Tarea 2 - Regresiones Marco Avila
2024-05-10
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library(readxl)
library(MASS)
library(stats)
library(psych)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(openxlsx)kc = read_xlsx("TENNIS.xlsx")
linearmod <- lm(kc$Player1_Odds ~ kc$Player1_Rank) #price is the dependent variable (y axis)plot(kc$Player1_Rank, kc$Player1_Odds)## Warning in xy.coords(x, y, xlabel, ylabel, log): NAs introduced by coercionabline(linearmod, col = "blue") #it draws a green line in the graph created above## Warning in abline(linearmod, col = "blue"): only using the first two of 525
## regression coefficients
summary(linearmod) #it gives us statistic information##
## Call:
## lm(formula = kc$Player1_Odds ~ kc$Player1_Rank)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.635 -1.143 -0.539 0.128 32.868
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.16009 0.18118 6.403 1.57e-10 ***
## kc$Player1_Rank10 0.44463 0.27445 1.620 0.105238
## kc$Player1_Rank100 2.97554 0.39846 7.468 8.64e-14 ***
## kc$Player1_Rank101 2.42338 0.36498 6.640 3.26e-11 ***
## kc$Player1_Rank102 1.94841 0.36907 5.279 1.32e-07 ***
## kc$Player1_Rank1024 1.72991 2.63808 0.656 0.512000
## kc$Player1_Rank103 2.52927 0.42450 5.958 2.61e-09 ***
## kc$Player1_Rank1032 13.87991 2.63808 5.261 1.45e-07 ***
## kc$Player1_Rank104 2.59471 0.40747 6.368 1.98e-10 ***
## kc$Player1_Rank1042 0.46657 1.53026 0.305 0.760450
## kc$Player1_Rank1045 2.80991 1.53026 1.836 0.066346 .
## kc$Player1_Rank105 1.85736 0.39846 4.661 3.17e-06 ***
## kc$Player1_Rank1059 5.47991 2.63808 2.077 0.037798 *
## kc$Player1_Rank106 1.53200 0.44036 3.479 0.000505 ***
## kc$Player1_Rank1062 3.16991 2.63808 1.202 0.229541
## kc$Player1_Rank1064 9.24991 2.63808 3.506 0.000456 ***
## kc$Player1_Rank107 2.52700 0.39846 6.342 2.34e-10 ***
## kc$Player1_Rank108 1.99991 0.46380 4.312 1.63e-05 ***
## kc$Player1_Rank1085 3.02991 2.63808 1.149 0.250771
## kc$Player1_Rank109 2.78582 0.41736 6.675 2.57e-11 ***
## kc$Player1_Rank1098 6.76491 1.86980 3.618 0.000298 ***
## kc$Player1_Rank11 0.44997 0.28000 1.607 0.108063
## kc$Player1_Rank110 2.24096 0.46380 4.832 1.37e-06 ***
## kc$Player1_Rank111 2.64522 0.49928 5.298 1.19e-07 ***
## kc$Player1_Rank112 3.43226 0.48637 7.057 1.78e-12 ***
## kc$Player1_Rank113 2.06205 0.44469 4.637 3.57e-06 ***
## kc$Player1_Rank1139 2.88991 2.63808 1.095 0.273335
## kc$Player1_Rank114 1.90391 0.43215 4.406 1.06e-05 ***
## kc$Player1_Rank115 1.69891 0.51353 3.308 0.000941 ***
## kc$Player1_Rank116 2.54758 0.44036 5.785 7.39e-09 ***
## kc$Player1_Rank117 1.93761 0.42087 4.604 4.18e-06 ***
## kc$Player1_Rank118 1.79819 0.48035 3.744 0.000182 ***
## kc$Player1_Rank1184 3.13991 2.63808 1.190 0.233979
## kc$Player1_Rank119 2.31543 0.46380 4.992 6.04e-07 ***
## kc$Player1_Rank12 0.62933 0.26994 2.331 0.019747 *
## kc$Player1_Rank120 3.52691 0.51353 6.868 6.78e-12 ***
## kc$Player1_Rank121 2.60476 0.48035 5.423 5.97e-08 ***
## kc$Player1_Rank1217 11.56991 2.63808 4.386 1.16e-05 ***
## kc$Player1_Rank122 2.00428 0.49928 4.014 5.99e-05 ***
## kc$Player1_Rank123 2.50122 0.46380 5.393 7.04e-08 ***
## kc$Player1_Rank124 2.06395 0.44469 4.641 3.49e-06 ***
## kc$Player1_Rank125 3.68935 0.64625 5.709 1.16e-08 ***
## kc$Player1_Rank126 2.55043 0.63039 4.046 5.24e-05 ***
## kc$Player1_Rank127 1.92887 0.52123 3.701 0.000216 ***
## kc$Player1_Rank128 3.23324 0.60222 5.369 8.05e-08 ***
## kc$Player1_Rank129 3.79643 0.57792 6.569 5.24e-11 ***
## kc$Player1_Rank13 0.58936 0.28332 2.080 0.037527 *
## kc$Player1_Rank130 2.01883 0.52935 3.814 0.000137 ***
## kc$Player1_Rank131 1.57509 0.53793 2.928 0.003416 **
## kc$Player1_Rank132 2.34116 0.56696 4.129 3.66e-05 ***
## kc$Player1_Rank133 3.01610 0.60222 5.008 5.56e-07 ***
## kc$Player1_Rank134 1.68705 0.72635 2.323 0.020213 *
## kc$Player1_Rank135 2.66991 0.64625 4.131 3.63e-05 ***
## kc$Player1_Rank136 1.97932 0.66353 2.983 0.002859 **
## kc$Player1_Rank137 1.89341 0.61576 3.075 0.002110 **
## kc$Player1_Rank138 2.48718 0.81396 3.056 0.002250 **
## kc$Player1_Rank139 1.71178 0.68245 2.508 0.012143 *
## kc$Player1_Rank14 0.59563 0.28390 2.098 0.035919 *
## kc$Player1_Rank140 2.07579 0.66353 3.128 0.001761 **
## kc$Player1_Rank141 1.32435 0.64625 2.049 0.040453 *
## kc$Player1_Rank142 1.86324 0.53793 3.464 0.000534 ***
## kc$Player1_Rank143 2.69675 0.63039 4.278 1.90e-05 ***
## kc$Player1_Rank144 2.32842 0.53793 4.328 1.51e-05 ***
## kc$Player1_Rank145 1.91935 0.64625 2.970 0.002983 **
## kc$Player1_Rank146 1.57943 0.60222 2.623 0.008733 **
## kc$Player1_Rank147 1.85541 0.61576 3.013 0.002590 **
## kc$Player1_Rank148 1.58991 0.68245 2.330 0.019837 *
## kc$Player1_Rank149 3.51857 0.70328 5.003 5.71e-07 ***
## kc$Player1_Rank15 0.78440 0.27169 2.887 0.003893 **
## kc$Player1_Rank150 2.10205 0.72635 2.894 0.003810 **
## kc$Player1_Rank1502 1.03991 2.63808 0.394 0.693447
## kc$Player1_Rank151 2.48741 0.78106 3.185 0.001452 **
## kc$Player1_Rank152 2.64633 0.72635 3.643 0.000270 ***
## kc$Player1_Rank153 2.15464 0.63039 3.418 0.000633 ***
## kc$Player1_Rank154 2.33191 0.85176 2.738 0.006194 **
## kc$Player1_Rank155 2.34491 0.68245 3.436 0.000592 ***
## kc$Player1_Rank1557 15.32991 2.63808 5.811 6.34e-09 ***
## kc$Player1_Rank156 1.76991 0.57792 3.063 0.002199 **
## kc$Player1_Rank157 1.79172 0.81396 2.201 0.027734 *
## kc$Player1_Rank158 2.12907 0.78106 2.726 0.006421 **
## kc$Player1_Rank159 2.31900 0.81396 2.849 0.004391 **
## kc$Player1_Rank16 0.93657 0.27946 3.351 0.000806 ***
## kc$Player1_Rank160 2.78705 0.72635 3.837 0.000125 ***
## kc$Player1_Rank161 3.82991 0.78106 4.903 9.52e-07 ***
## kc$Player1_Rank162 3.03727 0.63039 4.818 1.46e-06 ***
## kc$Player1_Rank163 2.71657 0.78106 3.478 0.000507 ***
## kc$Player1_Rank164 3.51375 0.75209 4.672 3.01e-06 ***
## kc$Player1_Rank165 1.22691 0.85176 1.440 0.149766
## kc$Player1_Rank166 3.55226 0.66353 5.354 8.76e-08 ***
## kc$Player1_Rank167 1.28879 0.89580 1.439 0.150255
## kc$Player1_Rank168 2.34991 0.78106 3.009 0.002629 **
## kc$Player1_Rank169 2.92133 1.01111 2.889 0.003868 **
## kc$Player1_Rank17 0.87370 0.27689 3.155 0.001606 **
## kc$Player1_Rank170 1.74991 1.53026 1.144 0.252837
## kc$Player1_Rank171 1.97391 1.19086 1.658 0.097432 .
## kc$Player1_Rank172 1.24191 0.85176 1.458 0.144849
## kc$Player1_Rank173 1.67991 0.66353 2.532 0.011360 *
## kc$Player1_Rank174 5.24419 1.01111 5.187 2.17e-07 ***
## kc$Player1_Rank175 1.73191 1.19086 1.454 0.145878
## kc$Player1_Rank176 2.02791 0.85176 2.381 0.017286 *
## kc$Player1_Rank177 3.32263 0.81396 4.082 4.49e-05 ***
## kc$Player1_Rank178 1.89324 1.08962 1.738 0.082316 .
## kc$Player1_Rank179 2.00809 0.81396 2.467 0.013634 *
## kc$Player1_Rank18 0.58897 0.27590 2.135 0.032800 *
## kc$Player1_Rank180 2.25591 1.19086 1.894 0.058200 .
## kc$Player1_Rank1809 1.30991 2.63808 0.497 0.619523
## kc$Player1_Rank181 4.52991 1.08962 4.157 3.24e-05 ***
## kc$Player1_Rank182 2.69768 0.89580 3.011 0.002604 **
## kc$Player1_Rank183 3.89324 1.53026 2.544 0.010965 *
## kc$Player1_Rank184 2.22096 0.63039 3.523 0.000428 ***
## kc$Player1_Rank185 2.98991 0.89580 3.338 0.000847 ***
## kc$Player1_Rank186 2.70741 1.32834 2.038 0.041550 *
## kc$Player1_Rank187 5.48491 0.94798 5.786 7.36e-09 ***
## kc$Player1_Rank188 3.96809 0.81396 4.875 1.10e-06 ***
## kc$Player1_Rank189 3.50616 0.94798 3.699 0.000218 ***
## kc$Player1_Rank19 1.08309 0.29207 3.708 0.000209 ***
## kc$Player1_Rank190 3.02991 1.01111 2.997 0.002735 **
## kc$Player1_Rank191 1.53241 1.32834 1.154 0.248674
## kc$Player1_Rank192 4.90157 0.78106 6.276 3.58e-10 ***
## kc$Player1_Rank193 2.64616 0.94798 2.791 0.005255 **
## kc$Player1_Rank194 3.14324 0.89580 3.509 0.000451 ***
## kc$Player1_Rank195 1.91546 0.89580 2.138 0.032512 *
## kc$Player1_Rank196 1.88705 1.01111 1.866 0.062019 .
## kc$Player1_Rank197 1.21657 1.53026 0.795 0.426622
## kc$Player1_Rank198 4.28491 1.32834 3.226 0.001259 **
## kc$Player1_Rank199 4.82491 1.08962 4.428 9.58e-06 ***
## kc$Player1_Rank2 0.10920 0.26041 0.419 0.674974
## kc$Player1_Rank20 0.99531 0.29006 3.431 0.000602 ***
## kc$Player1_Rank200 1.77324 1.53026 1.159 0.246566
## kc$Player1_Rank201 1.49391 1.19086 1.254 0.209691
## kc$Player1_Rank202 2.09991 1.19086 1.763 0.077864 .
## kc$Player1_Rank203 4.49116 0.94798 4.738 2.18e-06 ***
## kc$Player1_Rank204 0.87657 1.53026 0.573 0.566773
## kc$Player1_Rank205 2.22791 1.19086 1.871 0.061389 .
## kc$Player1_Rank206 4.93991 1.32834 3.719 0.000201 ***
## kc$Player1_Rank207 2.63591 1.19086 2.213 0.026883 *
## kc$Player1_Rank208 2.74324 1.53026 1.793 0.073049 .
## kc$Player1_Rank209 2.03191 1.19086 1.706 0.087984 .
## kc$Player1_Rank21 1.00962 0.26867 3.758 0.000172 ***
## kc$Player1_Rank210 5.10991 1.53026 3.339 0.000842 ***
## kc$Player1_Rank211 1.04241 1.32834 0.785 0.432618
## kc$Player1_Rank212 2.30657 1.53026 1.507 0.131755
## kc$Player1_Rank213 1.60991 1.53026 1.052 0.292797
## kc$Player1_Rank214 2.03791 1.19086 1.711 0.087051 .
## kc$Player1_Rank215 1.83546 0.89580 2.049 0.040484 *
## kc$Player1_Rank2159 4.83991 2.63808 1.835 0.066581 .
## kc$Player1_Rank216 3.75241 1.32834 2.825 0.004736 **
## kc$Player1_Rank217 7.22491 1.86980 3.864 0.000112 ***
## kc$Player1_Rank218 4.25491 1.86980 2.276 0.022885 *
## kc$Player1_Rank219 5.52133 1.01111 5.461 4.82e-08 ***
## kc$Player1_Rank22 1.06380 0.29275 3.634 0.000280 ***
## kc$Player1_Rank221 5.24824 1.08962 4.817 1.48e-06 ***
## kc$Player1_Rank222 2.23991 0.94798 2.363 0.018149 *
## kc$Player1_Rank223 2.28991 0.78106 2.932 0.003375 **
## kc$Player1_Rank224 4.11241 1.32834 3.096 0.001966 **
## kc$Player1_Rank225 1.93241 0.94798 2.038 0.041523 *
## kc$Player1_Rank226 6.10741 1.32834 4.598 4.31e-06 ***
## kc$Player1_Rank227 4.22491 1.32834 3.181 0.001473 **
## kc$Player1_Rank228 1.91419 1.01111 1.893 0.058358 .
## kc$Player1_Rank229 1.89991 0.94798 2.004 0.045071 *
## kc$Player1_Rank23 1.03416 0.29558 3.499 0.000469 ***
## kc$Player1_Rank230 3.07991 1.01111 3.046 0.002323 **
## kc$Player1_Rank231 4.29241 1.32834 3.231 0.001235 **
## kc$Player1_Rank232 2.04991 1.32834 1.543 0.122803
## kc$Player1_Rank233 1.40391 1.19086 1.179 0.238459
## kc$Player1_Rank234 3.84657 1.53026 2.514 0.011959 *
## kc$Player1_Rank235 7.34324 1.08962 6.739 1.65e-11 ***
## kc$Player1_Rank236 4.36191 1.19086 3.663 0.000250 ***
## kc$Player1_Rank237 1.27991 1.86980 0.685 0.493661
## kc$Player1_Rank238 2.72191 1.19086 2.286 0.022289 *
## kc$Player1_Rank239 2.65991 2.63808 1.008 0.313341
## kc$Player1_Rank24 1.00070 0.27445 3.646 0.000267 ***
## kc$Player1_Rank240 3.48991 1.19086 2.931 0.003389 **
## kc$Player1_Rank241 4.20991 2.63808 1.596 0.110551
## kc$Player1_Rank242 8.43991 1.53026 5.515 3.54e-08 ***
## kc$Player1_Rank243 3.73824 1.08962 3.431 0.000604 ***
## kc$Player1_Rank244 2.41241 1.32834 1.816 0.069376 .
## kc$Player1_Rank245 2.67191 1.19086 2.244 0.024869 *
## kc$Player1_Rank246 6.43276 1.01111 6.362 2.05e-10 ***
## kc$Player1_Rank247 3.11241 1.32834 2.343 0.019139 *
## kc$Player1_Rank248 0.97241 1.32834 0.732 0.464153
## kc$Player1_Rank249 3.64324 1.53026 2.381 0.017289 *
## kc$Player1_Rank25 1.30672 0.28813 4.535 5.80e-06 ***
## kc$Player1_Rank250 1.63324 1.53026 1.067 0.285858
## kc$Player1_Rank251 6.34324 1.53026 4.145 3.42e-05 ***
## kc$Player1_Rank252 1.77991 1.32834 1.340 0.180284
## kc$Player1_Rank253 1.26491 1.86980 0.676 0.498739
## kc$Player1_Rank254 7.88741 1.32834 5.938 2.96e-09 ***
## kc$Player1_Rank255 2.55324 1.53026 1.668 0.095240 .
## kc$Player1_Rank256 3.87991 1.01111 3.837 0.000125 ***
## kc$Player1_Rank257 2.67991 1.86980 1.433 0.151806
## kc$Player1_Rank258 2.36657 1.53026 1.547 0.122003
## kc$Player1_Rank259 1.10491 1.86980 0.591 0.554582
## kc$Player1_Rank26 1.11842 0.27842 4.017 5.92e-05 ***
## kc$Player1_Rank260 8.18991 1.86980 4.380 1.19e-05 ***
## kc$Player1_Rank261 1.48241 1.32834 1.116 0.264449
## kc$Player1_Rank262 7.62991 2.63808 2.892 0.003831 **
## kc$Player1_Rank263 4.77324 1.53026 3.119 0.001817 **
## kc$Player1_Rank264 1.66991 2.63808 0.633 0.526744
## kc$Player1_Rank265 1.18324 1.53026 0.773 0.439402
## kc$Player1_Rank266 3.06191 1.19086 2.571 0.010146 *
## kc$Player1_Rank267 7.75991 1.53026 5.071 4.01e-07 ***
## kc$Player1_Rank268 2.38991 2.63808 0.906 0.364991
## kc$Player1_Rank269 4.08491 1.86980 2.185 0.028929 *
## kc$Player1_Rank27 0.89827 0.29934 3.001 0.002697 **
## kc$Player1_Rank270 2.31991 1.53026 1.516 0.129538
## kc$Player1_Rank271 0.13991 2.63808 0.053 0.957706
## kc$Player1_Rank272 1.15991 2.63808 0.440 0.660177
## kc$Player1_Rank273 1.92419 1.01111 1.903 0.057055 .
## kc$Player1_Rank274 1.41741 1.32834 1.067 0.285968
## kc$Player1_Rank275 3.60491 1.32834 2.714 0.006659 **
## kc$Player1_Rank277 5.80991 2.63808 2.202 0.027659 *
## kc$Player1_Rank278 1.96491 1.86980 1.051 0.293339
## kc$Player1_Rank279 24.81991 2.63808 9.408 < 2e-16 ***
## kc$Player1_Rank28 1.00690 0.28507 3.532 0.000414 ***
## kc$Player1_Rank280 1.06991 2.63808 0.406 0.685071
## kc$Player1_Rank281 3.07991 1.86980 1.647 0.099542 .
## kc$Player1_Rank282 5.92491 1.08962 5.438 5.49e-08 ***
## kc$Player1_Rank283 1.08991 1.53026 0.712 0.476332
## kc$Player1_Rank284 1.26491 1.32834 0.952 0.340989
## kc$Player1_Rank285 1.41241 1.32834 1.063 0.287671
## kc$Player1_Rank286 14.76491 1.86980 7.897 3.08e-15 ***
## kc$Player1_Rank287 2.44324 1.53026 1.597 0.110375
## kc$Player1_Rank288 0.06991 2.63808 0.026 0.978860
## kc$Player1_Rank289 3.04991 1.53026 1.993 0.046274 *
## kc$Player1_Rank29 1.46589 0.28275 5.184 2.20e-07 ***
## kc$Player1_Rank290 1.42657 1.53026 0.932 0.351229
## kc$Player1_Rank291 1.29991 2.63808 0.493 0.622199
## kc$Player1_Rank292 1.25991 1.32834 0.948 0.342901
## kc$Player1_Rank293 1.67324 1.08962 1.536 0.124654
## kc$Player1_Rank294 2.78241 1.32834 2.095 0.036220 *
## kc$Player1_Rank295 6.17324 1.53026 4.034 5.51e-05 ***
## kc$Player1_Rank296 7.30191 1.19086 6.132 8.93e-10 ***
## kc$Player1_Rank299 3.58991 2.63808 1.361 0.173598
## kc$Player1_Rank3 0.25715 0.26785 0.960 0.337033
## kc$Player1_Rank30 1.17609 0.28751 4.091 4.33e-05 ***
## kc$Player1_Rank300 5.20491 1.86980 2.784 0.005382 **
## kc$Player1_Rank301 1.28991 2.63808 0.489 0.624881
## kc$Player1_Rank302 0.92491 1.86980 0.495 0.620852
## kc$Player1_Rank303 9.74991 2.63808 3.696 0.000220 ***
## kc$Player1_Rank304 2.05657 1.53026 1.344 0.178992
## kc$Player1_Rank306 2.41491 1.86980 1.292 0.196541
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## kc$Player1_Rank312 1.38991 1.53026 0.908 0.363747
## kc$Player1_Rank313 11.16991 2.63808 4.234 2.31e-05 ***
## kc$Player1_Rank314 4.58991 2.63808 1.740 0.081904 .
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## kc$Player1_Rank317 4.60324 1.53026 3.008 0.002633 **
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## kc$Player1_Rank32 1.20392 0.28275 4.258 2.08e-05 ***
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## kc$Player1_Rank325 3.20491 1.86980 1.714 0.086544 .
## kc$Player1_Rank326 4.25991 1.86980 2.278 0.022725 *
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## kc$Player1_Rank328 6.75991 1.32834 5.089 3.65e-07 ***
## kc$Player1_Rank329 5.22991 2.63808 1.982 0.047446 *
## kc$Player1_Rank33 1.32302 0.29006 4.561 5.13e-06 ***
## kc$Player1_Rank330 2.17324 1.53026 1.420 0.155580
## kc$Player1_Rank332 8.28491 1.86980 4.431 9.45e-06 ***
## kc$Player1_Rank333 2.10991 2.63808 0.800 0.423847
## kc$Player1_Rank334 7.05491 1.86980 3.773 0.000162 ***
## kc$Player1_Rank335 4.23991 2.63808 1.607 0.108034
## kc$Player1_Rank337 2.58991 1.86980 1.385 0.166036
## kc$Player1_Rank338 3.75657 1.53026 2.455 0.014106 *
## kc$Player1_Rank34 1.34224 0.29139 4.606 4.13e-06 ***
## kc$Player1_Rank340 1.98991 1.08962 1.826 0.067835 .
## kc$Player1_Rank344 3.73991 1.86980 2.000 0.045502 *
## kc$Player1_Rank345 4.90991 1.86980 2.626 0.008651 **
## kc$Player1_Rank347 2.41491 1.86980 1.292 0.196541
## kc$Player1_Rank349 3.84991 2.63808 1.459 0.144489
## kc$Player1_Rank35 1.88914 0.28507 6.627 3.55e-11 ***
## kc$Player1_Rank350 1.53991 2.63808 0.584 0.559417
## kc$Player1_Rank351 1.53991 2.63808 0.584 0.559417
## kc$Player1_Rank352 1.42991 1.53026 0.934 0.350105
## kc$Player1_Rank354 3.01991 2.63808 1.145 0.252338
## kc$Player1_Rank355 4.65991 2.63808 1.766 0.077350 .
## kc$Player1_Rank358 2.71991 1.86980 1.455 0.145788
## kc$Player1_Rank36 1.60786 0.29207 5.505 3.75e-08 ***
## kc$Player1_Rank361 2.70324 1.53026 1.767 0.077331 .
## kc$Player1_Rank362 1.15991 2.63808 0.440 0.660177
## kc$Player1_Rank363 4.19991 1.53026 2.745 0.006067 **
## kc$Player1_Rank364 1.39991 2.63808 0.531 0.595668
## kc$Player1_Rank365 5.69991 2.63808 2.161 0.030741 *
## kc$Player1_Rank366 3.75991 1.86980 2.011 0.044359 *
## kc$Player1_Rank369 0.81991 1.86980 0.438 0.661031
## kc$Player1_Rank37 1.44576 0.29486 4.903 9.53e-07 ***
## kc$Player1_Rank370 4.11657 1.53026 2.690 0.007151 **
## kc$Player1_Rank371 2.21991 2.63808 0.841 0.400091
## kc$Player1_Rank372 2.42991 2.63808 0.921 0.357020
## kc$Player1_Rank373 4.41991 1.86980 2.364 0.018100 *
## kc$Player1_Rank376 4.86991 2.63808 1.846 0.064913 .
## kc$Player1_Rank377 4.16991 2.63808 1.581 0.113979
## kc$Player1_Rank378 9.90991 2.63808 3.756 0.000173 ***
## kc$Player1_Rank379 0.74991 2.63808 0.284 0.776214
## kc$Player1_Rank38 1.30365 0.29275 4.453 8.53e-06 ***
## kc$Player1_Rank380 5.95991 1.32834 4.487 7.29e-06 ***
## kc$Player1_Rank382 4.01991 2.63808 1.524 0.127581
## kc$Player1_Rank383 1.62991 2.63808 0.618 0.536693
## kc$Player1_Rank384 5.07491 1.86980 2.714 0.006653 **
## kc$Player1_Rank385 0.25991 2.63808 0.099 0.921520
## kc$Player1_Rank386 2.58157 1.08962 2.369 0.017838 *
## kc$Player1_Rank387 2.48241 1.32834 1.869 0.061671 .
## kc$Player1_Rank388 2.55991 2.63808 0.970 0.331881
## kc$Player1_Rank389 1.70991 2.63808 0.648 0.516890
## kc$Player1_Rank39 1.35888 0.30336 4.479 7.54e-06 ***
## kc$Player1_Rank393 1.36991 2.63808 0.519 0.603573
## kc$Player1_Rank394 0.66991 2.63808 0.254 0.799548
## kc$Player1_Rank395 2.34991 2.63808 0.891 0.373072
## kc$Player1_Rank397 1.47991 2.63808 0.561 0.574822
## kc$Player1_Rank399 4.12991 2.63808 1.565 0.117489
## kc$Player1_Rank4 0.23997 0.27894 0.860 0.389637
## kc$Player1_Rank40 1.58124 0.29558 5.350 8.95e-08 ***
## kc$Player1_Rank401 0.97991 1.32834 0.738 0.460714
## kc$Player1_Rank402 5.88741 1.32834 4.432 9.40e-06 ***
## kc$Player1_Rank404 2.19991 2.63808 0.834 0.404350
## kc$Player1_Rank405 3.13241 1.32834 2.358 0.018381 *
## kc$Player1_Rank406 2.40991 2.63808 0.914 0.360992
## kc$Player1_Rank407 1.59991 2.63808 0.606 0.544215
## kc$Player1_Rank409 1.38991 2.63808 0.527 0.598298
## kc$Player1_Rank41 1.73366 0.30769 5.634 1.79e-08 ***
## kc$Player1_Rank411 3.08991 2.63808 1.171 0.241510
## kc$Player1_Rank412 5.84991 2.63808 2.217 0.026606 *
## kc$Player1_Rank416 3.63491 1.32834 2.736 0.006219 **
## kc$Player1_Rank417 3.35991 1.32834 2.529 0.011437 *
## kc$Player1_Rank418 8.95991 2.63808 3.396 0.000685 ***
## kc$Player1_Rank419 8.38491 1.86980 4.484 7.37e-06 ***
## kc$Player1_Rank42 1.40181 0.28567 4.907 9.35e-07 ***
## kc$Player1_Rank420 0.53991 1.86980 0.289 0.772777
## kc$Player1_Rank421 4.13491 1.86980 2.211 0.027023 *
## kc$Player1_Rank422 11.43991 2.63808 4.336 1.46e-05 ***
## kc$Player1_Rank425 5.79991 2.63808 2.199 0.027927 *
## kc$Player1_Rank426 3.75991 2.63808 1.425 0.154109
## kc$Player1_Rank427 7.90991 1.53026 5.169 2.39e-07 ***
## kc$Player1_Rank429 4.44991 1.86980 2.380 0.017331 *
## kc$Player1_Rank43 1.44709 0.28163 5.138 2.81e-07 ***
## kc$Player1_Rank433 1.70491 1.86980 0.912 0.361883
## kc$Player1_Rank435 0.16991 2.63808 0.064 0.948649
## kc$Player1_Rank436 8.59991 2.63808 3.260 0.001117 **
## kc$Player1_Rank437 2.16991 1.53026 1.418 0.156215
## kc$Player1_Rank438 3.49491 1.32834 2.631 0.008522 **
## kc$Player1_Rank439 7.85991 2.63808 2.979 0.002893 **
## kc$Player1_Rank44 1.47440 0.29415 5.012 5.44e-07 ***
## kc$Player1_Rank440 5.99991 1.53026 3.921 8.87e-05 ***
## kc$Player1_Rank441 3.77991 2.63808 1.433 0.151930
## kc$Player1_Rank442 4.11991 1.86980 2.203 0.027583 *
## kc$Player1_Rank447 4.33991 2.63808 1.645 0.099972 .
## kc$Player1_Rank449 1.13991 1.86980 0.610 0.542110
## kc$Player1_Rank45 1.29616 0.28941 4.479 7.57e-06 ***
## kc$Player1_Rank450 2.99741 1.32834 2.257 0.024054 *
## kc$Player1_Rank455 0.19991 2.63808 0.076 0.939598
## kc$Player1_Rank457 2.76991 2.63808 1.050 0.293750
## kc$Player1_Rank46 1.41945 0.27894 5.089 3.65e-07 ***
## kc$Player1_Rank462 2.71991 1.86980 1.455 0.145788
## kc$Player1_Rank469 2.92991 2.63808 1.111 0.266751
## kc$Player1_Rank47 1.26373 0.29857 4.233 2.32e-05 ***
## kc$Player1_Rank470 9.97991 2.63808 3.783 0.000156 ***
## kc$Player1_Rank472 1.98991 2.63808 0.754 0.450682
## kc$Player1_Rank473 3.33991 1.86980 1.786 0.074082 .
## kc$Player1_Rank475 0.27991 2.63808 0.106 0.915503
## kc$Player1_Rank479 1.92991 2.63808 0.732 0.464452
## kc$Player1_Rank48 2.03161 0.29857 6.805 1.05e-11 ***
## kc$Player1_Rank480 12.10991 2.63808 4.590 4.46e-06 ***
## kc$Player1_Rank483 1.69991 2.63808 0.644 0.519345
## kc$Player1_Rank486 3.36991 2.63808 1.277 0.201479
## kc$Player1_Rank487 8.20991 2.63808 3.112 0.001861 **
## kc$Player1_Rank489 4.84991 1.86980 2.594 0.009502 **
## kc$Player1_Rank49 1.79771 0.29207 6.155 7.70e-10 ***
## kc$Player1_Rank490 1.44991 1.86980 0.775 0.438097
## kc$Player1_Rank491 2.26657 1.53026 1.481 0.138585
## kc$Player1_Rank492 9.09991 2.63808 3.449 0.000563 ***
## kc$Player1_Rank495 2.28991 2.63808 0.868 0.385399
## kc$Player1_Rank496 0.19991 2.63808 0.076 0.939598
## kc$Player1_Rank5 0.45317 0.25716 1.762 0.078047 .
## kc$Player1_Rank50 2.06288 0.31845 6.478 9.61e-11 ***
## kc$Player1_Rank502 3.98241 1.32834 2.998 0.002722 **
## kc$Player1_Rank503 2.93991 2.63808 1.114 0.265122
## kc$Player1_Rank507 5.21991 2.63808 1.979 0.047872 *
## kc$Player1_Rank508 2.41991 2.63808 0.917 0.359002
## kc$Player1_Rank51 1.68008 0.30592 5.492 4.05e-08 ***
## kc$Player1_Rank510 1.56491 1.86980 0.837 0.402642
## kc$Player1_Rank513 7.50991 2.63808 2.847 0.004423 **
## kc$Player1_Rank516 5.00991 2.63808 1.899 0.057575 .
## kc$Player1_Rank52 2.04567 0.29705 6.887 5.96e-12 ***
## kc$Player1_Rank524 3.47991 2.63808 1.319 0.187156
## kc$Player1_Rank526 3.65324 1.53026 2.387 0.016985 *
## kc$Player1_Rank53 1.50120 0.27894 5.382 7.49e-08 ***
## kc$Player1_Rank54 1.75019 0.31533 5.550 2.90e-08 ***
## kc$Player1_Rank542 1.57491 1.86980 0.842 0.399642
## kc$Player1_Rank543 5.26991 2.63808 1.998 0.045776 *
## kc$Player1_Rank544 1.15991 2.63808 0.440 0.660177
## kc$Player1_Rank546 0.49991 1.86980 0.267 0.789198
## kc$Player1_Rank547 5.27657 1.53026 3.448 0.000566 ***
## kc$Player1_Rank55 2.08899 0.29275 7.136 1.01e-12 ***
## kc$Player1_Rank550 0.54991 2.63808 0.208 0.834881
## kc$Player1_Rank551 2.67491 1.86980 1.431 0.152572
## kc$Player1_Rank553 3.30491 1.86980 1.768 0.077163 .
## kc$Player1_Rank557 3.90991 2.63808 1.482 0.138335
## kc$Player1_Rank56 1.46759 0.32518 4.513 6.44e-06 ***
## kc$Player1_Rank564 4.06991 2.63808 1.543 0.122913
## kc$Player1_Rank565 3.86991 2.63808 1.467 0.142415
## kc$Player1_Rank567 1.73991 2.63808 0.660 0.509563
## kc$Player1_Rank569 7.90991 2.63808 2.998 0.002719 **
## kc$Player1_Rank57 2.41503 0.29705 8.130 4.65e-16 ***
## kc$Player1_Rank570 22.03991 2.63808 8.355 < 2e-16 ***
## kc$Player1_Rank578 3.44991 2.63808 1.308 0.190985
## kc$Player1_Rank58 1.83306 0.32518 5.637 1.76e-08 ***
## kc$Player1_Rank581 1.89791 1.19086 1.594 0.111021
## kc$Player1_Rank583 2.11991 2.63808 0.804 0.421654
## kc$Player1_Rank584 2.24991 2.63808 0.853 0.393753
## kc$Player1_Rank585 2.23991 2.63808 0.849 0.395859
## kc$Player1_Rank589 4.65991 1.86980 2.492 0.012707 *
## kc$Player1_Rank59 1.31831 0.33398 3.947 7.94e-05 ***
## kc$Player1_Rank594 3.52991 2.63808 1.338 0.180899
## kc$Player1_Rank599 4.02991 2.63808 1.528 0.126637
## kc$Player1_Rank6 0.33317 0.25907 1.286 0.198455
## kc$Player1_Rank60 1.43365 0.29857 4.802 1.59e-06 ***
## kc$Player1_Rank605 5.14491 1.86980 2.752 0.005938 **
## kc$Player1_Rank607 8.03991 2.63808 3.048 0.002311 **
## kc$Player1_Rank61 1.46241 0.30769 4.753 2.03e-06 ***
## kc$Player1_Rank612 3.83991 2.63808 1.456 0.145534
## kc$Player1_Rank613 7.97991 2.63808 3.025 0.002492 **
## kc$Player1_Rank614 5.88991 2.63808 2.233 0.025588 *
## kc$Player1_Rank616 11.37991 2.63808 4.314 1.62e-05 ***
## kc$Player1_Rank62 1.80284 0.30420 5.926 3.17e-09 ***
## kc$Player1_Rank628 2.00991 2.63808 0.762 0.446144
## kc$Player1_Rank63 2.08608 0.29486 7.075 1.57e-12 ***
## kc$Player1_Rank630 1.95991 2.63808 0.743 0.457537
## kc$Player1_Rank635 0.85991 1.86980 0.460 0.645601
## kc$Player1_Rank636 4.71991 2.63808 1.789 0.073613 .
## kc$Player1_Rank639 6.88991 2.63808 2.612 0.009019 **
## kc$Player1_Rank64 1.85654 0.31533 5.888 4.00e-09 ***
## kc$Player1_Rank640 4.01991 2.63808 1.524 0.127581
## kc$Player1_Rank646 11.65991 2.63808 4.420 9.95e-06 ***
## kc$Player1_Rank65 2.02495 0.31635 6.401 1.59e-10 ***
## kc$Player1_Rank655 4.53991 2.63808 1.721 0.085289 .
## kc$Player1_Rank658 6.38324 1.53026 4.171 3.05e-05 ***
## kc$Player1_Rank66 1.98757 0.29780 6.674 2.58e-11 ***
## kc$Player1_Rank660 0.72991 2.63808 0.277 0.782030
## kc$Player1_Rank663 0.31991 2.63808 0.121 0.903483
## kc$Player1_Rank667 7.82491 1.86980 4.185 2.87e-05 ***
## kc$Player1_Rank67 1.37592 0.31635 4.349 1.37e-05 ***
## kc$Player1_Rank674 1.97991 2.63808 0.751 0.452960
## kc$Player1_Rank68 1.98368 0.31333 6.331 2.51e-10 ***
## kc$Player1_Rank680 6.80991 1.86980 3.642 0.000271 ***
## kc$Player1_Rank686 3.84991 2.63808 1.459 0.144489
## kc$Player1_Rank69 2.17161 0.34249 6.341 2.36e-10 ***
## kc$Player1_Rank692 5.52991 2.63808 2.096 0.036084 *
## kc$Player1_Rank693 1.13991 1.86980 0.610 0.542110
## kc$Player1_Rank698 4.65741 1.32834 3.506 0.000456 ***
## kc$Player1_Rank7 0.45963 0.26547 1.731 0.083399 .
## kc$Player1_Rank70 1.73004 0.35381 4.890 1.02e-06 ***
## kc$Player1_Rank700 1.63991 2.63808 0.622 0.534197
## kc$Player1_Rank71 1.87096 0.33811 5.534 3.19e-08 ***
## kc$Player1_Rank715 5.23991 2.63808 1.986 0.047024 *
## kc$Player1_Rank718 13.52991 2.63808 5.129 2.96e-07 ***
## kc$Player1_Rank719 1.10991 2.63808 0.421 0.673963
## kc$Player1_Rank72 1.80118 0.33670 5.349 8.96e-08 ***
## kc$Player1_Rank73 1.93207 0.32286 5.984 2.23e-09 ***
## kc$Player1_Rank732 5.84991 2.63808 2.217 0.026606 *
## kc$Player1_Rank733 0.97991 2.63808 0.371 0.710311
## kc$Player1_Rank738 13.52991 2.63808 5.129 2.96e-07 ***
## kc$Player1_Rank7380 3.61991 2.63808 1.372 0.170031
## kc$Player1_Rank74 1.90798 0.34876 5.471 4.56e-08 ***
## kc$Player1_Rank75 1.92316 0.34100 5.640 1.74e-08 ***
## kc$Player1_Rank752 2.50324 1.53026 1.636 0.101899
## kc$Player1_Rank757 10.71991 2.63808 4.064 4.86e-05 ***
## kc$Player1_Rank759 0.61991 1.86980 0.332 0.740245
## kc$Player1_Rank76 2.09912 0.35209 5.962 2.55e-09 ***
## kc$Player1_Rank761 6.99991 1.86980 3.744 0.000182 ***
## kc$Player1_Rank762 3.53991 1.86980 1.893 0.058352 .
## kc$Player1_Rank765 2.81991 2.63808 1.069 0.285123
## kc$Player1_Rank77 1.95295 0.32881 5.939 2.93e-09 ***
## kc$Player1_Rank772 2.29991 2.63808 0.872 0.383327
## kc$Player1_Rank78 2.30083 0.32286 7.126 1.08e-12 ***
## kc$Player1_Rank787 2.72991 2.63808 1.035 0.300777
## kc$Player1_Rank789 1.12991 2.63808 0.428 0.668435
## kc$Player1_Rank79 2.01685 0.33811 5.965 2.50e-09 ***
## kc$Player1_Rank790 3.70991 2.63808 1.406 0.159660
## kc$Player1_Rank793 1.41991 2.63808 0.538 0.590424
## kc$Player1_Rank798 7.88991 2.63808 2.991 0.002787 **
## kc$Player1_Rank8 0.51816 0.26785 1.935 0.053064 .
## kc$Player1_Rank80 2.20922 0.33533 6.588 4.61e-11 ***
## kc$Player1_Rank808 2.14991 2.63808 0.815 0.415115
## kc$Player1_Rank809 12.28991 2.63808 4.659 3.21e-06 ***
## kc$Player1_Rank81 2.31284 0.32881 7.034 2.10e-12 ***
## kc$Player1_Rank813 7.56991 2.63808 2.869 0.004118 **
## kc$Player1_Rank82 1.65063 0.34100 4.841 1.31e-06 ***
## kc$Player1_Rank824 2.14491 1.32834 1.615 0.106393
## kc$Player1_Rank826 2.80991 1.86980 1.503 0.132917
## kc$Player1_Rank829 3.99991 2.63808 1.516 0.129487
## kc$Player1_Rank83 2.46312 0.33954 7.254 4.25e-13 ***
## kc$Player1_Rank836 3.53991 2.63808 1.342 0.179667
## kc$Player1_Rank84 1.93652 0.36109 5.363 8.31e-08 ***
## kc$Player1_Rank847 2.26991 2.63808 0.860 0.389562
## kc$Player1_Rank849 0.48991 2.63808 0.186 0.852679
## kc$Player1_Rank85 2.01446 0.34714 5.803 6.65e-09 ***
## kc$Player1_Rank86 1.65383 0.34714 4.764 1.92e-06 ***
## kc$Player1_Rank861 4.20991 2.63808 1.596 0.110551
## kc$Player1_Rank869 5.41991 2.63808 2.054 0.039947 *
## kc$Player1_Rank87 2.51177 0.33670 7.460 9.16e-14 ***
## kc$Player1_Rank874 9.78991 2.63808 3.711 0.000207 ***
## kc$Player1_Rank88 2.85229 0.37786 7.549 4.67e-14 ***
## kc$Player1_Rank89 1.92498 0.36907 5.216 1.86e-07 ***
## kc$Player1_Rank9 0.69996 0.26951 2.597 0.009409 **
## kc$Player1_Rank90 2.36812 0.35737 6.627 3.56e-11 ***
## kc$Player1_Rank91 2.30804 0.38759 5.955 2.67e-09 ***
## kc$Player1_Rank92 2.75643 0.36498 7.552 4.54e-14 ***
## kc$Player1_Rank93 1.53042 0.35041 4.368 1.27e-05 ***
## kc$Player1_Rank94 2.72233 0.37118 7.334 2.35e-13 ***
## kc$Player1_Rank941 3.76991 2.63808 1.429 0.153017
## kc$Player1_Rank946 7.55991 2.63808 2.866 0.004167 **
## kc$Player1_Rank95 2.27991 0.34876 6.537 6.48e-11 ***
## kc$Player1_Rank96 2.56514 0.37786 6.789 1.18e-11 ***
## kc$Player1_Rank97 2.43684 0.41736 5.839 5.37e-09 ***
## kc$Player1_Rank98 2.28387 0.40438 5.648 1.66e-08 ***
## kc$Player1_Rank99 2.70176 0.40137 6.731 1.75e-11 ***
## kc$Player1_RankN/A 9.36643 0.57792 16.207 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.632 on 14210 degrees of freedom
## Multiple R-squared: 0.1516, Adjusted R-squared: 0.1203
## F-statistic: 4.844 on 524 and 14210 DF, p-value: < 2.2e-16kc = read_xlsx("PIB.xlsx")
linearmod <- lm(kc$`Annual 2022` ~ kc$`Anua 2023`) #price is the dependent variable (y axis)plot(kc$`Anua 2023`, kc$`Annual 2022`)
abline(linearmod, col = "green") #it draws a green line in the graph created above
summary(linearmod) #it gives us statistic information##
## Call:
## lm(formula = kc$`Annual 2022` ~ kc$`Anua 2023`)
##
## Residuals:
## Min 1Q Median 3Q Max
## -351339 -853 -853 -837 387444
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.534e+02 1.148e+03 0.743 0.458
## kc$`Anua 2023` 9.330e-01 6.281e-04 1485.363 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30960 on 734 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.9997, Adjusted R-squared: 0.9997
## F-statistic: 2.206e+06 on 1 and 734 DF, p-value: < 2.2e-16