Quiz5
Tyler Miller
- Q1 Import data.
- Q2 Create a scatter plot to visualize the relationship between in_state_total and percent_minority.
- Q3 Calculate and interpret the Pearson correlation coefficient.
- Q4 Based on your analysis in Q2 and Q3, can you conclude that the share of minority students in total enrollment (measured by percent_minority) causes in_state_total to fall? Why or why not?
- Q5 You suspect that there may be other variables that are asociated with in_state_total. Create a correlation plot.
- Q6 List any variables with a strong positive association with in_state_total, if any.
- Q7 Your classmate argues that foreign students tend to attend more expensive colleges in the United States. Would you agree? Argue your case based on the correlation coefficient between in_state_total and percent_foreign.
- Q8 Hide the messages and warnings, but display the code and its results on the webpage.
- Q9 Display the title and your name correctly at the top of the webpage.
- Q10 Use the correct slug.
You will use college tuition and diversity data for this quiz. See below for the definition of some of the variables.
- in_state_total: Total cost for in-state residents in USD (sum of room & board + in state tuition)
- out_of_state_total: Total cost for in-state residents in USD (sum of room & board + out of state tuition)
- percent_minority: share of minority students in total enrollment
- percent_foreign: share of foreign students in total enrollment
Q1 Import data.
Hint: The data file is posted in Moodle. See Module 5. It’s named as “college_tuition.csv”.
data <- read.csv("~/busStat/Data/college_tuition (1).csv")
head(data)## name state state_code type
## 1 Aaniiih Nakoda College Montana MT Public
## 2 Abilene Christian University Texas TX Private
## 3 Abraham Baldwin Agricultural College Georgia GA Public
## 4 Academy College Minnesota MN For Profit
## 5 Academy of Art University California CA For Profit
## 6 Adams State University Colorado CO Public
## degree_length room_and_board in_state_tuition in_state_total
## 1 2 Year 4280 2380 2380
## 2 4 Year 10350 34850 45200
## 3 2 Year 8474 4128 12602
## 4 2 Year 8474 17661 17661
## 5 4 Year 16648 27810 44458
## 6 4 Year 8782 9440 18222
## out_of_state_tuition out_of_state_total total_enrollment percent_minority
## 1 2380 2380 291 0.8865979
## 2 34850 45200 4427 0.2737746
## 3 12550 21024 3458 0.1966455
## 4 17661 17661 127 0.2755906
## 5 27810 44458 15212 0.2584144
## 6 20456 29238 3154 0.3845910
## percent_foreign total_minority foreign_enrollment name_imp state_imp
## 1 0.00000000 258 0 FALSE FALSE
## 2 0.04178902 1212 185 FALSE FALSE
## 3 0.01417004 680 49 FALSE FALSE
## 4 0.00000000 35 0 FALSE FALSE
## 5 0.34006048 3931 5173 FALSE FALSE
## 6 0.00000000 1213 0 FALSE FALSE
## state_code_imp type_imp degree_length_imp room_and_board_imp
## 1 FALSE FALSE FALSE TRUE
## 2 FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE TRUE
## 5 FALSE FALSE FALSE FALSE
## 6 FALSE FALSE FALSE FALSE
## in_state_tuition_imp in_state_total_imp out_of_state_tuition_imp
## 1 FALSE FALSE FALSE
## 2 FALSE FALSE FALSE
## 3 FALSE FALSE FALSE
## 4 FALSE FALSE FALSE
## 5 FALSE FALSE FALSE
## 6 FALSE FALSE FALSE
## out_of_state_total_imp total_enrollment_imp percent_minority_imp
## 1 FALSE FALSE FALSE
## 2 FALSE FALSE FALSE
## 3 FALSE FALSE FALSE
## 4 FALSE FALSE FALSE
## 5 FALSE FALSE FALSE
## 6 FALSE FALSE FALSE
## percent_foreign_imp total_minority_imp foreign_enrollment_imp
## 1 FALSE FALSE FALSE
## 2 FALSE FALSE FALSE
## 3 FALSE FALSE FALSE
## 4 FALSE FALSE FALSE
## 5 FALSE FALSE FALSE
## 6 FALSE FALSE FALSEsummary(data)## name state state_code type
## Length:2154 Length:2154 Length:2154 Length:2154
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## degree_length room_and_board in_state_tuition in_state_total
## Length:2154 Min. : 30 Min. : 480 Min. : 962
## Class :character 1st Qu.: 6700 1st Qu.: 4696 1st Qu.: 5562
## Mode :character Median : 8696 Median :10165 Median :17765
## Mean : 8957 Mean :17064 Mean :23576
## 3rd Qu.:11000 3rd Qu.:28805 3rd Qu.:38616
## Max. :21300 Max. :59985 Max. :75003
## out_of_state_tuition out_of_state_total total_enrollment percent_minority
## Min. : 480 Min. : 1376 Min. : 15 Min. :0.0000
## 1st Qu.: 9297 1st Qu.:11018 1st Qu.: 1352 1st Qu.:0.1591
## Median :17151 Median :23168 Median : 3132 Median :0.2625
## Mean :20818 Mean :27330 Mean : 6185 Mean :0.3273
## 3rd Qu.:29925 3rd Qu.:40210 3rd Qu.: 7623 3rd Qu.:0.4312
## Max. :59985 Max. :75003 Max. :81459 Max. :1.0000
## percent_foreign total_minority foreign_enrollment name_imp
## Min. :0.000000 Min. : 0.0 Min. : 0.0 Mode :logical
## 1st Qu.:0.002103 1st Qu.: 283.2 1st Qu.: 5.0 FALSE:2154
## Median :0.013331 Median : 766.5 Median : 38.5
## Mean :0.035544 Mean : 2265.7 Mean : 272.0
## 3rd Qu.:0.039816 3rd Qu.: 2441.0 3rd Qu.: 160.0
## Max. :0.966216 Max. :56561.0 Max. :11495.0
## state_imp state_code_imp type_imp degree_length_imp
## Mode :logical Mode :logical Mode :logical Mode :logical
## FALSE:2154 FALSE:2154 FALSE:2154 FALSE:2154
##
##
##
##
## room_and_board_imp in_state_tuition_imp in_state_total_imp
## Mode :logical Mode :logical Mode :logical
## FALSE:1395 FALSE:2154 FALSE:2154
## TRUE :759
##
##
##
## out_of_state_tuition_imp out_of_state_total_imp total_enrollment_imp
## Mode :logical Mode :logical Mode :logical
## FALSE:2154 FALSE:2154 FALSE:2154
##
##
##
##
## percent_minority_imp percent_foreign_imp total_minority_imp
## Mode :logical Mode :logical Mode :logical
## FALSE:2154 FALSE:2154 FALSE:2154
##
##
##
##
## foreign_enrollment_imp
## Mode :logical
## FALSE:2154
##
##
##
## Q2 Create a scatter plot to visualize the relationship between in_state_total and percent_minority.
Hint: For the code, refer to one of our textbooks, Data Visualization with R: Chapter 4.2. Map in_state_total to the y-axis and percent_minority to the x-axis.
library(tidyverse)
ggplot(data,
aes(x = in_state_total,
y = percent_minority)) +
geom_point()
Q3 Calculate and interpret the Pearson correlation coefficient.
Hint: Interpret both the direction and the strength of the correlation
cor(data$in_state_total, data$percent_minority)## [1] -0.245447The relationship of this correlation is a weak negative correlation.
Q5 You suspect that there may be other variables that are asociated with in_state_total. Create a correlation plot.
Hint: For the code, refer to one of our textbooks, Data Visualization with R: Chapter 8.1.
# select numeric variables
df <- dplyr::select_if(data, is.numeric)
# calulate the correlations
r <- cor(df, use="complete.obs")
round(r,2)## room_and_board in_state_tuition in_state_total
## room_and_board 1.00 0.72 0.78
## in_state_tuition 0.72 1.00 0.98
## in_state_total 0.78 0.98 1.00
## out_of_state_tuition 0.77 0.95 0.95
## out_of_state_total 0.82 0.93 0.97
## total_enrollment 0.10 -0.17 -0.13
## percent_minority -0.16 -0.24 -0.25
## percent_foreign 0.34 0.39 0.40
## total_minority -0.01 -0.22 -0.21
## foreign_enrollment 0.29 0.16 0.20
## out_of_state_tuition out_of_state_total total_enrollment
## room_and_board 0.77 0.82 0.10
## in_state_tuition 0.95 0.93 -0.17
## in_state_total 0.95 0.97 -0.13
## out_of_state_tuition 1.00 0.98 -0.01
## out_of_state_total 0.98 1.00 -0.01
## total_enrollment -0.01 -0.01 1.00
## percent_minority -0.25 -0.25 0.13
## percent_foreign 0.41 0.41 0.09
## total_minority -0.11 -0.12 0.85
## foreign_enrollment 0.28 0.29 0.62
## percent_minority percent_foreign total_minority
## room_and_board -0.16 0.34 -0.01
## in_state_tuition -0.24 0.39 -0.22
## in_state_total -0.25 0.40 -0.21
## out_of_state_tuition -0.25 0.41 -0.11
## out_of_state_total -0.25 0.41 -0.12
## total_enrollment 0.13 0.09 0.85
## percent_minority 1.00 -0.09 0.40
## percent_foreign -0.09 1.00 0.03
## total_minority 0.40 0.03 1.00
## foreign_enrollment -0.01 0.46 0.44
## foreign_enrollment
## room_and_board 0.29
## in_state_tuition 0.16
## in_state_total 0.20
## out_of_state_tuition 0.28
## out_of_state_total 0.29
## total_enrollment 0.62
## percent_minority -0.01
## percent_foreign 0.46
## total_minority 0.44
## foreign_enrollment 1.00Q6 List any variables with a strong positive association with in_state_total, if any.
# select numeric variables
df <- dplyr::select_if(data, is.numeric)
# calulate the correlations
r <- cor(df, use="complete.obs")
round(r,2)## room_and_board in_state_tuition in_state_total
## room_and_board 1.00 0.72 0.78
## in_state_tuition 0.72 1.00 0.98
## in_state_total 0.78 0.98 1.00
## out_of_state_tuition 0.77 0.95 0.95
## out_of_state_total 0.82 0.93 0.97
## total_enrollment 0.10 -0.17 -0.13
## percent_minority -0.16 -0.24 -0.25
## percent_foreign 0.34 0.39 0.40
## total_minority -0.01 -0.22 -0.21
## foreign_enrollment 0.29 0.16 0.20
## out_of_state_tuition out_of_state_total total_enrollment
## room_and_board 0.77 0.82 0.10
## in_state_tuition 0.95 0.93 -0.17
## in_state_total 0.95 0.97 -0.13
## out_of_state_tuition 1.00 0.98 -0.01
## out_of_state_total 0.98 1.00 -0.01
## total_enrollment -0.01 -0.01 1.00
## percent_minority -0.25 -0.25 0.13
## percent_foreign 0.41 0.41 0.09
## total_minority -0.11 -0.12 0.85
## foreign_enrollment 0.28 0.29 0.62
## percent_minority percent_foreign total_minority
## room_and_board -0.16 0.34 -0.01
## in_state_tuition -0.24 0.39 -0.22
## in_state_total -0.25 0.40 -0.21
## out_of_state_tuition -0.25 0.41 -0.11
## out_of_state_total -0.25 0.41 -0.12
## total_enrollment 0.13 0.09 0.85
## percent_minority 1.00 -0.09 0.40
## percent_foreign -0.09 1.00 0.03
## total_minority 0.40 0.03 1.00
## foreign_enrollment -0.01 0.46 0.44
## foreign_enrollment
## room_and_board 0.29
## in_state_tuition 0.16
## in_state_total 0.20
## out_of_state_tuition 0.28
## out_of_state_total 0.29
## total_enrollment 0.62
## percent_minority -0.01
## percent_foreign 0.46
## total_minority 0.44
## foreign_enrollment 1.00The variables that have a strong positive correlation with in_state_total include the following: room_and_board, in_state_tuition, in_state_total, out_of_state_tuition, out_of_state_total, total_enrollment
Q7 Your classmate argues that foreign students tend to attend more expensive colleges in the United States. Would you agree? Argue your case based on the correlation coefficient between in_state_total and percent_foreign.
Hint: A correct answer must include all of the following: 1) direction and strength of the correlation coefficient, and 2) linear versus non-linear relationship.
cor(data$in_state_total, data$percent_foreign)## [1] 0.3951583I would agree with my classmate. The correlation coefficient of 0.395 tells us that there is a weak to moderate positive correlation. This is a linear correlation because the correlation coefficient only shows linear correlations.
Q8 Hide the messages and warnings, but display the code and its results on the webpage.
Hint: Use message, warning, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.