Section 1 of Exam 1: Regression Model

Read the csv file titled Training Data into R. All rows of this dataset should be used as your training set in the development of a regression model. This dataset contains information about some of Pfizer’s patent applications. Each patent application has a unique ID given to it, and this ID is listed in the Patent_Number column. The column titled Cites_Patent_Count lists the number of patent citations made within the corresponding patent application, and the column titled Cited_by_Patent_Count lists the number of patents which cite the document identified by the Patent_Number. The Cited_by_Patent_Count column can be seen as a measure of the influence and strength of the innovation, and as such, it can be useful to try to predict this column to help firms understand the potential influence of their innovations.

##  Patent_Number      Cites_Patent_Count Cited_by_Patent_Count
##  Length:626         Min.   :  0.000    Min.   :0.0000       
##  Class :character   1st Qu.:  0.000    1st Qu.:0.0000       
##  Mode  :character   Median :  0.000    Median :0.0000       
##                     Mean   :  4.358    Mean   :0.0639       
##                     3rd Qu.:  0.000    3rd Qu.:0.0000       
##                     Max.   :335.000    Max.   :4.0000
##        Patent_Number Cites_Patent_Count Cited_by_Patent_Count
## 1      PL 3341367 T3                  0                     0
## 2    HR P20210871 T1                  0                     0
## 3      CR 20210284 A                  0                     0
## 4 US 2021/0205309 A1                  0                     0
## 5    JP 2021100972 A                  3                     0
## 6  AU 2021/203768 A1                  0                     0
## [1] "Patent_Number"         "Cites_Patent_Count"    "Cited_by_Patent_Count"
  1. Use regression to try to predict the Cited_by_Patent_Count, with Cites_Patent_Count used as a covariate. Based on your results, write an equation using the following format:
Cited_by_Patent_Count ≈ B1(Cites_Patent_Count) + B2, where B1 and B2 are real numbers
training$Patent_Number <- NULL
training_model <- lm(Cited_by_Patent_Count~.,data = training)
summary(training_model)
## 
## Call:
## lm(formula = Cited_by_Patent_Count ~ ., data = training)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9469 -0.0523 -0.0523 -0.0523  3.7661 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        0.0522603  0.0130896   3.993 7.32e-05 ***
## Cites_Patent_Count 0.0026705  0.0005322   5.018 6.81e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3223 on 624 degrees of freedom
## Multiple R-squared:  0.03879,    Adjusted R-squared:  0.03725 
## F-statistic: 25.18 on 1 and 624 DF,  p-value: 6.811e-07

Fill-in the blanks for the following statements:

  1. Your regression equation provides an “estimate” of the actual values for the numbers B1 and B2. There is a 90% probability that the actual value of B1 lies between 0.001793859 and 0.003547102.
  2. There is a 90% probability that the actual value of B2 lies between 0.030697775 and 0.073822761.
##                            5 %        95 %
## (Intercept)        0.030697775 0.073822761
## Cites_Patent_Count 0.001793859 0.003547102
  1. Based on Cook’s Distance, are there outliers that may possibly need to be removed and/or treated differently in the dataset? Create a plot using R to support your answer.
cooks.distance(training_model)
##            1            2            3            4            5            6 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.810625e-05 2.174933e-05 
##            7            8            9           10           11           12 
## 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           13           14           15           16           17           18 
## 5.071376e-05 2.174933e-05 2.174933e-05 8.574799e-05 2.174933e-05 2.174933e-05 
##           19           20           21           22           23           24 
## 2.372145e-05 2.174933e-05 2.174933e-05 2.174933e-05 3.021095e-02 2.372145e-05 
##           25           26           27           28           29           30 
## 2.174933e-05 2.174933e-05 2.583357e-05 2.372145e-05 7.152876e-03 2.174933e-05 
##           31           32           33           34           35           36 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           37           38           39           40           41           42 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           43           44           45           46           47           48 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           49           50           51           52           53           54 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.583357e-05 2.174933e-05 2.174933e-05 
##           55           56           57           58           59           60 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           61           62           63           64           65           66 
## 2.174933e-05 2.174933e-05 2.174933e-05 3.612723e-05 2.174933e-05 2.174933e-05 
##           67           68           69           70           71           72 
## 2.174933e-05 6.914970e-03 2.174933e-05 2.174933e-05 3.612723e-05 2.174933e-05 
##           73           74           75           76           77           78 
## 6.580877e-05 6.111181e-02 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           79           80           81           82           83           84 
## 2.810625e-05 5.071376e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##           85           86           87           88           89           90 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 3.322685e-05 
##           91           92           93           94           95           96 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 7.152876e-03 6.580877e-05 
##           97           98           99          100          101          102 
## 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 4.284078e-04 2.174933e-05 
##          103          104          105          106          107          108 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          109          110          111          112          113          114 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          115          116          117          118          119          120 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          121          122          123          124          125          126 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.810625e-05 2.174933e-05 4.275628e-05 
##          127          128          129          130          131          132 
## 9.239691e-02 5.071376e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.372145e-05 
##          133          134          135          136          137          138 
## 2.174933e-05 1.273912e-02 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          139          140          141          142          143          144 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          145          146          147          148          149          150 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          151          152          153          154          155          156 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          157          158          159          160          161          162 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          163          164          165          166          167          168 
## 2.810625e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          169          170          171          172          173          174 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          175          176          177          178          179          180 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 7.381892e-02 2.174933e-05 
##          181          182          183          184          185          186 
## 2.838903e-02 2.174933e-05 2.174933e-05 2.174933e-05 1.570643e-03 2.174933e-05 
##          187          188          189          190          191          192 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          193          194          195          196          197          198 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          199          200          201          202          203          204 
## 2.174933e-05 1.335152e-04 7.152876e-03 2.174933e-05 3.612723e-05 2.174933e-05 
##          205          206          207          208          209          210 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          211          212          213          214          215          216 
## 2.372145e-05 2.174933e-05 2.810625e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          217          218          219          220          221          222 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 
##          223          224          225          226          227          228 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.372145e-05 
##          229          230          231          232          233          234 
## 2.174933e-05 2.174933e-05 8.849406e-01 2.174933e-05 2.174933e-05 2.174933e-05 
##          235          236          237          238          239          240 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          241          242          243          244          245          246 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          247          248          249          250          251          252 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          253          254          255          256          257          258 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          259          260          261          262          263          264 
## 3.021095e-02 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 3.612723e-05 
##          265          266          267          268          269          270 
## 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          271          272          273          274          275          276 
## 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          277          278          279          280          281          282 
## 1.222411e-04 2.174933e-05 2.174933e-05 2.174933e-05 2.810625e-05 2.174933e-05 
##          283          284          285          286          287          288 
## 2.174933e-05 2.583357e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          289          290          291          292          293          294 
## 2.174933e-05 2.174933e-05 2.174933e-05 3.929307e-05 2.174933e-05 2.174933e-05 
##          295          296          297          298          299          300 
## 2.174933e-05 9.727993e-02 9.369997e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          301          302          303          304          305          306 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          307          308          309          310          311          312 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          313          314          315          316          317          318 
## 2.174933e-05 2.174933e-05 2.174933e-05 3.963990e-04 2.174933e-05 2.174933e-05 
##          319          320          321          322          323          324 
## 7.152876e-03 2.174933e-05 1.796726e-02 2.174933e-05 2.174933e-05 2.810625e-05 
##          325          326          327          328          329          330 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          331          332          333          334          335          336 
## 2.174933e-05 2.372145e-05 2.174933e-05 1.913967e-02 2.174933e-05 2.174933e-05 
##          337          338          339          340          341          342 
## 2.174933e-05 7.185379e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          343          344          345          346          347          348 
## 2.174933e-05 2.485777e-03 2.174933e-05 3.322685e-05 2.174933e-05 1.118882e-04 
##          349          350          351          352          353          354 
## 2.174933e-05 2.174933e-05 7.702738e-04 2.372145e-05 2.174933e-05 2.174933e-05 
##          355          356          357          358          359          360 
## 6.996241e-03 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 
##          361          362          363          364          365          366 
## 2.174933e-05 2.174933e-05 3.322685e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          367          368          369          370          371          372 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 7.152876e-03 6.030046e-05 
##          373          374          375          376          377          378 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          379          380          381          382          383          384 
## 2.174933e-05 3.056231e-05 7.152876e-03 2.174933e-05 2.174933e-05 2.174933e-05 
##          385          386          387          388          389          390 
## 2.174933e-05 2.174933e-05 1.335152e-04 2.174933e-05 2.174933e-05 2.174933e-05 
##          391          392          393          394          395          396 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 
##          397          398          399          400          401          402 
## 2.174933e-05 2.174933e-05 5.528323e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          403          404          405          406          407          408 
## 2.174933e-05 2.174933e-05 3.021095e-02 2.174933e-05 2.372145e-05 2.174933e-05 
##          409          410          411          412          413          414 
## 3.056231e-05 7.152876e-03 2.174933e-05 2.174933e-05 3.929307e-05 2.174933e-05 
##          415          416          417          418          419          420 
## 2.174933e-05 2.174933e-05 7.111225e-02 2.174933e-05 5.528323e-05 7.152876e-03 
##          421          422          423          424          425          426 
## 2.174933e-05 4.655102e-05 8.574799e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          427          428          429          430          431          432 
## 2.174933e-05 2.174933e-05 2.174933e-05 3.056231e-05 2.174933e-05 2.583357e-05 
##          433          434          435          436          437          438 
## 2.174933e-05 2.583357e-05 2.174933e-05 2.810625e-05 2.174933e-05 2.174933e-05 
##          439          440          441          442          443          444 
## 2.174933e-05 2.174933e-05 1.222411e-04 2.174933e-05 5.071376e-05 2.174933e-05 
##          445          446          447          448          449          450 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          451          452          453          454          455          456 
## 3.056231e-05 2.174933e-05 2.174933e-05 2.174933e-05 6.030046e-05 2.174933e-05 
##          457          458          459          460          461          462 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 9.369997e-05 
##          463          464          465          466          467          468 
## 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          469          470          471          472          473          474 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          475          476          477          478          479          480 
## 2.174933e-05 2.810625e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          481          482          483          484          485          486 
## 3.322685e-05 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 2.174933e-05 
##          487          488          489          490          491          492 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.372145e-05 2.174933e-05 
##          493          494          495          496          497          498 
## 2.174933e-05 2.174933e-05 2.174933e-05 6.773844e-03 2.583357e-05 2.583357e-05 
##          499          500          501          502          503          504 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          505          506          507          508          509          510 
## 6.775879e-01 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          511          512          513          514          515          516 
## 2.174933e-05 2.174933e-05 2.583357e-05 2.583357e-05 2.810625e-05 2.372145e-05 
##          517          518          519          520          521          522 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          523          524          525          526          527          528 
## 2.174933e-05 2.174933e-05 3.612723e-05 2.174933e-05 2.810625e-05 2.583357e-05 
##          529          530          531          532          533          534 
## 2.174933e-05 2.174933e-05 7.848345e-05 2.174933e-05 1.150560e-03 2.174933e-05 
##          535          536          537          538          539          540 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          541          542          543          544          545          546 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          547          548          549          550          551          552 
## 2.174933e-05 2.583357e-05 2.174933e-05 2.174933e-05 2.810625e-05 2.174933e-05 
##          553          554          555          556          557          558 
## 2.174933e-05 7.152876e-03 2.174933e-05 2.174933e-05 3.021095e-02 2.174933e-05 
##          559          560          561          562          563          564 
## 2.174933e-05 7.185379e-05 2.174933e-05 2.174933e-05 3.612723e-05 2.174933e-05 
##          565          566          567          568          569          570 
## 2.174933e-05 2.174933e-05 2.635251e+00 1.523294e-02 2.174933e-05 2.174933e-05 
##          571          572          573          574          575          576 
## 2.174933e-05 8.756098e-03 2.174933e-05 2.174933e-05 6.914970e-03 2.174933e-05 
##          577          578          579          580          581          582 
## 2.174933e-05 3.021095e-02 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          583          584          585          586          587          588 
## 5.282779e-03 2.174933e-05 2.174933e-05 2.174933e-05 3.664304e-04 2.174933e-05 
##          589          590          591          592          593          594 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          595          596          597          598          599          600 
## 6.914970e-03 2.810625e-05 2.174933e-05 2.174933e-05 2.174933e-05 3.056231e-05 
##          601          602          603          604          605          606 
## 2.174933e-05 2.463827e+00 3.056231e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          607          608          609          610          611          612 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          613          614          615          616          617          618 
## 2.174933e-05 2.174933e-05 4.275628e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          619          620          621          622          623          624 
## 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 2.174933e-05 
##          625          626 
## 2.174933e-05 2.583357e-05
cbind(training, cooks.distance(training_model))
##     Cites_Patent_Count Cited_by_Patent_Count cooks.distance(training_model)
## 1                    0                     0                   2.174933e-05
## 2                    0                     0                   2.174933e-05
## 3                    0                     0                   2.174933e-05
## 4                    0                     0                   2.174933e-05
## 5                    3                     0                   2.810625e-05
## 6                    0                     0                   2.174933e-05
## 7                    0                     0                   2.174933e-05
## 8                    1                     0                   2.372145e-05
## 9                    0                     0                   2.174933e-05
## 10                   0                     0                   2.174933e-05
## 11                   0                     0                   2.174933e-05
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## 493                  0                     0                   2.174933e-05
## 494                  0                     0                   2.174933e-05
## 495                  0                     0                   2.174933e-05
## 496                  4                     1                   6.773844e-03
## 497                  2                     0                   2.583357e-05
## 498                  2                     0                   2.583357e-05
## 499                  0                     0                   2.174933e-05
## 500                  0                     0                   2.174933e-05
## 501                  0                     0                   2.174933e-05
## 502                  0                     0                   2.174933e-05
## 503                  0                     0                   2.174933e-05
## 504                  0                     0                   2.174933e-05
## 505                139                     2                   6.775879e-01
## 506                  0                     0                   2.174933e-05
## 507                  0                     0                   2.174933e-05
## 508                  0                     0                   2.174933e-05
## 509                  0                     0                   2.174933e-05
## 510                  0                     0                   2.174933e-05
## 511                  0                     0                   2.174933e-05
## 512                  0                     0                   2.174933e-05
## 513                  2                     0                   2.583357e-05
## 514                  2                     0                   2.583357e-05
## 515                  3                     0                   2.810625e-05
## 516                  1                     0                   2.372145e-05
## 517                  0                     0                   2.174933e-05
## 518                  0                     0                   2.174933e-05
## 519                  0                     0                   2.174933e-05
## 520                  0                     0                   2.174933e-05
## 521                  0                     0                   2.174933e-05
## 522                  0                     0                   2.174933e-05
## 523                  0                     0                   2.174933e-05
## 524                  0                     0                   2.174933e-05
## 525                  6                     0                   3.612723e-05
## 526                  0                     0                   2.174933e-05
## 527                  3                     0                   2.810625e-05
## 528                  2                     0                   2.583357e-05
## 529                  0                     0                   2.174933e-05
## 530                  0                     0                   2.174933e-05
## 531                 15                     0                   7.848345e-05
## 532                  0                     0                   2.174933e-05
## 533                 49                     0                   1.150560e-03
## 534                  0                     0                   2.174933e-05
## 535                  0                     0                   2.174933e-05
## 536                  0                     0                   2.174933e-05
## 537                  0                     0                   2.174933e-05
## 538                  0                     0                   2.174933e-05
## 539                  0                     0                   2.174933e-05
## 540                  0                     0                   2.174933e-05
## 541                  0                     0                   2.174933e-05
## 542                  0                     0                   2.174933e-05
## 543                  0                     0                   2.174933e-05
## 544                  0                     0                   2.174933e-05
## 545                  0                     0                   2.174933e-05
## 546                  0                     0                   2.174933e-05
## 547                  0                     0                   2.174933e-05
## 548                  2                     0                   2.583357e-05
## 549                  0                     0                   2.174933e-05
## 550                  0                     0                   2.174933e-05
## 551                  3                     0                   2.810625e-05
## 552                  0                     0                   2.174933e-05
## 553                  0                     0                   2.174933e-05
## 554                  0                     1                   7.152876e-03
## 555                  0                     0                   2.174933e-05
## 556                  0                     0                   2.174933e-05
## 557                  0                     2                   3.021095e-02
## 558                  0                     0                   2.174933e-05
## 559                  0                     0                   2.174933e-05
## 560                 14                     0                   7.185379e-05
## 561                  0                     0                   2.174933e-05
## 562                  0                     0                   2.174933e-05
## 563                  6                     0                   3.612723e-05
## 564                  0                     0                   2.174933e-05
## 565                  0                     0                   2.174933e-05
## 566                  0                     0                   2.174933e-05
## 567                335                     0                   2.635251e+00
## 568                 36                     1                   1.523294e-02
## 569                  0                     0                   2.174933e-05
## 570                  0                     0                   2.174933e-05
## 571                  0                     0                   2.174933e-05
## 572                 20                     1                   8.756098e-03
## 573                  0                     0                   2.174933e-05
## 574                  0                     0                   2.174933e-05
## 575                  2                     1                   6.914970e-03
## 576                  0                     0                   2.174933e-05
## 577                  0                     0                   2.174933e-05
## 578                  0                     2                   3.021095e-02
## 579                  0                     0                   2.174933e-05
## 580                  0                     0                   2.174933e-05
## 581                  0                     0                   2.174933e-05
## 582                  0                     0                   2.174933e-05
## 583                 77                     0                   5.282779e-03
## 584                  0                     0                   2.174933e-05
## 585                  0                     0                   2.174933e-05
## 586                  0                     0                   2.174933e-05
## 587                 33                     0                   3.664304e-04
## 588                  0                     0                   2.174933e-05
## 589                  0                     0                   2.174933e-05
## 590                  0                     0                   2.174933e-05
## 591                  0                     0                   2.174933e-05
## 592                  0                     0                   2.174933e-05
## 593                  0                     0                   2.174933e-05
## 594                  0                     0                   2.174933e-05
## 595                  2                     1                   6.914970e-03
## 596                  3                     0                   2.810625e-05
## 597                  0                     0                   2.174933e-05
## 598                  0                     0                   2.174933e-05
## 599                  0                     0                   2.174933e-05
## 600                  4                     0                   3.056231e-05
## 601                  0                     0                   2.174933e-05
## 602                331                     0                   2.463827e+00
## 603                  4                     0                   3.056231e-05
## 604                  0                     0                   2.174933e-05
## 605                  0                     0                   2.174933e-05
## 606                  0                     0                   2.174933e-05
## 607                  0                     0                   2.174933e-05
## 608                  0                     0                   2.174933e-05
## 609                  0                     0                   2.174933e-05
## 610                  0                     0                   2.174933e-05
## 611                  0                     0                   2.174933e-05
## 612                  0                     0                   2.174933e-05
## 613                  0                     0                   2.174933e-05
## 614                  0                     0                   2.174933e-05
## 615                  8                     0                   4.275628e-05
## 616                  0                     0                   2.174933e-05
## 617                  0                     0                   2.174933e-05
## 618                  0                     0                   2.174933e-05
## 619                  0                     0                   2.174933e-05
## 620                  0                     0                   2.174933e-05
## 621                  0                     0                   2.174933e-05
## 622                  0                     0                   2.174933e-05
## 623                  0                     0                   2.174933e-05
## 624                  0                     0                   2.174933e-05
## 625                  0                     0                   2.174933e-05
## 626                  2                     0                   2.583357e-05
plot(training_model)

There are three outliers that need to be removed or treated differently. Data point 231 sits just at 1 and data points 602 and 567 sit will outside of 1.

  1. Check the normality of residuals by creating a QQ-plot. Based on the plot, are the residuals normally distributed?
qqnorm(training_model$residuals)
qqline(training_model$residuals)

The residuals are not normally distributd; the plot is considered a heavily tailed distribution.

  1. Use the regression model that you created in #2 to predict the Cited_by_Patent_Count in each of the following scenarios:
  1. Cites_Patent_Count = 340 -> 0.9602238
  2. Cites_Patent_Count = 300 -> 0.8534046
Q3A = data.frame(Cites_Patent_Count = c(340))
Q3B = data.frame(Cites_Patent_Count = c(300))
predictA<-predict(training_model, Q3A, type = "response")
predictB<-predict(training_model, Q3B, type = "response")
predictA
##         1 
## 0.9602238
predictB
##         1 
## 0.8534046
    1. Was the prediction made in part a of #3 considered to be extrapolation? Yes, the result falls outside of the range of calculated leverage.
    2. Was the prediction made in part b of #3 considered to be extrapolation? Yes, the result falls outside of the range of calculated leverage.
min(hatvalues(training_model))
## [1] 0.001597793
mean(hatvalues(training_model))
## [1] 0.003194888
max(hatvalues(training_model))
## [1] 0.2995991
PRED = model.matrix(training_model)
pred_newA = c(.9602238, 0)
t(pred_newA)%*%solve(t(PRED)%*%PRED)%*%pred_newA
##             [,1]
## [1,] 0.001520621
pred_newB = c(.8534046, 0)
t(pred_newB)%*%solve(t(PRED)%*%PRED)%*%pred_newB
##             [,1]
## [1,] 0.001201119
  1. Fill in the blanks based on the regression model that you created in #2, and the corresponding prediction that you made in part b of #3:
  1. When Cites_Patent_Count is 300 (as in part b of #3), there is a 95% chance that Cited_by_Patent_Count will be between 0.1486074 and 1.558202.
predictB_prediction<-predict(training_model, Q3B, interval = "prediction", level = .95, type = "response")
predictB_prediction
##         fit       lwr      upr
## 1 0.8534046 0.1486074 1.558202
  1. When Cites_Patent_Count is 300, there is a 95% chance that the mean response will fall between 0.5434141 and 1.163395.
predictB_confidence<-predict(training_model, Q3B, interval = "confidence", level = .95, type = "response")
predictB_confidence
##         fit       lwr      upr
## 1 0.8534046 0.5434141 1.163395

Section 2 of Exam 1: Joining Data

The four types of mutating joins learned in class are:

  1. Open the Training Data and Sequence Counts csv files, and notice that each file has a column listing the patent application number. For full credit, perform the following joins in R without changing any column titles in either dataset:
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.2.1
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6     ✔ purrr   0.3.4
## ✔ tibble  3.1.7     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.0
## ✔ readr   2.1.2     ✔ forcats 0.5.1
## Warning: package 'ggplot2' was built under R version 4.2.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
training <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 621/Exams/Exam 1/Training Data.csv")
sequence <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 621/Exams/Exam 1/Sequence Counts.csv")
colnames(training)
## [1] "Patent_Number"         "Cites_Patent_Count"    "Cited_by_Patent_Count"
colnames(sequence)
## [1] "Patent_No."     "Sequence_Count"
colnames(sequence) <- c("Patent_Number", "Sequence_Count")
colnames(sequence)
## [1] "Patent_Number"  "Sequence_Count"
  1. Perform an inner join
training%>%inner_join(sequence, by = "Patent_Number")->Inner_Join_TraSeq
Inner_Join_TraSeq
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Sequence_Count
## 1          CA 189065 S                  0                     0              0
## 2       NI 202000072 A                  0                     0              0
## 3     KR 20210032013 A                  0                     0             80
## 4    PH 12020550461 A1                  0                     0              0
## 5         TW I722568 B                  0                     0              0
## 6       CN 112533674 A                  0                     2              0
## 7     CO 2021002954 A2                  0                     0              0
## 8      JP 2021040642 A                  1                     0              0
## 9    AU 2019/341683 A1                  0                     0              0
## 10     JP 2021042204 A                  4                     0              0
## 11  US 2021/0077463 A1                  0                     1             24
## 12       CA 3153676 A1                  0                     0              0
## 13         CA 200622 S                  0                     0              0
## 14   WO 2021/048736 A1                  7                     0              0
## 15   AU 2021/200232 A1                  0                     0              0
## 16      PE 20210554 A1                  0                     0              0
## 17        AR 115987 A1                  0                     0              0
## 18      US 10946086 B2                111                     1              0
## 19      TW 202111125 A                  0                     0              0
## 20      US 10947494 B2                 11                     0              0
## 21      CN 112513070 A                  0                     1              0
## 22      TW 202110480 A                  0                     0              0
## 23      US 10946031 B2                  9                     0              0
## 24      US 10945994 B2                 16                     0              2
## 25  BR 112020025701 A2                  0                     0              0
## 26      TW 202110446 A                  0                     0              0
## 27      PE 20210488 A1                  0                     0              0
## 28    KR 20210029234 A                  0                     0              0
## 29       ES 2811523 T3                  0                     0              0
## 30  US 2021/0069219 A1                  0                     0              0
## 31     JP 2021038265 A                  4                     0              0
## 32  US 2021/0069326 A1                  0                     0             41
## 33        EA 037318 B1                  2                     0              0
## 34   AU 2019/329884 A1                  0                     0              0
## 35   AU 2016/286108 B2                  2                     0              0
## 36   AU 2019/323790 A1                  0                     0              0
## 37     JP 2021036873 A                  3                     0              0
## 38       EP 3334760 B1                  0                     0              0
## 39        UA 123270 C2                  0                     0              0
## 40       EP 3091981 B1                  0                     0              0
## 41      LT C2534153 I2                  0                     0              0
## 42      US 10941216 B2                 20                     0             82
## 43  BR 112020024956 A2                  0                     0              0
## 44      US 10941118 B2                 10                     0              0
## 45      CN 112469473 A                  0                     0              0
## 46       PL 3096785 T3                  0                     0              0
## 47       PL 3310784 T3                  0                     0              0
## 48    CO 2021002230 A2                  0                     0              0
## 49    CO 2021001893 A2                  0                     0              0
## 50    CO 2020015305 A2                  0                     0              0
## 51      PE 20210468 A1                  0                     0              0
## 52        EA 037288 B1                  4                     0              0
## 53      PE 20210412 A1                  0                     0              0
## 54  US 2021/0061902 A1                  0                     0            225
## 55  US 2021/0061923 A1                  0                     0              0
## 56       EP 2968155 B1                 12                     0              0
## 57       EP 3784664 A1                  0                     0              0
## 58          MA 52360 A                  0                     0              0
## 59  BR 112014018192 A8                  0                     0              0
## 60  BR 112020020941 A2                  0                     0              0
## 61       ES 2808987 T3                  0                     0              0
## 62  BR 112020024470 A2                  0                     0              0
## 63      US 10934279 B2                 17                     0              0
## 64      TW 202108167 A                  0                     0              0
## 65        TW I720272 B                  1                     0              0
## 66         IL 280292 A                  0                     0              0
## 67        TW I720448 B                  0                     0              0
## 68         IL 279591 A                  0                     0              0
## 69         IL 280317 A                  0                     0              0
## 70         IL 279926 A                  0                     0              0
## 71    DO P2020000191 A                  0                     0              0
## 72         IL 248667 B                  0                     0              0
## 73         IL 254131 B                  0                     0              0
## 74         IL 244437 B                  0                     0              0
## 75         IL 255444 B                  0                     0              0
## 76        PT 3137114 T                  0                     0              0
## 77       RU 2743793 C1                  3                     0              0
## 78    CL 2020002507 A1                  0                     0              0
## 79          UY 38786 A                  0                     0              0
## 80   SG 11202100888W A                  0                     0              0
## 81  US 2021/0054087 A1                  0                     0            502
## 82   AU 2018/208844 B2                  5                     0              0
## 83       EP 3781132 A1                  0                     0              0
## 84       EP 3341367 B1                  0                     0              0
## 85       EP 3148587 B1                  1                     0              0
## 86       ES 2807591 T3                  0                     0              0
## 87      US 10927178 B2                  0                     0            173
## 88  BR 112020022897 A2                  0                     0              0
## 89    KR 20210020095 A                  0                     0              0
## 90    KR 20210019529 A                  0                     0              0
## 91      CN 112384282 A                  0                     0              0
## 92   AU 2018/349259 B2                  1                     0              0
## 93  US 2021/0047298 A1                  0                     0              0
## 94     JP 2021020890 A                  0                     0              0
## 95   AU 2019/325400 A1                  0                     0              0
## 96   AU 2019/336197 A1                  0                     0              0
## 97   WO 2021/029854 A1                  4                     1              0
## 98     JP 2021019632 A                  2                     0              0
## 99  US 2021/0047325 A1                  2                     0              2
## 100      CA 3150424 A1                  0                     0              0
## 101    BR PI0915166 B1                  0                     0              0
## 102   KR 20210018529 A                  0                     0              6
## 103      EP 3774863 A1                  0                     0              0
## 104   KR 20210018341 A                  0                     0              0
## 105 BR 112020019368 A2                  0                     0              0
## 106     US 10918708 B2                139                     2             40
## 107       PT 3327027 T                  0                     0              0
## 108      DK 3242888 T3                  0                     0              0
## 109  PH 12020550596 A1                  0                     0              0
## 110      DK 3328849 T5                  0                     0              0
## 111   CL 2020002748 A1                  0                     0              0
## 112 US 2021/0040182 A1                  0                     0            518
## 113 US 2021/0040045 A1                  0                     0              0
## 114       TW I718758 B                  2                     0              0
## 115       TW I718644 B                  2                     0              0
## 116       TW I718427 B                  3                     0              0
## 117       TW I718144 B                  1                     0              0
## 118     CN 112336854 A                  0                     0              0
## 119 BR 112020022595 A2                  0                     0              0
## 120   KR 20210014763 A                  0                     0              0
## 121 BR 112020023891 A2                  0                     0              0
## 122 BR 112020017935 A2                  0                     0              0
## 123   KR 20210013777 A                  0                     0             62
## 124 US 2021/0032308 A1                  0                     0            130
## 125  AU 2019/304198 A1                  0                     0              0
## 126  AU 2016/280137 B2                  6                     0              0
## 127  AU 2019/290212 A1                  0                     0              0
## 128      RU 2742260 C2                  3                     0              0
## 129    JP 2021011493 A                  2                     0              0
## 130   KR 20210013167 A                  0                     0            200
## 131   KR 20210013165 A                  0                     0            890
## 132     US 10906955 B2                 15                     0             25
## 133     CN 112313219 A                  0                     0              0
## 134     US 10906888 B2                 49                     0              0
## 135     TW 202104224 A                  0                     0              0
## 136        IL 254073 B                  0                     0              0
## 137        IL 279396 A                  0                     0              0
## 138        IL 278924 A                  0                     0              0
## 139        IL 278926 A                  0                     0              0
## 140        IL 279224 A                  0                     0              0
## 141        IL 279300 A                  0                     0              0
## 142        IL 255224 B                  0                     0              0
## 143        IL 279270 A                  0                     0              0
## 144        IL 252158 B                  0                     0              0
## 145      SI 3500564 T1                  0                     0              0
## 146         UY 38768 A                  0                     0              0
## 147    EC SP20078651 A                  0                     0              0
## 148         UY 38752 A                  0                     0              0
## 149   KR 20210011076 A                  2                     0            798
## 150  SG 11202100021T A                  0                     0              0
## 151 US 2021/0024497 A1                  0                     0              0
## 152  AU 2019/210579 B2                  3                     0              0
## 153 US 2021/0023134 A1                  0                     0             10
## 154    JP 2021008452 A                  0                     0              0
## 155 US 2021/0024903 A1                  0                     1            761
## 156 US 2021/0024589 A1                  0                     0             81
## 157 US 2021/0023200 A1                  0                     0            326
## 158 US 2021/0023193 A1                  0                     2             40
## 159       PT 3143019 T                  0                     0              0
## 160      HU E050811 T2                  0                     0              0
## 161  WO 2021/014360 A1                 14                     0              0
## 162 US 2021/0024536 A1                  0                     0              0
## 163       AR 115498 A1                  0                     0              0
## 164      EP 3770164 A1                  6                     0              0
## 165      EP 3768669 A1                  0                     0              0
## 166 BR 112020021689 A2                  0                     0              0
## 167     CN 112263677 A                  0                     0              0
## 168     US 10899802 B2                335                     0             22
## 169     US 10899840 B2                 36                     1             36
## 170      DK 3137114 T3                  0                     0              0
## 171      PL 3339303 T3                  0                     0              0
## 172     GE P20217211 B                  0                     0              0
## 173  WO 2021/009676 A1                 20                     1              0
## 174      CA 3147266 A1                  0                     0              0
## 175 US 2021/0017206 A1                  0                     0              0
## 176 US 2021/0017553 A1                  2                     1              5
## 177 US 2021/0017205 A1                  0                     0              0
## 178 US 2021/0017254 A1                  0                     0             12
## 179 US 2021/0017172 A1                  0                     2              0
## 180      CR 20200612 A                  0                     0              0
## 181      EP 3765474 A1                  0                     0              0
## 182   KR 20210008177 A                  0                     0              4
## 183      EP 3765027 A1                  0                     0              0
## 184      EP 3766885 A1                 77                     0              0
## 185      EP 3765019 A1                  0                     0              0
## 186    SA 516371030 B1                  0                     0              0
## 187         MA 52012 A                  0                     0              0
## 188     US 10894083 B2                 33                     0             10
## 189     PE 20210127 A1                  0                     0              0
## 190 BR 112016029612 B1                  0                     0              0
## 191      DK 3327027 T3                  0                     0              0
## 192        MY 182282 A                  0                     0              0
## 193        MY 182168 A                  0                     0              0
## 194     CN 112236446 A                  0                     0              0
## 195 US 2021/0009601 A1                  0                     0             15
## 196 US 2021/0009657 A1                  2                     1             36
## 197      RU 2740309 C2                  3                     0              0
## 198      EP 3761954 A1                  0                     0              0
## 199       PT 3328867 T                  0                     0              0
## 200       CA 2928908 C                  0                     0             66
## 201     CN 112218618 A                  4                     0              0
## 202        MY 181891 A                  0                     0              0
## 203     US 10888611 B2                331                     0             22
## 204      RU 2740135 C1                  4                     0              0
## 205     NI 202000058 A                  0                     0              0
## 206   KR 20210002757 A                  0                     0             46
## 207     CN 112195169 A                  0                     0              0
## 208   KR 20210002642 A                  0                     0              2
## 209 US 2021/0002369 A1                  0                     0             11
## 210 US 2021/0002371 A1                  0                     0              9
## 211 US 2021/0002251 A1                  0                     0              0
## 212    JP 2021001170 A                  0                     0              0
## 213  AU 2020/281105 A1                  0                     0              0
## 214 US 2021/0000930 A1                  0                     0              3
## 215  AU 2019/299666 A1                  0                     0              0
## 216  WO 2021/001741 A1                  8                     0             11
## 217      EP 3327027 B1                  0                     0              0
## 218      EP 3759129 A1                  0                     0              0
## 219      EP 3328849 B9                  0                     0              0
## 220      EP 3759134 A1                  0                     0              0
## 221      EP 3758753 A1                  0                     0              0
## 222 BR 112020015641 A2                  0                     0              0
  1. Perform a full join
training%>%full_join(sequence, by = "Patent_Number")->Full_Join_TraSeq
Full_Join_TraSeq
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Sequence_Count
## 1        PL 3341367 T3                  0                     0             NA
## 2      HR P20210871 T1                  0                     0             NA
## 3        CR 20210284 A                  0                     0             NA
## 4   US 2021/0205309 A1                  0                     0             NA
## 5      JP 2021100972 A                  3                     0             NA
## 6    AU 2021/203768 A1                  0                     0             NA
## 7        ES 2841400 T3                  0                     0             NA
## 8   US 2021/0206757 A1                  1                     0             NA
## 9       PE 20211235 A1                  0                     0             NA
## 10  US 2021/0205463 A1                  0                     0             NA
## 11        AR 117073 A1                  0                     0             NA
## 12       EP 3327027 B9                  0                     0             NA
## 13       EP 3096786 B1                 10                     0             NA
## 14       EP 3844288 A1                  0                     0             NA
## 15       EP 3843740 A1                  0                     0             NA
## 16       EP 3096783 B1                 16                     0             NA
## 17  BR 112021006223 A2                  0                     0             NA
## 18       DK 2909307 T3                  0                     0             NA
## 19   AU 2018/372109 B2                  1                     0             NA
## 20      TW 202124414 A                  0                     0             NA
## 21  US 2021/0198365 A1                  0                     0             NA
## 22      TW 202123937 A                  0                     0             NA
## 23  US 2021/0196810 A1                  0                     2             NA
## 24   AU 2018/275359 B2                  1                     0             NA
## 25  US 2021/0196823 A1                  0                     0             NA
## 26   AU 2019/404250 A1                  0                     0             NA
## 27     JP 2021098716 A                  2                     0             NA
## 28        TW I732431 B                  1                     0             NA
## 29  US 2021/0198305 A1                  0                     1             NA
## 30      TW 202123940 A                  0                     0             NA
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  1. Join the two datasets so that only the patents in the Sequence Counts dataset are included
training%>%right_join(sequence, by = "Patent_Number")->right_Join_TraSeq
right_Join_TraSeq
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Sequence_Count
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  1. Read the Training and Testing Data csv file into R. This file contains a binary column called Partition which is 0 when the patent was part of the training set used to develop the regression model in #2, and is equal to 1 otherwise. Use R to perform the following on this dataset:
tratest <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 621/Exams/Exam 1/Training and Testing Data.csv")
tratest
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Partition
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  1. Group the dataset by Partition. Summarize each grouping by calculating the standard deviation of Cites_Patent_Count for each group.
colnames(tratest)
## [1] "Patent_Number"         "Cites_Patent_Count"    "Cited_by_Patent_Count"
## [4] "Partition"
by_partition <- group_by(tratest, Cites_Patent_Count, Cited_by_Patent_Count, Partition)
summarise(by_partition, Cites_Patent_Count = sd(Cites_Patent_Count, na.rm = TRUE))
## `summarise()` has grouped output by 'Cites_Patent_Count',
## 'Cited_by_Patent_Count'. You can override using the `.groups` argument.
## # A tibble: 64 × 3
## # Groups:   Cites_Patent_Count, Cited_by_Patent_Count [9]
##    Cites_Patent_Count Cited_by_Patent_Count Partition
##                 <dbl>                 <int>     <int>
##  1                  0                     0         0
##  2                  0                     0         1
##  3                  0                     1         0
##  4                  0                     2         0
##  5                  0                     0         0
##  6                 NA                     0         1
##  7                  0                     0         0
##  8                  0                     1         0
##  9                  0                     0         0
## 10                  0                     0         1
## # … with 54 more rows
  1. Identify the top 3 patents with the highest number of citations in the Cited_by_Patent_Count column.
arrange(tratest, desc(Cited_by_Patent_Count))
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Partition
## 1    WO 2021/250648 A1                  3                    11         1
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  1. Filter the dataset to display only those rows for which the Cites_Patent_Count is greater than zero.
filter(tratest, Cites_Patent_Count>0)
##          Patent_Number Cites_Patent_Count Cited_by_Patent_Count Partition
## 1      JP 2021100972 A                  3                     0         0
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