final stat project

8/17/2019 Final Stat Project

1/16

November 21

2011[By: Parth Patel Period 2 and

Rachel Seitsinger Period 5]


2/16

Table o !ontents

"# "ntrod$ction

a# %$estion

b# Problem

c# Prediction

""# &ata table

"""# 'ra(h yo$r data

a# N$mber o contacts gra(h and analysis

i# )((ro(riate statistical meas$res or n$mber o contacts

b# N$mber o *aceboo+ riends gra(h and analysis

i# )((ro(riate Statistical ,eas$res or n$mber o *aceboo+riends

c# -.(loring the )ssociation

i# Scatter Plot

ii# /east S $ares Regression /ine

iii# Resid$al Plot

iv# !orrelation !oe cient

v# n$s$al 3bservations

d# &isc$ss

"# The association o o$r variables

ii# The strength o the linear association

iii# The $se $lness o this linear model or (rediction

# )lligator &ata

g# !hoosing an e.(lanatory val$e

h# )ns4ering the original $estion


3/16

"# "ntrod$ction

a#%$estion: The $estion that 4e 4ill beans4ering is:&oes the n$mber o *aceboo+ riendsdetermine the n$mber o riends a (ersonhas in real li e

b#Problem: The $estion 4e 4o$ld li+e toans4er is i the n$mber o *aceboo+ riends a(erson has is an acc$rate (redictor o

4hether or not a (erson has a lot o riends inreal li e# To meas$re the n$mber o riends a(erson has in real li e6 4e decided to ta+e then$mber o (hone n$mbers one has in theircell (hone6 4ith the ho(e that thismeas$rement gives $s a good idea o ho4

many (eo(le they tal+ to# This interests $sbeca$se *aceboo+ is s$ch a h$ge (art oteenager7s everyday lives and 4e 4o$ld li+eto determine i this social net4or+ing sitehold any tr$th 4hen it states on a (ro8le ho4many 9 riends someone has#

c# Prediction: ;e (redict that the more*aceboo+ riends someone has6 the more

riends they 4ill have in real li e6 there orethe more contacts they 4ill have in their


4/16

(hone# The scatter (lot sho$ld have a(ositive6 linear association#

""# &ata Table

#Name # of contacts in cell

phone# Of FacebookFriends

1 )nh Tr$ong 100 2ho$


5/16

@0 =enny *oster C


6/16

i# )((ro(riate Statistical ,eas$re or n$mber o contacts

Measure

# ofcontacts

,inim$m 15%1


7/16

b#N$mber o *aceboo+ *riends

1

2

3

4

5

6

7

Collection 1 His

Collection 1 B

The sha(e o the histogram or n$mber o *aceboo+ riends isbimodal and s+e4ed to the lo4er n$mbers# This sho4s that most(eo(le had a n$mber o riends aro$nd 500 or 006 and e4er(eo(le had riends belo4 C00# =$dging by the bo. (lot6 the middle50K o (eo(le had riend n$mbers rom abo$t C00 riends toabo$t


8/16

i# )((ro(riate Statistical ,eas$res or n$mbero *aceboo+ riends

Measure# of FacebookFriends

,inim$m ?0%1 C00,edian 5@?#5%@


9/16

c# -.(loring the )ssociation

i# Scatter Plot

050

100150

200

250

300

350

400

450

500Collection 1

The scatter (lot bet4een n$mber o *aceboo+ riends L.M and n$mber o contacts in one7s cell (hone LyM has a (ositive6 moderately 4ea+6 linearassociation#

ii# /east S $ares Regression /ine


10/16

number_o _contacts ! 0"166number_o _ b_ rien#s $ 70 % r 2 ! 0"21

0

100

200

300

400

500

number_of_fb_friends

Collection 1

N$mber o !ontacts


11/16

The correlation coe cient is 0#CC


12/16

iii# se $lness o this /inear ,odel orPrediction

3$r r 2 val$e6 4hich is 0#200C tells $s that 20#0CK o the variationin n$mber o contacts can be e.(lained by the linear model orn$mber o *aceboo+ riends6 and n$mber o (hone contracts# Thismeans that the other


13/16

This is the data be ore the trans ormation#

The resid$al (lot is clearly c$rved ma+ing the linear modelina((ro(riate or this set o data#

To re e.(ress the data6 4e 8rst $sed the nat$ral log o thede(endent variable L;eight in lbsM# The data came o$tstraightened li+e this:


14/16


15/16

e /nL4eightM e C#


16/16

meant that only a small 20#0CK o variation in n$mber ocontacts can be e.(lained by the linear model or n$mbero *aceboo+ riends# So 4hile there 4as a clear linear

association6 the 4ea+ness o the association means thatthe n$mber o *aceboo+ riends can only 4ea+lydetermine the n$mber o real riends# Io4ever6 some

a4s co$ld be that not everyone ($ts riends into theircell (hones6 or may have had their contacts deletedrecently6 4hich 4o$ld change the data#

final stat project

Documents