_smoking_206, "\n")
## Predicted probability of smoking for person 206: 0.005239246
#C4
# Load necessary libraries
library(wooldridge)
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(sandwich)
# Load the dataset
data.frame("vote1")
## X.vote1.
## 1 vote1
# (i) Estimate a model and obtain OLS residuals
model_voteA <- lm(voteA ~ prtystrA + democA + log(expendA) + log(expendB), data = vote1)
residuals_voteA <- resid(model_voteA)
# Regress residuals on independent variables
residuals_model <- lm(residuals_voteA ~ prtystrA + democA + log(expendA) + log(expendB), data = vote1)
# Obtain summary to explain R-squared = 0
summary(residuals_model)
##
## Call:
## lm(formula = residuals_voteA ~ prtystrA + democA + log(expendA) +
## log(expendB), data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.576 -4.864 -1.146 4.903 24.566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.029e-15 4.736e+00 0 1
## prtystrA 3.001e-17 7.129e-02 0 1
## democA -2.151e-15 1.407e+00 0 1
## log(expendA) 7.193e-17 3.918e-01 0 1
## log(expendB) -1.305e-15 3.975e-01 0 1
##
## Residual standard error: 7.573 on 168 degrees of freedom
## Multiple R-squared: 8.097e-32, Adjusted R-squared: -0.02381
## F-statistic: 3.401e-30 on 4 and 168 DF, p-value: 1
# (ii) Compute Breusch-Pagan test for heteroskedasticity (F statistic version)
bptest_model <- lm(residuals_voteA^2 ~ prtystrA + democA + log(expendA) + log(expendB), data = vote1)
summary(bptest_model)
##
## Call:
## lm(formula = residuals_voteA^2 ~ prtystrA + democA + log(expendA) +
## log(expendB), data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -94.88 -46.16 -23.51 15.84 508.32
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 113.9635 50.8150 2.243 0.0262 *
## prtystrA -0.2993 0.7649 -0.391 0.6961
## democA 15.6192 15.0912 1.035 0.3022
## log(expendA) -10.3057 4.2040 -2.451 0.0153 *
## log(expendB) -0.0514 4.2645 -0.012 0.9904
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 81.25 on 168 degrees of freedom
## Multiple R-squared: 0.05256, Adjusted R-squared: 0.03
## F-statistic: 2.33 on 4 and 168 DF, p-value: 0.05806
# (iii) Compute White test for heteroskedasticity (F statistic form)
bptest(model_voteA, studentize = FALSE)
##
## Breusch-Pagan test
##
## data: model_voteA
## BP = 9.9195, df = 4, p-value = 0.04181
#C13
library(sandwich)
library(lmtest)
# Assuming 'children', 'age', 'age_squared', 'educ', 'electric', 'urban' are columns in the dataset
model <- lm(children ~ age + I(age^2) + educ + electric + urban, data = fertil2)
# Calculate robust standard errors
robust_se <- sqrt(diag(vcovHC(model)))
# Combine non-robust and robust standard errors
summary_with_robust_se <- cbind(coef(model), "Robust SE" = robust_se)
summary(model)
##
## Call:
## lm(formula = children ~ age + I(age^2) + educ + electric + urban,
## data = fertil2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.9012 -0.7136 -0.0039 0.7119 7.4318
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.2225162 0.2401888 -17.580 < 2e-16 ***
## age 0.3409255 0.0165082 20.652 < 2e-16 ***
## I(age^2) -0.0027412 0.0002718 -10.086 < 2e-16 ***
## educ -0.0752323 0.0062966 -11.948 < 2e-16 ***
## electric -0.3100404 0.0690045 -4.493 7.20e-06 ***
## urban -0.2000339 0.0465062 -4.301 1.74e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.452 on 4352 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.5734, Adjusted R-squared: 0.5729
## F-statistic: 1170 on 5 and 4352 DF, p-value: < 2.2e-16
print(summary_with_robust_se)
## Robust SE
## (Intercept) -4.222516228 0.2443961935
## age 0.340925520 0.0192199445
## I(age^2) -0.002741209 0.0003513959
## educ -0.075232323 0.0063159137
## electric -0.310040409 0.0640737262
## urban -0.200033857 0.0455162364
# Assuming 'relig1', 'relig2', and 'relig3' are the religious dummy variables in the dataset
joint_test <- coeftest(model, vcov = vcovHC)
print(joint_test[, "Pr(>|t|)"])
## (Intercept) age I(age^2) educ electric urban
## 9.635281e-65 5.015759e-68 7.640643e-15 3.247461e-32 1.351408e-06 1.135260e-05
# Obtain fitted values and residuals
fitted_values <- fitted(model)
residuals <- resid(model)
# Regression of residuals on fitted values
hetero_test <- lm(residuals^2 ~ fitted_values)
summary(hetero_test)
##
## Call:
## lm(formula = residuals^2 ~ fitted_values)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.336 -1.897 -0.321 0.682 49.275
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.54042 0.09451 -5.718 1.15e-08 ***
## fitted_values 1.16693 0.03347 34.863 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.717 on 4356 degrees of freedom
## Multiple R-squared: 0.2182, Adjusted R-squared: 0.218
## F-statistic: 1215 on 1 and 4356 DF, p-value: < 2.2e-16
#Chapter 9
# 1.) Problem 11 in Chapter 4:
data.frame(ceosal2)
## salary age college grad comten ceoten sales profits mktval lsalary
## 1 1161 49 1 1 9 2 6200 966 23200 7.057037
## 2 600 43 1 1 10 10 283 48 1100 6.396930
## 3 379 51 1 1 9 3 169 40 1100 5.937536
## 4 651 55 1 0 22 22 1100 -54 1000 6.478509
## 5 497 44 1 1 8 6 351 28 387 6.208590
## 6 1067 64 1 1 7 7 19000 614 3900 6.972606
## 7 945 59 1 0 35 10 536 24 623 6.851185
## 8 1261 63 1 1 32 8 4800 191 2100 7.139660
## 9 503 47 1 1 4 4 610 7 454 6.220590
## 10 1094 64 1 1 39 5 2900 230 3900 6.997596
## 11 601 54 1 1 26 7 1200 34 533 6.398595
## 12 355 66 1 0 39 8 560 8 477 5.872118
## 13 1200 72 1 0 37 37 796 35 678 7.090077
## 14 697 51 1 0 25 1 8200 234 5700 6.546785
## 15 1041 63 1 1 21 11 4300 91 1400 6.947937
## 16 245 44 1 1 7 7 135 24 558 5.501258
## 17 817 68 1 0 38 4 1300 55 847 6.705639
## 18 1675 71 0 0 31 12 674 115 1200 7.423568
## 19 971 72 1 1 33 24 1400 69 609 6.878326
## 20 609 58 1 0 36 1 1100 69 880 6.411819
## 21 470 60 1 1 20 6 2300 210 2200 6.152733
## 22 867 59 1 0 36 14 884 81 1500 6.765039
## 23 752 54 1 0 32 4 1600 193 3200 6.622736
## 24 246 51 1 0 8 8 78 13 458 5.505332
## 25 825 56 1 1 4 4 10700 295 5900 6.715384
## 26 358 50 1 1 23 4 99 25 2300 5.880533
## 27 1162 58 1 0 24 6 3800 226 1800 7.057898
## 28 270 43 1 0 15 2 150 28 713 5.598422
## 29 829 56 1 0 14 8 2200 184 1500 6.720220
## 30 300 77 0 0 45 26 6900 483 4700 5.703783
## 31 1627 62 1 1 13 4 8300 596 9100 7.394493
## 32 1237 63 1 1 37 9 4600 108 6200 7.120444
## 33 540 61 1 1 37 1 5200 549 5600 6.291569
## 34 1798 66 1 1 21 14 24300 338 12500 7.494430
## 35 474 40 1 0 18 1 2700 117 2000 6.161207
## 36 1336 60 1 1 21 13 4500 562 4300 7.197435
## 37 541 51 1 0 30 4 1400 82 1200 6.293419
## 38 129 66 1 1 4 4 59 28 412 4.859812
## 39 1700 54 1 1 21 5 6800 1200 20400 7.438384
## 40 1750 66 1 1 31 24 16200 1400 17900 7.467371
## 41 624 61 1 1 21 13 1100 109 934 6.436151
## 42 791 66 1 0 14 8 2300 -60 487 6.673298
## 43 1487 51 1 0 3 3 22200 182 2800 7.304516
## 44 2021 56 1 0 34 3 51300 2700 42900 7.611348
## 45 1550 47 1 1 19 3 1100 120 4900 7.346010
## 46 401 64 1 0 44 8 571 57 670 5.993961
## 47 1295 62 1 0 8 8 10700 1300 16400 7.166266
## 48 449 56 1 0 31 1 661 37 538 6.107023
## 49 456 56 1 1 9 3 381 34 6700 6.122493
## 50 1142 53 1 1 30 1 28000 1900 26300 7.040536
## 51 577 64 1 0 26 2 3000 287 5700 6.357842
## 52 600 56 1 1 18 7 11700 -40 4000 6.396930
## 53 649 44 1 1 4 4 336 17 475 6.475433
## 54 822 60 1 0 22 20 896 77 752 6.711740
## 55 1080 52 1 0 18 5 388 55 1600 6.984716
## 56 1738 54 0 0 34 12 10700 842 15400 7.460490
## 57 581 54 1 0 19 19 408 23 403 6.364751
## 58 912 54 1 0 9 9 2600 239 2400 6.815640
## 59 650 69 1 0 37 13 261 40 817 6.476973
## 60 2199 52 1 1 8 8 5600 475 6300 7.695758
## 61 609 53 1 1 15 15 567 34 498 6.411819
## 62 1946 73 1 0 25 21 7800 484 8000 7.573531
## 63 552 52 1 0 30 1 2800 308 3500 6.313548
## 64 481 59 1 1 26 4 611 90 667 6.175867
## 65 526 45 1 0 8 7 2400 106 2000 6.265301
## 66 471 60 1 0 3 2 160 7 425 6.154858
## 67 630 56 1 0 29 1 1700 -55 420 6.445720
## 68 622 57 1 0 35 4 2500 143 1200 6.432940
## 69 999 52 1 0 28 17 159 21 398 6.906755
## 70 585 60 1 1 36 10 1700 33 449 6.371612
## 71 1107 57 1 0 17 6 2200 149 1100 7.009409
## 72 1099 59 1 0 34 10 8600 182 1800 7.002156
## 73 425 86 1 1 13 13 36 11 644 6.052089
## 74 2792 40 1 0 11 11 534 35 888 7.934514
## 75 350 54 1 0 31 4 1000 46 812 5.857933
## 76 363 58 1 1 36 6 717 80 880 5.894403
## 77 2265 63 1 1 35 6 18000 1700 18800 7.725330
## 78 377 45 1 0 7 5 238 57 1200 5.932245
## 79 879 63 1 1 21 9 1700 212 4900 6.778785
## 80 720 49 1 0 12 12 672 23 1400 6.579251
## 81 950 63 1 0 27 14 2600 6 1500 6.856462
## 82 1143 67 0 0 23 3 1800 56 918 7.041412
## 83 1064 58 1 0 27 3 3500 195 2600 6.969790
## 84 1253 60 1 1 36 5 2600 142 3700 7.133296
## 85 462 58 1 1 23 0 1400 50 769 6.135565
## 86 174 69 1 0 13 13 29 6 390 5.159055
## 87 474 63 1 0 41 4 2200 175 2600 6.161207
## 88 1248 48 1 1 21 7 3500 423 7300 7.129298
## 89 1101 62 1 1 32 3 954 96 1200 7.003974
## 90 348 43 1 1 12 10 586 79 1400 5.852202
## 91 650 55 1 1 28 5 5700 -438 817 6.476973
## 92 875 58 1 1 32 10 5300 308 2200 6.774224
## 93 1600 61 1 0 4 1 12300 877 9400 7.377759
## 94 1500 55 1 1 30 4 7900 665 4800 7.313221
## 95 323 39 1 1 15 3 637 63 517 5.777652
## 96 459 59 1 0 33 3 785 40 1400 6.129050
## 97 925 56 1 1 26 12 3300 67 2200 6.829794
## 98 375 46 1 1 4 4 599 20 501 5.926926
## 99 447 53 1 0 4 1 143 16 527 6.102559
## 100 1340 55 1 0 13 10 1400 131 2900 7.200425
## 101 1749 57 1 1 26 11 8100 40 10000 7.466799
## 102 491 43 1 1 21 2 561 54 521 6.196444
## 103 5299 64 1 0 42 13 2400 119 1500 8.575274
## 104 431 58 1 1 33 3 815 36 550 6.066108
## 105 729 50 1 1 15 3 2000 182 2600 6.591674
## 106 1284 54 1 1 32 3 12300 1300 19600 7.157735
## 107 1373 57 1 0 36 8 14300 1600 23600 7.224753
## 108 989 40 1 0 18 5 439 30 582 6.896694
## 109 515 52 1 1 27 1 1100 51 889 6.244167
## 110 1301 50 1 1 19 15 1800 130 1600 7.170888
## 111 834 58 1 0 35 1 4400 63 890 6.726233
## 112 849 46 1 1 24 24 538 36 473 6.744059
## 113 100 61 1 1 26 26 2700 394 10100 4.605170
## 114 679 62 1 0 40 6 4900 -463 1400 6.520621
## 115 567 56 1 0 31 10 597 65 1700 6.340359
## 116 559 54 1 0 22 2 2100 13 686 6.326149
## 117 704 52 1 1 6 6 50 8 903 6.556778
## 118 308 45 1 1 14 14 210 39 1900 5.730100
## 119 1392 48 1 1 6 6 4800 51 1100 7.238497
## 120 389 55 1 0 29 4 478 38 420 5.963579
## 121 790 69 1 0 45 37 1200 140 3200 6.672033
## 122 396 80 1 0 58 28 513 53 963 5.981414
## 123 398 54 1 0 4 4 633 69 1800 5.986452
## 124 707 46 1 1 6 1 130 26 1200 6.561031
## 125 984 60 1 0 7 4 1500 135 1700 6.891626
## 126 410 55 1 0 36 20 501 34 590 6.016157
## 127 1095 60 1 1 33 5 27600 1400 17100 6.998509
## 128 694 61 1 1 35 19 4200 75 1000 6.542472
## 129 834 61 1 1 32 0 7600 364 5300 6.726233
## 130 1630 39 1 1 8 8 227 27 822 7.396335
## 131 493 55 1 1 4 1 1300 80 834 6.200509
## 132 625 57 0 0 36 9 1400 87 979 6.437752
## 133 483 52 1 1 18 14 1000 35 548 6.180017
## 134 733 60 1 0 8 8 347 18 778 6.597146
## 135 2102 67 1 1 41 20 10300 1700 45400 7.650645
## 136 853 58 1 0 34 34 818 33 411 6.748760
## 137 345 54 1 1 33 0 994 56 781 5.843544
## 138 800 57 1 1 12 9 1800 32 479 6.684612
## 139 764 55 1 1 31 16 1100 145 2100 6.638568
## 140 806 59 1 1 3 3 3000 257 3900 6.692084
## 141 310 40 1 0 18 1 2400 60 1300 5.736572
## 142 1119 61 1 0 34 9 2500 71 1200 7.020191
## 143 1287 59 1 1 4 3 4700 222 2700 7.160069
## 144 1170 57 1 1 9 3 1900 208 5600 7.064759
## 145 880 62 1 0 36 12 5300 229 4000 6.779922
## 146 1091 33 1 0 9 9 181 36 1300 6.994850
## 147 1100 65 1 0 18 6 563 -271 544 7.003066
## 148 650 53 1 1 5 4 1482 40 557 6.476973
## 149 607 38 1 1 7 3 231 38 599 6.408529
## 150 1133 63 1 0 9 9 870 37 686 7.032624
## 151 393 58 1 1 36 6 285 40 956 5.973810
## 152 605 53 1 0 16 4 422 30 505 6.405229
## 153 1444 59 1 1 2 2 6204 401 10700 7.275172
## 154 1033 62 1 1 30 1 5400 478 7300 6.940222
## 155 1142 50 1 1 11 3 2600 166 2200 7.040536
## 156 537 46 1 1 20 20 1200 17 669 6.285998
## 157 693 42 1 0 17 12 1400 206 3000 6.541030
## 158 439 57 1 1 26 12 2600 280 3800 6.084499
## 159 358 64 1 0 43 11 584 45 423 5.880533
## 160 1276 64 1 0 41 17 635 52 1300 7.151485
## 161 873 41 1 1 2 2 149 21 567 6.771935
## 162 537 57 1 1 35 1 11400 210 4800 6.285998
## 163 713 57 1 1 12 2 1600 55 1300 6.569481
## 164 1350 68 1 1 5 5 3300 92 2100 7.207860
## 165 1268 47 1 0 20 4 1100 47 2500 7.145196
## 166 465 64 1 1 31 3 2400 326 2400 6.142037
## 167 693 46 1 1 7 3 2200 44 533 6.541030
## 168 369 49 1 1 4 1 65 -132 1200 5.910797
## 169 381 54 1 0 30 2 2700 386 4500 5.942800
## 170 467 49 1 1 13 0 513 49 534 6.146329
## 171 559 57 1 1 34 16 605 56 653 6.326149
## 172 218 57 1 1 33 5 504 41 421 5.384495
## 173 264 63 1 0 42 3 334 43 480 5.575949
## 174 185 58 1 0 39 1 766 49 560 5.220356
## 175 387 71 1 1 32 13 432 28 477 5.958425
## 176 2220 63 1 1 18 18 277 -80 540 7.705263
## 177 445 69 1 0 23 0 249 31 828 6.098074
## lsales lmktval comtensq ceotensq profmarg
## 1 8.732305 10.051908 81 4 15.5806456
## 2 5.645447 7.003066 100 100 16.9611301
## 3 5.129899 7.003066 81 9 23.6686382
## 4 7.003066 6.907755 484 484 -4.9090910
## 5 5.860786 5.958425 64 36 7.9772081
## 6 9.852194 8.268732 49 49 3.2315791
## 7 6.284134 6.434546 1225 100 4.4776120
## 8 8.476371 7.649693 1024 64 3.9791667
## 9 6.413459 6.118097 16 16 1.1475409
## 10 7.972466 8.268732 1521 25 7.9310346
## 11 7.090077 6.278522 676 49 2.8333333
## 12 6.327937 6.167517 1521 64 1.4285715
## 13 6.679599 6.519147 1369 1369 4.3969851
## 14 9.011889 8.648221 625 1 2.8536584
## 15 8.366370 7.244227 441 121 2.1162791
## 16 4.905275 6.324359 49 49 17.7777786
## 17 7.170120 6.741701 1444 16 4.2307692
## 18 6.513230 7.090077 961 144 17.0623150
## 19 7.244227 6.411819 1089 576 4.9285712
## 20 7.003066 6.779922 1296 1 6.2727275
## 21 7.740664 7.696213 400 36 9.1304350
## 22 6.784457 7.313221 1296 196 9.1628962
## 23 7.377759 8.070906 1024 16 12.0625000
## 24 4.356709 6.126869 64 64 16.6666660
## 25 9.277999 8.682708 16 16 2.7570093
## 26 4.595120 7.740664 529 16 25.2525253
## 27 8.242756 7.495542 576 36 5.9473686
## 28 5.010635 6.569481 225 4 18.6666660
## 29 7.696213 7.313221 196 64 8.3636360
## 30 8.839276 8.455317 2025 676 7.0000000
## 31 9.024011 9.116030 169 16 7.1807227
## 32 8.433811 8.732305 1369 81 2.3478260
## 33 8.556414 8.630522 1369 1 10.5576925
## 34 10.098231 9.433484 441 196 1.3909465
## 35 7.901007 7.600903 324 1 4.3333335
## 36 8.411833 8.366370 441 169 12.4888887
## 37 7.244227 7.090077 900 16 5.8571429
## 38 4.077538 6.021023 16 16 47.4576263
## 39 8.824677 9.923290 441 25 17.6470585
## 40 9.692766 9.792556 961 576 8.6419754
## 41 7.003066 6.839477 441 169 9.9090910
## 42 7.740664 6.188264 196 64 -2.6086957
## 43 10.007848 7.937375 9 9 0.8198198
## 44 10.845446 10.666627 1156 9 5.2631578
## 45 7.003066 8.496990 361 9 10.9090910
## 46 6.347389 6.507277 1936 64 9.9824867
## 47 9.277999 9.705036 64 64 12.1495323
## 48 6.493754 6.287858 961 1 5.5975795
## 49 5.942800 8.809863 81 9 8.9238844
## 50 10.239960 10.177324 900 1 6.7857141
## 51 8.006368 8.648221 676 4 9.5666666
## 52 9.367344 8.294049 324 49 -0.3418804
## 53 5.817111 6.163315 16 16 5.0595236
## 54 6.797940 6.622736 484 400 8.5937500
## 55 5.961005 7.377759 324 25 14.1752577
## 56 9.277999 9.642123 1156 144 7.8691587
## 57 6.011267 5.998937 361 361 5.6372547
## 58 7.863267 7.783224 81 81 9.1923075
## 59 5.564520 6.705639 1369 169 15.3256702
## 60 8.630522 8.748305 64 64 8.4821424
## 61 6.340359 6.210600 225 225 5.9964728
## 62 8.961879 8.987197 625 441 6.2051282
## 63 7.937375 8.160519 900 1 11.0000000
## 64 6.415097 6.502790 676 16 14.7299509
## 65 7.783224 7.600903 64 49 4.4166665
## 66 5.075174 6.052089 9 4 4.3750000
## 67 7.438384 6.040255 841 1 -3.2352941
## 68 7.824046 7.090077 1225 16 5.7199998
## 69 5.068904 5.986452 784 289 13.2075472
## 70 7.438384 6.107023 1296 100 1.9411764
## 71 7.696213 7.003066 289 36 6.7727275
## 72 9.059518 7.495542 1156 100 2.1162791
## 73 3.583519 6.467699 169 169 30.5555553
## 74 6.280396 6.788972 121 121 6.5543070
## 75 6.907755 6.699501 961 16 4.5999999
## 76 6.575076 6.779922 1296 36 11.1576014
## 77 9.798127 9.841612 1225 36 9.4444447
## 78 5.472270 7.090077 49 25 23.9495792
## 79 7.438384 8.496990 441 81 12.4705887
## 80 6.510258 7.244227 144 144 3.4226191
## 81 7.863267 7.313221 729 196 0.2307692
## 82 7.495542 6.822197 529 9 3.1111112
## 83 8.160519 7.863267 729 9 5.5714288
## 84 7.863267 8.216088 1296 25 5.4615383
## 85 7.244227 6.645091 529 0 3.5714285
## 86 3.367296 5.966147 169 169 20.6896553
## 87 7.696213 7.863267 1681 16 7.9545455
## 88 8.160519 8.895630 441 49 12.0857143
## 89 6.860664 7.090077 1024 9 10.0628929
## 90 6.373320 7.244227 144 100 13.4812288
## 91 8.648221 6.705639 784 25 -7.6842103
## 92 8.575462 7.696213 1024 100 5.8113208
## 93 9.417355 9.148465 16 1 7.1300812
## 94 8.974618 8.476371 900 16 8.4177217
## 95 6.456769 6.248043 225 9 9.8901100
## 96 6.665684 7.244227 1089 9 5.0955415
## 97 8.101678 7.696213 676 144 2.0303030
## 98 6.395262 6.216606 16 16 3.3388982
## 99 4.962845 6.267200 16 1 11.1888113
## 100 7.244227 7.972466 169 100 9.3571424
## 101 8.999619 9.210340 676 121 0.4938272
## 102 6.329721 6.255750 441 4 9.6256685
## 103 7.783224 7.313221 1764 169 4.9583335
## 104 6.703188 6.309918 1089 9 4.4171777
## 105 7.600903 7.863267 225 9 9.1000004
## 106 9.417355 9.883285 1024 9 10.5691061
## 107 9.568015 10.069002 1296 64 11.1888113
## 108 6.084499 6.366470 324 25 6.8337131
## 109 7.003066 6.790097 729 1 4.6363635
## 110 7.495542 7.377759 361 225 7.2222223
## 111 8.389359 6.791222 1225 1 1.4318181
## 112 6.287858 6.159095 576 576 6.6914496
## 113 7.901007 9.220291 676 676 14.5925922
## 114 8.496990 7.244227 1600 36 -9.4489794
## 115 6.391917 7.438384 961 100 10.8877726
## 116 7.649693 6.530878 484 4 0.6190476
## 117 3.912023 6.805723 36 36 16.0000000
## 118 5.347107 7.549609 196 196 18.5714283
## 119 8.476371 7.003066 36 36 1.0625000
## 120 6.169611 6.040255 841 16 7.9497910
## 121 7.090077 8.070906 2025 1369 11.6666670
## 122 6.240276 6.870053 3364 784 10.3313837
## 123 6.450470 7.495542 16 16 10.9004736
## 124 4.867535 7.090077 36 1 20.0000000
## 125 7.313221 7.438384 49 16 9.0000000
## 126 6.216606 6.380123 1296 400 6.7864270
## 127 10.225571 9.746834 1089 25 5.0724640
## 128 8.342840 6.907755 1225 361 1.7857143
## 129 8.935904 8.575462 1024 0 4.7894735
## 130 5.424950 6.711740 64 64 11.8942728
## 131 7.170120 6.726233 16 1 6.1538463
## 132 7.244227 6.886532 1296 81 6.2142859
## 133 6.907755 6.306275 324 196 3.5000000
## 134 5.849325 6.656726 64 64 5.1873198
## 135 9.239900 10.723268 1681 400 16.5048542
## 136 6.706862 6.018593 1156 1156 4.0342298
## 137 6.901737 6.660575 1089 0 5.6338029
## 138 7.495542 6.171700 144 81 1.7777778
## 139 7.003066 7.649693 961 256 13.1818180
## 140 8.006368 8.268732 9 9 8.5666666
## 141 7.783224 7.170120 324 1 2.5000000
## 142 7.824046 7.090077 1156 81 2.8399999
## 143 8.455317 7.901007 16 9 4.7234044
## 144 7.549609 8.630522 81 9 10.9473686
## 145 8.575462 8.294049 1296 144 4.3207545
## 146 5.198497 7.170120 81 81 19.8895035
## 147 6.333280 6.298949 324 36 -48.1349907
## 148 7.301148 6.322565 25 16 2.6990554
## 149 5.442418 6.395262 49 9 16.4502163
## 150 6.768493 6.530878 81 81 4.2528734
## 151 5.652489 6.862758 1296 36 14.0350876
## 152 6.045005 6.224558 256 16 7.1090050
## 153 8.732949 9.277999 4 4 6.4635720
## 154 8.594154 8.895630 900 1 8.8518515
## 155 7.863267 7.696213 121 9 6.3846154
## 156 7.090077 6.505784 400 400 1.4166666
## 157 7.244227 8.006368 289 144 14.7142859
## 158 7.863267 8.242756 676 144 10.7692308
## 159 6.369901 6.047372 1849 121 7.7054796
## 160 6.453625 7.170120 1681 289 8.1889763
## 161 5.003946 6.340359 4 4 14.0939598
## 162 9.341369 8.476371 1225 1 1.8421053
## 163 7.377759 7.170120 144 4 3.4375000
## 164 8.101678 7.649693 25 25 2.7878788
## 165 7.003066 7.824046 400 16 4.2727275
## 166 7.783224 7.783224 961 9 13.5833330
## 167 7.696213 6.278522 49 9 2.0000000
## 168 4.174387 7.090077 16 1 -203.0769196
## 169 7.901007 8.411833 900 4 14.2962961
## 170 6.240276 6.280396 169 0 9.5516567
## 171 6.405229 6.481577 1156 256 9.2561979
## 172 6.222576 6.042633 1089 25 8.1349211
## 173 5.811141 6.173786 1764 9 12.8742514
## 174 6.641182 6.327937 1521 1 6.3968668
## 175 6.068426 6.167517 1024 169 6.4814816
## 176 5.624018 6.291569 324 324 -28.8808670
## 177 5.517453 6.719013 529 0 12.4497995
# Original model
original_model <- lm(log(salary) ~ log(sales) + log(mktval) + profmarg + ceoten + comten, data = ceosal2)
original_r_squared <- summary(original_model)$r.squared # R-squared for the original model
# Model with additional variables
model_with_additional <- lm(log(salary) ~ log(sales) + log(mktval) + profmarg + ceoten + comten + ceoten^2 + comten^2, data = ceosal2)
additional_r_squared <- summary(model_with_additional)$r.squared # R-squared for the model with additional variables
# Check for change in R-squared to assess functional form misspecification
change_in_r_squared <- additional_r_squared - original_r_squared
if (change_in_r_squared > 0) {
cat("The addition of ceoten² and comten² slightly improved R-squared, indicating a slight improvement in model fit.\n")
} else {
cat("The change in R-squared suggests no significant improvement in model fit with the added variables.\n")
}
## The change in R-squared suggests no significant improvement in model fit with the added variables.
# 5.) Example 4.4:
# Load the 'wooldridge' package
library(wooldridge)
# Load the 'campus' dataset
data.frame("campus")
## X.campus.
## 1 campus
# Given estimated coefficients and standard errors
b0 <- -6.63
se_b0 <- 1.03
b1 <- 1.27
se_b1 <- 0.11
n <- nrow(campus)
# Extracting estimated coefficients from the dataset (if they're not provided)
# b0 <- coef(model)[1] # Replace 'model' with the linear regression model of log(crime) ~ log(enroll)
# se_b0 <- sqrt(diag(vcov(model)))[1] # Standard error of b0
# b1 <- coef(model)[2] # Replace 'model' with the linear regression model of log(crime) ~ log(enroll)
# se_b1 <- sqrt(diag(vcov(model)))[2] # Standard error of b1
# Calculate t-statistic
t_stat <- (b1 - 1) / se_b1
# Degrees of freedom
df <- n - 2
# Calculate critical value at alpha = 0.05
critical_value <- qt(0.95, df)
# Perform the test
if (t_stat > critical_value) {
cat("Reject the null hypothesis H0: B1 = 1 in favor of H1: B1 > 1 at the 5% level.\n")
} else {
cat("Fail to reject the null hypothesis H0: B1 = 1 at the 5% level.\n")
}
## Reject the null hypothesis H0: B1 = 1 in favor of H1: B1 > 1 at the 5% level.
cat("The concept of exogenous sample selection refers to the process where the selection of data points is unrelated to the variables under study. In the context of Example 4.4, the absence of reporting campus crimes by many schools in 1992 could potentially be considered as exogenous sample selection under certain circumstances.\n\n")
## The concept of exogenous sample selection refers to the process where the selection of data points is unrelated to the variables under study. In the context of Example 4.4, the absence of reporting campus crimes by many schools in 1992 could potentially be considered as exogenous sample selection under certain circumstances.
cat("However, whether the failure to report crimes can be viewed as exogenous depends on the reasons behind the non-reporting. If the non-reporting is influenced by factors unrelated to the actual occurrence of crimes on campuses, it could be deemed exogenous. For instance:\n\n")
## However, whether the failure to report crimes can be viewed as exogenous depends on the reasons behind the non-reporting. If the non-reporting is influenced by factors unrelated to the actual occurrence of crimes on campuses, it could be deemed exogenous. For instance:
cat("1. Administrative or Reporting Policies: If colleges didn't report crimes due to administrative or policy reasons, such as lacking standardized reporting systems or confusion about reporting requirements, it might be considered exogenous.\n\n")
## 1. Administrative or Reporting Policies: If colleges didn't report crimes due to administrative or policy reasons, such as lacking standardized reporting systems or confusion about reporting requirements, it might be considered exogenous.
cat("2. Fear of Reputation Damage: Schools might avoid reporting crimes to maintain a positive public image or avoid negative publicity. If this motivation doesn’t correlate with the actual crime rates, it could be seen as exogenous.\n\n")
## 2. Fear of Reputation Damage: Schools might avoid reporting crimes to maintain a positive public image or avoid negative publicity. If this motivation doesn’t correlate with the actual crime rates, it could be seen as exogenous.
cat("However, if non-reporting is correlated with the underlying crime rates (e.g., schools with higher crime rates intentionally not reporting), it may not be considered exogenous. For instance, if higher-crime schools purposefully avoid reporting, this correlation could bias the analysis.\n\n")
## However, if non-reporting is correlated with the underlying crime rates (e.g., schools with higher crime rates intentionally not reporting), it may not be considered exogenous. For instance, if higher-crime schools purposefully avoid reporting, this correlation could bias the analysis.
cat("In summary, whether the failure to report crimes constitutes exogenous sample selection depends on the underlying reasons for non-reporting. If the decision not to report is independent of the actual crime occurrences, it might be viewed as exogenous. Otherwise, it could introduce bias and affect the interpretation of the analysis.\n")
## In summary, whether the failure to report crimes constitutes exogenous sample selection depends on the underlying reasons for non-reporting. If the decision not to report is independent of the actual crime occurrences, it might be viewed as exogenous. Otherwise, it could introduce bias and affect the interpretation of the analysis.
#C4
# Load the 'wooldridge' package
library(wooldridge)
# Load the 'infmrt' dataset
data.frame("infmrt")
## X.infmrt.
## 1 infmrt
# Filter the dataset for the year 1990
infmrt_1990 <- subset(infmrt, year == 1990)
# Re-estimate equation 9.43 including a dummy variable for the observation on the District of Columbia (DC)
model_with_dummy <- lm(infmort ~ log(pcinc) + log(physic) + log(popul) + DC, data = infmrt_1990)
# Print the summary of the model
summary(model_with_dummy)
##
## Call:
## lm(formula = infmort ~ log(pcinc) + log(physic) + log(popul) +
## DC, data = infmrt_1990)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4964 -0.8076 0.0000 0.9358 2.6077
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.9548 12.4195 1.929 0.05994 .
## log(pcinc) -0.5669 1.6412 -0.345 0.73135
## log(physic) -2.7418 1.1908 -2.303 0.02588 *
## log(popul) 0.6292 0.1911 3.293 0.00191 **
## DC 16.0350 1.7692 9.064 8.43e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.246 on 46 degrees of freedom
## Multiple R-squared: 0.691, Adjusted R-squared: 0.6641
## F-statistic: 25.71 on 4 and 46 DF, p-value: 3.146e-11
#Chapter 10
# Load required libraries
library(wooldridge)
# Load the intdef dataset
data.frame(intdef)
## year i3 inf rec out def i3_1 inf_1 def_1 ci3
## 1 1948 1.04 8.1 16.2 11.6 -4.6000004 NA NA NA NA
## 2 1949 1.10 -1.2 14.5 14.3 -0.1999998 1.04 8.1 -4.6000004 0.06000006
## 3 1950 1.22 1.3 14.4 15.6 1.2000008 1.10 -1.2 -0.1999998 0.12000000
## 4 1951 1.55 7.9 16.1 14.2 -1.9000006 1.22 1.3 1.2000008 0.32999992
## 5 1952 1.77 1.9 19.0 19.4 0.3999996 1.55 7.9 -1.9000006 0.22000003
## 6 1953 1.93 0.8 18.7 20.4 1.6999989 1.77 1.9 0.3999996 0.15999997
## 7 1954 0.95 0.7 18.5 18.8 0.2999992 1.93 0.8 1.6999989 -0.97999996
## 8 1955 1.75 -0.4 16.5 17.3 0.7999992 0.95 0.7 0.2999992 0.80000001
## 9 1956 2.66 1.5 17.5 16.5 -1.0000000 1.75 -0.4 0.7999992 0.91000009
## 10 1957 3.27 3.3 17.7 17.0 -0.7000008 2.66 1.5 -1.0000000 0.60999990
## 11 1958 1.84 2.8 17.3 17.9 0.6000004 3.27 3.3 -0.7000008 -1.42999995
## 12 1959 3.41 0.7 16.2 18.8 2.5999985 1.84 2.8 0.6000004 1.57000005
## 13 1960 2.93 1.7 17.8 17.8 0.0000000 3.41 0.7 2.5999985 -0.48000002
## 14 1961 2.38 1.0 17.8 18.4 0.6000004 2.93 1.7 0.0000000 -0.54999995
## 15 1962 2.78 1.0 17.6 18.8 1.1999989 2.38 1.0 0.6000004 0.39999986
## 16 1963 3.16 1.3 17.8 18.6 0.8000011 2.78 1.0 1.1999989 0.38000011
## 17 1964 3.55 1.3 17.6 18.5 0.8999996 3.16 1.3 0.8000011 0.38999987
## 18 1965 3.95 1.6 17.0 17.2 0.2000008 3.55 1.3 0.8999996 0.40000010
## 19 1966 4.88 2.9 17.3 17.8 0.5000000 3.95 1.6 0.2000008 0.93000007
## 20 1967 4.32 3.1 18.4 19.4 1.0000000 4.88 2.9 0.5000000 -0.55999994
## 21 1968 5.34 4.2 17.6 20.5 2.8999996 4.32 3.1 1.0000000 1.01999998
## 22 1969 6.68 5.5 19.7 19.4 -0.3000011 5.34 4.2 2.8999996 1.33999968
## 23 1970 6.46 5.7 19.0 19.3 0.2999992 6.68 5.5 -0.3000011 -0.21999979
## 24 1971 4.35 4.4 17.3 19.5 2.2000008 6.46 5.7 0.2999992 -2.11000013
## 25 1972 4.07 3.2 17.6 19.6 2.0000000 4.35 4.4 2.2000008 -0.27999973
## 26 1973 7.04 6.2 17.6 18.7 1.1000004 4.07 3.2 2.0000000 2.96999979
## 27 1974 7.89 11.0 18.3 18.7 0.4000015 7.04 6.2 1.1000004 0.84999990
## 28 1975 5.84 9.1 17.9 21.3 3.3999996 7.89 11.0 0.4000015 -2.04999971
## 29 1976 4.99 5.8 17.1 21.4 4.2999992 5.84 9.1 3.3999996 -0.85000038
## 30 1977 5.27 6.5 18.0 20.7 2.7000008 4.99 5.8 4.2999992 0.28000021
## 31 1978 7.22 7.6 18.0 20.7 2.7000008 5.27 6.5 2.7000008 1.94999981
## 32 1979 10.04 11.3 18.5 20.1 1.6000004 7.22 7.6 2.7000008 2.82000017
## 33 1980 11.51 13.5 19.0 21.7 2.7000008 10.04 11.3 1.6000004 1.47000027
## 34 1981 14.03 10.3 19.6 22.2 2.6000004 11.51 13.5 2.7000008 2.51999950
## 35 1982 10.69 6.2 19.2 23.1 3.8999996 14.03 10.3 2.6000004 -3.34000015
## 36 1983 8.63 3.2 17.4 23.5 6.1000004 10.69 6.2 3.8999996 -2.05999947
## 37 1984 9.58 4.3 17.3 22.1 4.8000011 8.63 3.2 6.1000004 0.94999981
## 38 1985 7.48 3.6 17.7 22.8 5.0999985 9.58 4.3 4.8000011 -2.09999990
## 39 1986 5.98 1.9 17.5 22.5 5.0000000 7.48 3.6 5.0999985 -1.50000000
## 40 1987 5.82 3.6 18.4 21.6 3.2000008 5.98 1.9 5.0000000 -0.15999985
## 41 1988 6.69 4.1 18.1 21.2 3.1000004 5.82 3.6 3.2000008 0.86999989
## 42 1989 8.12 4.8 18.3 21.2 2.9000015 6.69 4.1 3.1000004 1.42999983
## 43 1990 7.51 5.4 18.0 21.8 3.7999992 8.12 4.8 2.9000015 -0.60999966
## 44 1991 5.42 4.2 17.8 22.3 4.5000000 7.51 5.4 3.7999992 -2.09000015
## 45 1992 3.45 3.0 17.5 22.1 4.6000004 5.42 4.2 4.5000000 -1.97000003
## 46 1993 3.02 3.0 17.5 21.4 3.8999996 3.45 3.0 4.6000004 -0.43000007
## 47 1994 4.29 2.6 18.1 21.0 2.8999996 3.02 3.0 3.8999996 1.26999998
## 48 1995 5.51 2.8 18.5 20.7 2.2000008 4.29 2.6 2.8999996 1.22000027
## 49 1996 5.02 3.0 18.9 20.3 1.3999996 5.51 2.8 2.2000008 -0.49000025
## 50 1997 5.07 2.3 19.3 19.6 0.3000011 5.02 3.0 1.3999996 0.05000019
## 51 1998 4.81 1.6 20.0 19.2 -0.7999992 5.07 2.3 0.3000011 -0.26000023
## 52 1999 4.66 2.2 20.0 18.6 -1.3999996 4.81 1.6 -0.7999992 -0.15000010
## 53 2000 5.85 3.4 20.9 18.4 -2.5000000 4.66 2.2 -1.3999996 1.19000006
## 54 2001 3.45 2.8 19.8 18.6 -1.1999989 5.85 3.4 -2.5000000 -2.39999986
## 55 2002 1.62 1.6 17.9 19.4 1.5000000 3.45 2.8 -1.1999989 -1.83000004
## 56 2003 1.02 2.3 16.5 19.9 3.3999996 1.62 1.6 1.5000000 -0.60000002
## cinf cdef y77
## 1 NA NA 0
## 2 -9.3000002 4.40000057 0
## 3 2.5000000 1.40000057 0
## 4 6.6000004 -3.10000134 0
## 5 -6.0000000 2.30000019 0
## 6 -1.0999999 1.29999924 0
## 7 -0.1000000 -1.39999962 0
## 8 -1.1000000 0.50000000 0
## 9 1.9000000 -1.79999924 0
## 10 1.8000000 0.29999924 0
## 11 -0.5000000 1.30000114 0
## 12 -2.0999999 1.99999809 0
## 13 1.0000000 -2.59999847 0
## 14 -0.7000000 0.60000038 0
## 15 0.0000000 0.59999847 0
## 16 0.3000000 -0.39999771 0
## 17 0.0000000 0.09999847 0
## 18 0.3000001 -0.69999886 0
## 19 1.3000001 0.29999924 0
## 20 0.1999998 0.50000000 0
## 21 1.0999999 1.89999962 0
## 22 1.3000002 -3.20000076 0
## 23 0.1999998 0.60000038 0
## 24 -1.2999997 1.90000153 0
## 25 -1.2000000 -0.20000076 0
## 26 2.9999998 -0.89999962 0
## 27 4.8000002 -0.69999886 0
## 28 -1.8999996 2.99999809 0
## 29 -3.3000002 0.89999962 0
## 30 0.6999998 -1.59999847 1
## 31 1.0999999 0.00000000 1
## 32 3.7000003 -1.10000038 1
## 33 2.1999998 1.10000038 1
## 34 -3.1999998 -0.10000038 1
## 35 -4.1000004 1.29999924 1
## 36 -2.9999998 2.20000076 1
## 37 1.1000001 -1.29999924 1
## 38 -0.7000003 0.29999733 1
## 39 -1.6999999 -0.09999847 1
## 40 1.6999999 -1.79999924 1
## 41 0.5000000 -0.10000038 1
## 42 0.7000003 -0.19999886 1
## 43 0.5999999 0.89999771 1
## 44 -1.2000003 0.70000076 1
## 45 -1.1999998 0.10000038 1
## 46 0.0000000 -0.70000076 1
## 47 -0.4000001 -1.00000000 1
## 48 0.2000000 -0.69999886 1
## 49 0.2000000 -0.80000114 1
## 50 -0.7000000 -1.09999847 1
## 51 -0.6999999 -1.10000038 1
## 52 0.6000000 -0.60000038 1
## 53 1.2000000 -1.10000038 1
## 54 -0.6000001 1.30000114 1
## 55 -1.1999999 2.69999886 1
## 56 0.6999999 1.89999962 1
# 1. Answering Statements
# (i) Independently distributed time series observations
independence_statement <- "Disagree"
independence_explanation <- "Time series data often exhibits autocorrelation, violating independence assumptions."
# (ii) Unbiased OLS estimator in time series regression
ols_statement <- "Disagree"
ols_explanation <- "Time series often violates OLS assumptions, leading to bias."
# (iii) Trending variable as dependent in multiple regression
trending_statement <- "Disagree"
trending_explanation <- "Trending variables can be used but require attention to stationarity."
# (iv) Seasonality in annual time series observations
seasonality_statement <- "Disagree"
seasonality_explanation <- "Seasonality can exist in annual data, affecting analysis."
# 5. Model for Housing Starts
# Assuming data frame 'data' contains columns: housing_starts, interest_rates, real_income, and date
#model_housing_starts <- lm(housing_starts ~ trend_variable + seasonality_variable + interest_rates + real_income, data = data)
# C1. Using a Dummy Variable for Federal Reserve Policy Change
# Create a dummy variable for the policy change after 1979
intdef$dummy <- ifelse(intdef$year > 1979, 1, 0)
# Equation with dummy variable
model_with_dummy <- lm(inf ~ dummy + ci3 + cdef + cinf, data = intdef)
summary(model_with_dummy)
##
## Call:
## lm(formula = inf ~ dummy + ci3 + cdef + cinf, data = intdef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1867 -1.8047 -0.8382 0.9943 6.7831
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.3937 0.5193 6.535 3.21e-08 ***
## dummy 0.9400 0.7977 1.178 0.24423
## ci3 0.4391 0.3172 1.385 0.17233
## cdef 0.4382 0.3370 1.300 0.19954
## cinf 0.5707 0.2103 2.714 0.00909 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.799 on 50 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.2012, Adjusted R-squared: 0.1373
## F-statistic: 3.148 on 4 and 50 DF, p-value: 0.02196
# Conclusion
cat("Conclusion regarding the model:\n")
## Conclusion regarding the model:
cat("From the regression results:\n")
## From the regression results:
cat("- The policy change after 1979 represented by the 'dummy' variable doesn't appear to have a statistically significant impact on CPI inflation rates (p-value = 0.24423).\n")
## - The policy change after 1979 represented by the 'dummy' variable doesn't appear to have a statistically significant impact on CPI inflation rates (p-value = 0.24423).
cat("- Among additional variables, only 'cinf' (change in federal outlays minus federal receipts) shows a statistically significant relationship with CPI inflation rates (p-value = 0.00909).\n")
## - Among additional variables, only 'cinf' (change in federal outlays minus federal receipts) shows a statistically significant relationship with CPI inflation rates (p-value = 0.00909).
cat("- The overall model explains a small proportion of the variance in CPI inflation rates (Adjusted R-squared = 0.1373).\n")
## - The overall model explains a small proportion of the variance in CPI inflation rates (Adjusted R-squared = 0.1373).
cat("Therefore, while 'cinf' seems to be related to CPI inflation rates, the policy change after 1979, as represented by the 'dummy' variable, does not show a significant impact in this model.")
## Therefore, while 'cinf' seems to be related to CPI inflation rates, the policy change after 1979, as represented by the 'dummy' variable, does not show a significant impact in this model.
#C9
data <- as.data.frame(volat)
# Step 1: Hypothesize the signs of β1 and β2
# β1 (pcip): Positive (higher industrial production growth likely boosts stock returns)
# β2 (i3): Negative (higher T-bill rates may decrease stock returns due to opportunity cost)
# Step 2: Estimate the equation rsp500 = β0 + β1*pcip + β2*i3 + u_t
model <- lm(rsp500 ~ pcip + i3, data = data)
# Summarize the regression results
summary(model)
##
## Call:
## lm(formula = rsp500 ~ pcip + i3, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -157.871 -22.580 2.103 25.524 138.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.84306 3.27488 5.754 1.44e-08 ***
## pcip 0.03642 0.12940 0.281 0.7785
## i3 -1.36169 0.54072 -2.518 0.0121 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.13 on 554 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01189, Adjusted R-squared: 0.008325
## F-statistic: 3.334 on 2 and 554 DF, p-value: 0.03637
# Step 3: Identify statistically significant variables
# Check the p-values from the regression summary (p < 0.05 indicates significance)
# Step 4: Assess predictability of the S&P 500 returns
# Use the R-squared value and significance of predictors
cat("R-squared value:", summary(model)$r.squared, "\n")
## R-squared value: 0.01189219
#Chapter 11
#C7
# Load necessary libraries
library(wooldridge) # Contains the CONSUMP dataset
library(lmtest) # For hypothesis testing
library(car) # For F-tests and other diagnostics
## Loading required package: carData
# Load the CONSUMP dataset
data("consump")
# Calculate growth rates for consumption and income (using diff() on logs)
gc <- diff(log(consump$c)) # Growth in real per capita consumption
gy <- diff(log(consump$y)) # Growth in real per capita income
# Create lagged variables (lag by 1 period) and ensure alignment
gc_lag <- c(NA, gc[-length(gc)]) # Lagged gc (align with the time series)
gy_lag <- c(NA, gy[-length(gy)]) # Lagged gy (align with the time series)
i3_lag <- consump$i3[-1] # Lagged interest rate
inf_lag <- consump$inf[-1] # Lagged inflation
# Remove the first row of the original variables for alignment with lagged variables
# Remove the first element of the variables that were changed by diff() (i.e., gc, gy, etc.)
gc <- gc[-1] # Remove the first element of gc (to match the lagged variables)
gc_lag <- gc_lag[-1] # Remove the first element of gc_lag (to match the length of gc)
gy_lag <- gy_lag[-1] # Remove the first element of gy_lag
i3_lag <- i3_lag[-1] # Remove the first element of i3_lag
inf_lag <- inf_lag[-1] # Remove the first element of inf_lag
# Check lengths of all variables to ensure they are now the same
length(gc)
## [1] 35
length(gc_lag)
## [1] 35
length(gy_lag)
## [1] 35
length(i3_lag)
## [1] 35
length(inf_lag)
## [1] 35
# Now, all variables (gc, gc_lag, gy_lag, i3_lag, inf_lag) should have the same length
# Proceed with regression (i) and (ii)
# (i) Test the PIH by estimating: gc_t = B0 + B1 * gc_t-1 + u_t
model_i <- lm(gc ~ gc_lag)
summary(model_i)
##
## Call:
## lm(formula = gc ~ gc_lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027878 -0.005974 -0.001451 0.007142 0.020227
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.011431 0.003778 3.026 0.00478 **
## gc_lag 0.446141 0.156047 2.859 0.00731 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01161 on 33 degrees of freedom
## Multiple R-squared: 0.1985, Adjusted R-squared: 0.1742
## F-statistic: 8.174 on 1 and 33 DF, p-value: 0.00731
# (ii) Add variables gy_t-1, i3_t-1, and inf_t-1 to the regression
model_ii <- lm(gc ~ gc_lag + gy_lag + i3_lag + inf_lag)
summary(model_ii)
##
## Call:
## lm(formula = gc ~ gc_lag + gy_lag + i3_lag + inf_lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0262464 -0.0076663 0.0009074 0.0063952 0.0174974
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.007e-02 5.839e-03 3.438 0.00174 **
## gc_lag 5.398e-01 2.604e-01 2.073 0.04689 *
## gy_lag -1.017e-01 1.791e-01 -0.567 0.57464
## i3_lag -2.525e-05 1.028e-03 -0.025 0.98057
## inf_lag -1.701e-03 8.825e-04 -1.928 0.06341 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01069 on 30 degrees of freedom
## Multiple R-squared: 0.3819, Adjusted R-squared: 0.2995
## F-statistic: 4.635 on 4 and 30 DF, p-value: 0.004937
# (iii) Check the p-value for gc_lag in model_ii to see if it remains significant
gc_lag_p_value <- summary(model_ii)$coefficients["gc_lag", "Pr(>|t|)"]
gc_lag_p_value
## [1] 0.04688851
# (iv) Perform an F-test for the joint significance of the four explanatory variables
anova(model_ii)
## Analysis of Variance Table
##
## Response: gc
## Df Sum Sq Mean Sq F value Pr(>F)
## gc_lag 1 0.0011009 0.00110093 9.6360 0.00414 **
## gy_lag 1 0.0000647 0.00006471 0.5664 0.45756
## i3_lag 1 0.0005279 0.00052785 4.6201 0.03979 *
## inf_lag 1 0.0004245 0.00042455 3.7159 0.06341 .
## Residuals 30 0.0034275 0.00011425
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Load necessary libraries
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::recode() masks car::recode()
## ✖ purrr::some() masks car::some()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(wooldridge)
# Load the MINWAGE dataset
data("minwage")
# (i) Find the first-order autocorrelation in gwage232
# Remove rows with missing values for gwage232
minwage_clean <- minwage %>% filter(!is.na(gwage232))
# Compute the first-order autocorrelation for gwage232
acf(minwage_clean$gwage232, lag.max = 1)
# Alternatively, manually compute the first-order autocorrelation
gwage232_lag <- lag(minwage_clean$gwage232, 1) # Create lagged variable
autocorr <- cor(minwage_clean$gwage232[2:length(minwage_clean$gwage232)], gwage232_lag[2:length(gwage232_lag)])
cat("First-order autocorrelation: ", autocorr, "\n")
## First-order autocorrelation: -0.03494393
# (ii) Estimate the dynamic model
# Create lagged variable for gwage232
minwage$gwage232_lag <- lag(minwage$gwage232, 1)
# Run the OLS regression using gwage232 as the dependent variable and lagged gwage232 + gmwage as predictors
model_1 <- lm(gwage232 ~ gwage232_lag + gmwage, data = minwage)
# Summary of the dynamic model
cat("Dynamic Model Summary: \n")
## Dynamic Model Summary:
summary(model_1)
##
## Call:
## lm(formula = gwage232 ~ gwage232_lag + gmwage, data = minwage)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.045409 -0.003720 -0.001807 0.004261 0.041463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0032276 0.0003466 9.312 <2e-16 ***
## gwage232_lag -0.0660287 0.0343392 -1.923 0.055 .
## gmwage 0.1515466 0.0097208 15.590 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007948 on 607 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.2868, Adjusted R-squared: 0.2844
## F-statistic: 122 on 2 and 607 DF, p-value: < 2.2e-16
# (iii) Estimate the static model (without the lagged variable)
model_2 <- lm(gwage232 ~ gmwage, data = minwage)
# Summary of the static model
cat("Static Model Summary: \n")
## Static Model Summary:
summary(model_2)
##
## Call:
## lm(formula = gwage232 ~ gmwage, data = minwage)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.045213 -0.002988 -0.001598 0.004503 0.041112
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0029878 0.0003246 9.205 <2e-16 ***
## gmwage 0.1504800 0.0097189 15.483 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.00796 on 609 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.2825, Adjusted R-squared: 0.2813
## F-statistic: 239.7 on 1 and 609 DF, p-value: < 2.2e-16
# (iv) Compare the dynamic model to the static model
cat("\nComparison of Models:\n")
##
## Comparison of Models:
cat("Adjusted R-squared (Dynamic Model): ", summary(model_1)$adj.r.squared, "\n")
## Adjusted R-squared (Dynamic Model): 0.2844435
cat("Adjusted R-squared (Static Model): ", summary(model_2)$adj.r.squared, "\n")
## Adjusted R-squared (Static Model): 0.2812796
cat("AIC (Dynamic Model): ", AIC(model_1), "\n")
## AIC (Dynamic Model): -4162.391
cat("AIC (Static Model): ", AIC(model_2), "\n")
## AIC (Static Model): -4168.376
cat("BIC (Dynamic Model): ", BIC(model_1), "\n")
## BIC (Dynamic Model): -4144.737
cat("BIC (Static Model): ", BIC(model_2), "\n")
## BIC (Static Model): -4155.131
# (v) Interpretation of the results
cat("\nInterpretation:\n")
##
## Interpretation:
cat("In the dynamic model, the coefficient for gwage232_lag is: ", coef(model_1)["gwage232_lag"], "\n")
## In the dynamic model, the coefficient for gwage232_lag is: -0.06602873
cat("This suggests that past values of gwage232 have a relationship with the current value of gwage232. \n")
## This suggests that past values of gwage232 have a relationship with the current value of gwage232.
cat("In the dynamic model, the coefficient for gmwage is: ", coef(model_1)["gmwage"], "\n")
## In the dynamic model, the coefficient for gmwage is: 0.1515466
cat("This shows the relationship between gmwage and gwage232.\n")
## This shows the relationship between gmwage and gwage232.
cat("In the static model, the coefficient for gmwage is: ", coef(model_2)["gmwage"], "\n")
## In the static model, the coefficient for gmwage is: 0.15048
cat("This shows the relationship between gmwage and gwage232 without considering past values of gwage232.\n")
## This shows the relationship between gmwage and gwage232 without considering past values of gwage232.
#Chapter 12
#11
# Load necessary libraries
library(wooldridge)
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(lmtest)
library(dplyr)
library(ggplot2)
# Load the NYSE dataset
data("nyse")
returns <- nyse$return
# Remove NA values (if any)
returns <- na.omit(returns)
# (i) Create aligned returns and lagged returns manually to avoid length mismatches
aligned_returns <- returns[2:length(returns)] # Remove the first observation
lagged_returns <- returns[1:(length(returns) - 1)] # Remove the last observation
# OLS model for: return_t = beta0 + beta1 * return_(t-1) + u_t
ols_model <- lm(aligned_returns ~ lagged_returns)
residuals_squared <- ols_model$residuals^2 # Squared residuals for heteroskedasticity model
# Compute mean, min, and max of squared residuals
mean_residual_squared <- mean(residuals_squared)
min_residual_squared <- min(residuals_squared)
max_residual_squared <- max(residuals_squared)
cat("Mean squared residuals:", mean_residual_squared, "\n")
## Mean squared residuals: 4.440839
cat("Min squared residuals:", min_residual_squared, "\n")
## Min squared residuals: 7.35465e-06
cat("Max squared residuals:", max_residual_squared, "\n")
## Max squared residuals: 232.8946
# (ii) ARCH model: Var(u_t) = delta_0 + delta_1 * return_(t-1) + delta_2 * return_(t-1)^2
arch_model <- lm(residuals_squared ~ lagged_returns + I(lagged_returns^2))
summary(arch_model)
##
## Call:
## lm(formula = residuals_squared ~ lagged_returns + I(lagged_returns^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.459 -3.011 -1.975 0.676 221.469
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.25734 0.44085 7.389 4.32e-13 ***
## lagged_returns -0.78946 0.19569 -4.034 6.09e-05 ***
## I(lagged_returns^2) 0.29666 0.03552 8.351 3.75e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.66 on 686 degrees of freedom
## Multiple R-squared: 0.1303, Adjusted R-squared: 0.1278
## F-statistic: 51.4 on 2 and 686 DF, p-value: < 2.2e-16
# (iii) Plot: Conditional variance vs lagged returns
data_plot <- data.frame(LaggedReturn = lagged_returns, ConditionalVariance = residuals_squared)
ggplot(data_plot, aes(x = LaggedReturn, y = ConditionalVariance)) +
geom_point(color = "blue") +
labs(title = "Conditional Variance vs Lagged Return",
x = "Lagged Return", y = "Conditional Variance") +
theme_minimal()
# (iv) Check for negative variance estimates
negative_variances <- any(arch_model$fitted.values < 0)
cat("Are there negative variance estimates? ", negative_variances, "\n")
## Are there negative variance estimates? FALSE
# (v) ARCH(1) model using garch()
arch1_model <- garch(aligned_returns, order = c(1, 0))
##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 4.239685e+00 1.000e+00
## 2 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 8.612e+02
## 1 4 8.612e+02 1.02e-05 3.35e-05 1.2e-03 2.9e+02 1.0e-02 4.86e-03
## 2 5 8.612e+02 1.86e-06 1.89e-06 4.6e-04 0.0e+00 4.4e-03 1.89e-06
## 3 6 8.612e+02 4.00e-10 1.60e-08 5.1e-04 2.3e-01 4.4e-03 1.66e-08
## 4 7 8.612e+02 3.12e-10 1.36e-08 2.5e-04 1.8e+00 2.2e-03 1.71e-07
## 5 8 8.612e+02 8.02e-11 6.77e-09 1.3e-04 2.0e+00 1.1e-03 2.61e-06
## 6 9 8.612e+02 6.68e-11 3.40e-09 6.3e-05 2.0e+00 5.5e-04 1.52e-05
## 7 14 8.612e+02 1.30e-11 9.01e-11 1.4e-06 1.3e+00 1.3e-05 -5.87e-06
## 8 18 8.612e+02 4.82e-14 2.09e-11 3.8e-07 1.3e+00 3.3e-06 -5.87e-06
## 9 19 8.612e+02 2.44e-14 1.04e-11 1.9e-07 1.3e+00 1.6e-06 -5.88e-06
## 10 20 8.612e+02 1.31e-14 5.20e-12 9.6e-08 1.3e+00 8.2e-07 -5.88e-06
## 11 21 8.612e+02 9.77e-15 2.60e-12 4.8e-08 1.3e+00 4.1e-07 -5.88e-06
## 12 22 8.612e+02 4.09e-15 1.30e-12 2.4e-08 1.3e+00 2.0e-07 -5.88e-06
## 13 23 8.612e+02 1.45e-15 6.49e-13 1.2e-08 1.3e+00 1.0e-07 -5.88e-06
## 14 24 8.612e+02 1.19e-15 3.25e-13 6.0e-09 1.3e+00 5.1e-08 -5.88e-06
## 15 25 8.612e+02 1.58e-15 1.62e-13 3.0e-09 1.3e+00 2.5e-08 -5.88e-06
## 16 26 8.612e+02 3.96e-16 8.12e-14 1.5e-09 1.3e+00 1.3e-08 -5.88e-06
## 17 31 8.612e+02 3.96e-16 1.86e-15 3.4e-11 1.3e+00 2.9e-10 -5.88e-06
## 18 35 8.612e+02 3.96e-16 2.48e-17 4.6e-13 4.2e+08 3.9e-12 2.15e-05
## 19 38 8.612e+02 -1.32e-16 4.97e-19 9.1e-15 1.3e+00 7.8e-14 -5.88e-06
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION 8.612015e+02 RELDX 9.134e-15
## FUNC. EVALS 38 GRAD. EVALS 19
## PRELDF 4.970e-19 NPRELDF -5.879e-06
##
## I FINAL X(I) D(I) G(I)
##
## 1 4.229895e+00 1.000e+00 5.444e-03
## 2 5.954048e-02 1.000e+00 -7.006e-04
summary(arch1_model)
##
## Call:
## garch(x = aligned_returns, order = c(1, 0))
##
## Model:
## GARCH(1,0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.2246 -0.5199 0.1546 0.7274 3.9838
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 4.22990 153.77829 0.028 0.978
## b1 0.05954 34.19100 0.002 0.999
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 781.58, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 87.669, df = 1, p-value < 2.2e-16
# Compare AIC for ARCH(1) vs custom ARCH model
cat("AIC of ARCH(1) model:", AIC(arch1_model), "\n")
## AIC of ARCH(1) model: 2990.862
cat("AIC of custom ARCH model:", AIC(arch_model), "\n")
## AIC of custom ARCH model: 5221.068
# (vi) ARCH(2) model using garch()
arch2_model <- garch(aligned_returns, order = c(2, 0))
##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 4.016544e+00 1.000e+00
## 2 5.000000e-02 1.000e+00
## 3 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 8.604e+02
## 1 4 8.604e+02 5.44e-06 5.66e-05 8.7e-04 4.9e+02 1.0e-02 1.38e-02
## 2 5 8.604e+02 1.03e-05 1.04e-05 4.3e-04 1.9e+00 5.0e-03 1.07e-05
## 3 6 8.604e+02 2.28e-09 9.59e-08 6.1e-04 9.2e-01 5.0e-03 2.10e-07
## 4 7 8.604e+02 7.19e-10 5.40e-08 3.1e-04 1.9e+00 2.5e-03 2.12e-06
## 5 8 8.604e+02 9.30e-10 2.72e-08 1.5e-04 2.0e+00 1.2e-03 2.95e-06
## 6 13 8.604e+02 1.43e-11 4.87e-10 2.7e-06 9.1e+00 2.2e-05 3.63e-06
## 7 14 8.604e+02 4.71e-12 2.44e-10 1.4e-06 3.0e+04 1.1e-05 3.65e-06
## 8 15 8.604e+02 2.36e-12 1.22e-10 6.9e-07 9.0e+04 5.6e-06 5.49e-06
## 9 16 8.604e+02 1.18e-12 6.09e-11 3.4e-07 1.8e+05 2.8e-06 5.48e-06
## 10 17 8.604e+02 5.91e-13 3.05e-11 1.7e-07 3.6e+05 1.4e-06 5.48e-06
## 11 18 8.604e+02 2.95e-13 1.52e-11 8.6e-08 7.2e+05 7.0e-07 5.48e-06
## 12 19 8.604e+02 1.49e-13 7.61e-12 4.3e-08 1.4e+06 3.5e-07 5.47e-06
## 13 20 8.604e+02 7.41e-14 3.81e-12 2.2e-08 2.9e+06 1.8e-07 5.47e-06
## 14 21 8.604e+02 3.83e-14 1.90e-12 1.1e-08 5.7e+06 8.8e-08 5.47e-06
## 15 22 8.604e+02 1.66e-14 9.52e-13 5.4e-09 1.1e+07 4.4e-08 5.47e-06
## 16 23 8.604e+02 1.03e-14 4.76e-13 2.7e-09 2.3e+07 2.2e-08 5.47e-06
## 17 24 8.604e+02 3.83e-15 2.38e-13 1.3e-09 4.6e+07 1.1e-08 5.47e-06
## 18 25 8.604e+02 2.77e-15 1.19e-13 6.7e-10 9.2e+07 5.5e-09 5.47e-06
## 19 26 8.604e+02 1.72e-15 5.95e-14 3.4e-10 1.8e+08 2.7e-09 5.47e-06
## 20 27 8.604e+02 3.96e-16 2.97e-14 1.7e-10 3.7e+08 1.4e-09 5.47e-06
## 21 28 8.604e+02 1.32e-16 1.49e-14 8.4e-11 7.4e+08 6.9e-10 5.48e-06
## 22 29 8.604e+02 1.32e-16 7.44e-15 4.2e-11 1.5e+09 3.4e-10 5.47e-06
## 23 30 8.604e+02 1.32e-16 3.72e-15 2.1e-11 2.9e+09 1.7e-10 5.48e-06
## 24 33 8.604e+02 1.32e-16 3.27e-16 1.8e-12 3.3e+10 1.5e-11 5.47e-06
## 25 34 8.604e+02 2.64e-16 6.53e-16 3.7e-12 1.6e+10 3.0e-11 5.37e-06
## 26 37 8.604e+02 1.32e-16 2.17e-16 1.2e-12 5.1e+10 1.0e-11 5.50e-06
## 27 41 8.604e+02 0.00e+00 1.71e-18 9.7e-15 6.0e+12 7.9e-14 5.13e-06
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION 8.604279e+02 RELDX 9.701e-15
## FUNC. EVALS 41 GRAD. EVALS 27
## PRELDF 1.712e-18 NPRELDF 5.131e-06
##
## I FINAL X(I) D(I) G(I)
##
## 1 4.028323e+00 1.000e+00 -1.841e-02
## 2 5.240788e-02 1.000e+00 2.492e-03
## 3 5.291656e-02 1.000e+00 1.582e-03
## Warning in garch(aligned_returns, order = c(2, 0)): singular information
summary(arch2_model)
##
## Call:
## garch(x = aligned_returns, order = c(2, 0))
##
## Model:
## GARCH(2,0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.2207 -0.5202 0.1519 0.7279 3.9817
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 4.02832 NA NA NA
## b1 0.05241 NA NA NA
## b2 0.05292 NA NA NA
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 776.88, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 87.793, df = 1, p-value < 2.2e-16
cat("AIC of ARCH(2) model:", AIC(arch2_model), "\n")
## AIC of ARCH(2) model: 2989.477
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