Lesson 4

Scatterplots and Perceived Audience Size

Notes:

Scatterplots

Notes:

library(ggplot2)
pf <- read.csv('pseudo_facebook.tsv', sep ='\t')
qplot(x=age, y=friend_count, data = pf)

ggplot(data=pf, aes(age,friend_count))+
  geom_point()

What are some things that you notice right away?

Response: Majority of people under 30 have maximum friend count. This shows younger users have a lot of friends.There are few fake accounts or teenagers who have lied about their age age there is a surge in friend count at age 69 and also after 90 years. ***

ggplot Syntax

Notes:

ggplot(data=pf,aes(age,friend_count))+geom_point()+xlim(13,90)
## Warning: Removed 4906 rows containing missing values (geom_point).

summary(pf$age)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   13.00   20.00   28.00   37.28   50.00  113.00

Overplotting

Notes:

ggplot(data=pf,aes(age,friend_count))+geom_point(alpha=(1/20))+xlim(13,90)
## Warning: Removed 4906 rows containing missing values (geom_point).

ggplot(data=pf,aes(age,friend_count))+geom_jitter(alpha=(1/20))+xlim(13,90)
## Warning: Removed 5189 rows containing missing values (geom_point).

What do you notice in the plot?

Response: The friend count for young users are as high as it was evident from the initial chart. However, this chart shows that majority of young users and below 1000 friends. Also outliers or fake accounts are still evident at age 69. ***

Coord_trans()

Notes:

ggplot(data=pf,aes(age,friend_count))+geom_point(alpha=(1/20))+xlim(13,90)+coord_trans(y = "sqrt")
## Warning: Removed 4906 rows containing missing values (geom_point).

Look up the documentation for coord_trans() and add a layer to the plot that transforms friend_count using the square root function. Create your plot!

ggplot(data=pf,aes(age,friend_count))+geom_point(alpha=(1/20),position = position_jitter(h=0))+xlim(13,90)+coord_trans(y = "sqrt")
## Warning: Removed 5191 rows containing missing values (geom_point).

What do you notice?

Alpha and Jitter

Notes:

ggplot(data = pf, aes(x = age, y = friendships_initiated))+
 geom_point(alpha=1/10, position=position_jitter(h=0))+
 xlim(13,90)+
 coord_trans(y = "sqrt")
## Warning: Removed 5175 rows containing missing values (geom_point).

Overplotting and Domain Knowledge

Notes:

Conditional Means

Notes:

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
age_groups <- group_by(pf, age)
pf.fc_by_age <- summarise(age_groups, friend_count_mean = mean(friend_count),friend_count_median = median(friend_count), n = n())
head(pf.fc_by_age, 20)
## # A tibble: 20 x 4
##      age friend_count_mean friend_count_median     n
##    <int>             <dbl>               <dbl> <int>
##  1    13          164.7500                74.0   484
##  2    14          251.3901               132.0  1925
##  3    15          347.6921               161.0  2618
##  4    16          351.9371               171.5  3086
##  5    17          350.3006               156.0  3283
##  6    18          331.1663               162.0  5196
##  7    19          333.6921               157.0  4391
##  8    20          283.4991               135.0  3769
##  9    21          235.9412               121.0  3671
## 10    22          211.3948               106.0  3032
## 11    23          202.8426                93.0  4404
## 12    24          185.7121                92.0  2827
## 13    25          131.0211                62.0  3641
## 14    26          144.0082                75.0  2815
## 15    27          134.1473                72.0  2240
## 16    28          125.8354                66.0  2364
## 17    29          120.8182                66.0  1936
## 18    30          115.2080                67.5  1716
## 19    31          118.4599                63.0  1694
## 20    32          114.2800                63.0  1443

Create your plot!

ggplot(data = pf.fc_by_age)+
  geom_line(mapping = aes(x = age, y = friend_count_mean))+
  xlim(13,90)
## Warning: Removed 23 rows containing missing values (geom_path).

Overlaying Summaries with Raw Data

Notes:

ggplot(data=pf,aes(age,friend_count))+
  geom_point(alpha=(1/20),position = position_jitter(h=0),color = "orange")+
  xlim(13,90)+
  coord_trans(y = "sqrt")+
  geom_line(stat = 'summary', fun.y = mean)+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .1), linetype = 2, color ='blue')+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .9), linetype = 2, color ='blue')+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .5), color ='blue')
## Warning: Removed 4906 rows containing non-finite values (stat_summary).

## Warning: Removed 4906 rows containing non-finite values (stat_summary).

## Warning: Removed 4906 rows containing non-finite values (stat_summary).

## Warning: Removed 4906 rows containing non-finite values (stat_summary).
## Warning: Removed 5173 rows containing missing values (geom_point).

What are some of your observations of the plot?

Response: Having more than 1000 friends is rare even in the younger age group.90 percentile is well belo the 1000 mark showing that 90% of the users have friend count lower than 1000 mark. *** ###Adding Coord_cartesian

ggplot(data=pf,aes(age,friend_count))+
  geom_point(alpha=(1/20),position = position_jitter(h=0),color = "orange")+
  coord_cartesian(xlim=c(13,70), ylim=c(0,1000))+ 
  geom_line(stat = 'summary', fun.y = mean)+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .1), linetype = 2, color ='blue')+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .9), linetype = 2, color ='blue')+
  geom_line(stat = 'summary', fun.y = quantile, fun.args = list(probs = .5), color ='blue')

Moira: Histogram Summary and Scatterplot

See the Instructor Notes of this video to download Moira’s paper on perceived audience size and to see the final plot.

Notes:

Correlation

Notes:

cor.test(pf$age, pf$friend_count, method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  pf$age and pf$friend_count
## t = -8.6268, df = 99001, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.03363072 -0.02118189
## sample estimates:
##         cor 
## -0.02740737
with(pf, cor.test(age, friend_count, method = "pearson"))
## 
##  Pearson's product-moment correlation
## 
## data:  age and friend_count
## t = -8.6268, df = 99001, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.03363072 -0.02118189
## sample estimates:
##         cor 
## -0.02740737

Look up the documentation for the cor.test function.

What’s the correlation between age and friend count? Round to three decimal places. Response:

Correlation on Subsets

Notes:

with(filter(pf,age <= 70), cor.test(age, friend_count))
## 
##  Pearson's product-moment correlation
## 
## data:  age and friend_count
## t = -52.592, df = 91029, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1780220 -0.1654129
## sample estimates:
##        cor 
## -0.1717245

Correlation Methods

Notes:

with(filter(pf,age <= 70), cor.test(age, friend_count, method = "spearman"))
## Warning in cor.test.default(age, friend_count, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  age and friend_count
## S = 1.5782e+14, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.2552934

Create Scatterplots

Notes:

ggplot(data = pf)+
  geom_point(mapping = aes(x = www_likes_received, y = likes_received), position = position_jitter(h = 0))

Strong Correlations

Notes:

ggplot(data = pf,aes(x = www_likes_received, y = likes_received))+
  geom_jitter(alpha = (1/50), position = position_jitter(h = 0))+
  coord_cartesian(xlim = c(0, quantile(pf$www_likes_received, 0.95)), ylim = c(0, quantile(pf$likes_received, 0.95)))+geom_smooth(method ='lm',color ='red')

What’s the correlation betwen the two variables? Include the top 5% of values for the variable in the calculation and round to 3 decimal places.

cor.test(pf$www_likes_received,pf$likes_received)
## 
##  Pearson's product-moment correlation
## 
## data:  pf$www_likes_received and pf$likes_received
## t = 937.1, df = 99001, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9473553 0.9486176
## sample estimates:
##       cor 
## 0.9479902

Response:

Moira on Correlation

Notes:

More Caution with Correlation

Notes:

library(alr3)
## Loading required package: car
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode

Create your plot!

ggplot(data = Mitchell, aes(Temp, Month))+
  geom_point()

Noisy Scatterplots

  1. Take a guess for the correlation coefficient for the scatterplot. 0.04

  2. What is the actual correlation of the two variables? (Round to the thousandths place) 0.0574

with(Mitchell, cor.test(Temp, Month))
## 
##  Pearson's product-moment correlation
## 
## data:  Temp and Month
## t = 0.81816, df = 202, p-value = 0.4142
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.08053637  0.19331562
## sample estimates:
##        cor 
## 0.05747063

Making Sense of Data

Notes:

ggplot(data = Mitchell, aes(Temp, Month))+
  geom_point()+
  scale_x_continuous(breaks = seq(0,203,12))

A New Perspective

ggplot(aes(x=(Month%%12),y=Temp), data=Mitchell)+
  geom_point()

What do you notice? Response:

Watch the solution video and check out the Instructor Notes! Notes:

Understanding Noise: Age to Age Months

Notes:

pf$age_with_months <- pf$age + (1 - pf$dob_month/12)

Age with Months Means

pf.fc_by_age_months <- pf %>% group_by(age_with_months) %>% summarise(friend_count_mean = mean(friend_count), friend_count_median = median(friend_count),n = n()) %>% arrange(age_with_months)

Programming Assignment

head(pf.fc_by_age_months, 10)
## # A tibble: 10 x 4
##    age_with_months friend_count_mean friend_count_median     n
##              <dbl>             <dbl>               <dbl> <int>
##  1        13.16667          46.33333                30.5     6
##  2        13.25000         115.07143                23.5    14
##  3        13.33333         136.20000                44.0    25
##  4        13.41667         164.24242                72.0    33
##  5        13.50000         131.17778                66.0    45
##  6        13.58333         156.81481                64.0    54
##  7        13.66667         130.06522                75.5    46
##  8        13.75000         205.82609               122.0    69
##  9        13.83333         215.67742               111.0    62
## 10        13.91667         162.28462                71.0   130

Noise in Conditional Means

ggplot(data = subset(pf.fc_by_age_months, pf.fc_by_age_months$age_with_months < 71), aes(x = age_with_months, y = friend_count_mean))+
  geom_line()

Smoothing Conditional Means

Notes:

p1 <- ggplot(data = subset(pf.fc_by_age, age < 71),aes(x = age, y = friend_count_mean))+
  geom_line()+
  geom_smooth()
p2 <- ggplot(data = subset(pf.fc_by_age_months, pf.fc_by_age_months$age_with_months < 71), aes(x = age_with_months, y = friend_count_mean))+
  geom_line()+
  geom_smooth()
p3 <- ggplot(data = subset(pf, age < 71),aes(x = round(age/5)*5, y = friend_count))+
  geom_line(stat = "summary", fun.y = mean)
  
library(gridExtra)
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
grid.arrange(p1,p2,p3,ncol = 1)
## `geom_smooth()` using method = 'loess'
## `geom_smooth()` using method = 'loess'

Which Plot to Choose?

Notes:

Analyzing Two Variables

Reflection:

Click KnitHTML to see all of your hard work and to have an html page of this lesson, your answers, and your notes!