Exam 1
Lynx
2022-10-16
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.
library(readr)## Warning: package 'readr' was built under R version 4.2.1Training_Data <- read_csv("C:/Users/Lynx/Documents/MSDA/621/Exam 1/Training Data.csv")## Rows: 626 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Patent_Number
## dbl (2): Cites_Patent_Count, Cited_by_Patent_Count
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.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:
\[Cited\_by\_Patient\_Count ≈ B_1(Cities\_Patent\_Count) + B_2,\\where\ B_1\ and\ B_2\ are\ real\ numbers\]
str(Training_Data)## spec_tbl_df [626 × 3] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Patent_Number : chr [1:626] "PL 3341367 T3" "HR P20210871 T1" "CR 20210284 A" "US 2021/0205309 A1" ...
## $ Cites_Patent_Count : num [1:626] 0 0 0 0 3 0 0 1 0 0 ...
## $ Cited_by_Patent_Count: num [1:626] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "spec")=
## .. cols(
## .. Patent_Number = col_character(),
## .. Cites_Patent_Count = col_double(),
## .. Cited_by_Patent_Count = col_double()
## .. )
## - attr(*, "problems")=<externalptr>B1 <- Training_Data$Cites_Patent_Count
B2 <- Training_Data$Cited_by_Patent_Count
model <- lm(B2 ~ B1, data = Training_Data)
summary(model)##
## Call:
## lm(formula = B2 ~ B1, data = Training_Data)
##
## 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 ***
## B1 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-07Fill-in the blanks for the follwing statements:
# Confidence intervals for coefficients
confint(model, level = 0.90)## 5 % 95 %
## (Intercept) 0.030697775 0.073822761
## B1 0.001793859 0.003547102Your 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
0.0018and0.0035.There is a 90% probability that the actual value of B2 lies between
0.0307and0.0738.
cooks <- cooks.distance(model)
plot(model)
- 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.
max(cooks)## [1] 2.635251As the maximum Cook’s Distance is greater than 1, there exists outliers that may possibly need to be removed and/or treated differently in the dataset.
- Check the normality of residuals by creating a QQ-plot. Based on the plot, are the residuals normally distributed?
qqnorm(model$residuals, main = "model")
qqline(model$residuals)
Based on the QQ-plot above, the residuals are not normally
distributed.
Use the regression model that you created in #2 to predict the Cited_by_Patent_Count in each of the following scenarios:
Cites_Patent_Count= 340
X = model.matrix(model)
x_new = c(1, 340)
t(x_new)%*%solve(t(X)%*%X)%*%x_new## [,1]
## [1,] 0.3086801Cites_Patent_Count= 300
X = model.matrix(model)
x_new2 = c(1, 300)
t(x_new2)%*%solve(t(X)%*%X)%*%x_new2## [,1]
## [1,] 0.2398486## A prediction is considered to be extrapolation when the leverage is higher than the maximum within our dataset.
leverage <- hatvalues(model)
max(leverage)## [1] 0.2995991- Was the prediction made in part a of #3 considered to be extrapolation?
Yes, it was considered extrapolation.
- Was the prediction made in part b of #3 considered to be extrapolation?
No, it was not considered extrapolation.
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:
observation = data.frame(B1 = c(300))
observation## B1
## 1 300predict(model, observation, type = "response")## 1
## 0.8534046predict(model, observation, interval = "prediction", level = 0.95, type = "response")## fit lwr upr
## 1 0.8534046 0.1486074 1.558202- 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
0.1486and1.5582.
predict(model, observation, interval = "confidence", level = 0.95, type = "response")## fit lwr upr
## 1 0.8534046 0.5434141 1.163395- When Cites_Patent_Count is 300, there is a 95% chance that
the mean response will fall between
0.5434and1.1634.
Section 2 of Exam 1: Joining Data
Type the following in R Markdown, being sure to make the phrase “mutating joins” appear in bold in your HTML document:
The four types of mutating joins learned in class are:
- Inner join
- Full join
- Left join
- Right join
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:
Sequence_Counts <- read_csv("C:/Users/Lynx/Documents/MSDA/621/Exam 1/Sequence Counts.csv")## Rows: 222 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Patent_No.
## dbl (1): Sequence_Count
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.- Perform an inner join
library(dplyr)## Warning: package 'dplyr' was built under R version 4.2.1##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionx <- data.frame(key = c(Training_Data$Patent_Number, Training_Data$Cites_Patent_Count, Training_Data$Cited_by_Patent_Count), val = c("Patent Number", "Cites Patent Count", "Cited by Patent Count"))
y <- data.frame(key = c(Sequence_Counts$Patent_No., Sequence_Counts$Sequence_Count), val = c("Patent No.", "Sequence Count"))
x %>% inner_join(y, by = "key") -> joined_data
joined_data## key val.x val.y
## 1 CA 189065 S Patent Number Patent No.
## 2 NI 202000072 A Cites Patent Count Sequence Count
## 3 KR 20210032013 A Cited by Patent Count Patent No.
## 4 PH 12020550461 A1 Patent Number Sequence Count
## 5 TW I722568 B Cites Patent Count Patent No.
## 6 CN 112533674 A Cited by Patent Count Sequence Count
## 7 CO 2021002954 A2 Patent Number Patent No.
## 8 JP 2021040642 A Cites Patent Count Sequence Count
## 9 AU 2019/341683 A1 Cited by Patent Count Patent No.
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## 11 US 2021/0077463 A1 Cites Patent Count Patent No.
## 12 CA 3153676 A1 Cited by Patent Count Sequence Count
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## 14 WO 2021/048736 A1 Cites Patent Count Sequence Count
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## [ reached 'max' / getOption("max.print") -- omitted 169587 rows ]- Perform a full join
x %>% full_join(y, by = "key") -> joined_data
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## [ reached 'max' / getOption("max.print") -- omitted 170090 rows ]- Join the two datasets so that only the patents in the Sequence Counts dataset are included
x %>% right_join(y, by = "key") -> joined_data
joined_data## key val.x val.y
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## [ reached 'max' / getOption("max.print") -- omitted 169608 rows ]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:
Training_and_Testing_Data <- read_csv("C:/Users/Lynx/Documents/MSDA/621/Exam 1/Training and Testing Data.csv")## Rows: 725 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Patent_Number
## dbl (3): Cites_Patent_Count, Cited_by_Patent_Count, Partition
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.- Group the dataset by Partition. Summarize each grouping by calculating the standard deviation of Cites_Patent_Count for each group.
partition <- group_by(Training_and_Testing_Data, Partition)
partition## # A tibble: 725 × 4
## # Groups: Partition [2]
## Patent_Number Cites_Patent_Count Cited_by_Patent_Count Partition
## <chr> <dbl> <dbl> <dbl>
## 1 PL 3341367 T3 0 0 0
## 2 HR P20210871 T1 0 0 0
## 3 CR 20210284 A 0 0 0
## 4 US 2021/0205309 A1 0 0 0
## 5 JP 2021100972 A 3 0 0
## 6 AU 2021/203768 A1 0 0 0
## 7 ES 2841400 T3 0 0 0
## 8 US 2021/0206757 A1 1 0 0
## 9 PE 20211235 A1 0 0 0
## 10 US 2021/0205463 A1 0 0 0
## # … with 715 more rowssummarize(partition, standarddeviation = sd(Cites_Patent_Count, na.rm = TRUE))## # A tibble: 2 × 2
## Partition standarddeviation
## <dbl> <dbl>
## 1 0 24.2
## 2 1 16.7- Identify the top 3 patents with the highest number of citations in the Cited_by_Patent_Count column.
sum_part <- summarize(partition, standarddeviation = sd(Cited_by_Patent_Count, na.rm = TRUE))
arrange(sum_part, desc(standarddeviation))## # A tibble: 2 × 2
## Partition standarddeviation
## <dbl> <dbl>
## 1 1 1.11
## 2 0 0.328- Filter the dataset to display only those rows for which the Cites_Patent_Count is greater than zero
filter(Training_and_Testing_Data, Cites_Patent_Count > 0)## # A tibble: 137 × 4
## Patent_Number Cites_Patent_Count Cited_by_Patent_Count Partition
## <chr> <dbl> <dbl> <dbl>
## 1 JP 2021100972 A 3 0 0
## 2 US 2021/0206757 A1 1 0 0
## 3 EP 3096786 B1 10 0 0
## 4 EP 3096783 B1 16 0 0
## 5 AU 2018/372109 B2 1 0 0
## 6 AU 2018/275359 B2 1 0 0
## 7 JP 2021098716 A 2 0 0
## 8 TW I732431 B 1 0 0
## 9 RU 2750454 C2 2 0 0
## 10 WO 2021/124210 A1 6 0 0
## # … with 127 more rows