INFERENTIAL STATISTICS

Question 1

inferential stats?

Answer 1

reach conclusions that extend beyond immediate data sets

Question 2

Bernoulli distribution?

Answer 2

important case of discrete variables–>Binary only 2 possible outcomes (0 or 1)

Question 3

population parameter?

Answer 3

fixed feature of a particular population e.g. pop mean, pop variance

Question 4

sample stats?

Answer 4

quantity that vary from one sample to another (obtain population parameter using random sampling as surveying entire population not practical)

Question 5

Law of large numbers?

Answer 5

as sample size n increases, the sample mean gets closer to population mean

Question 6

Central limit theorem?

Answer 6

when sample size large (n>=30),sampling distribution of x is approximately normal, regardless of distribution we started out with

Question 7

hypothesis testing

Answer 7

tells us how extreme our sample outcome is. creates a rejection region, beyond which sample too extreme to maintain that null hypothesis is true

Question 8

standardisation

Answer 8

Z=(x-mean)/SD Z~N(0,1)

Question 9

test stat Z

Answer 9

(p observed-p)/sample variance (reject if >1.96)

Question 10

reject Ho?

Answer 10

p-value<0.05

Question 11

95% Confidence Interval

Answer 11

(pop mean-1.96SD, pop mean+1.96SD) reject if observed P not in range

Question 12

import data from file?

Answer 12

Auto=read.csv(‘link’,header=TRUE,na.strings=’?’)

Question 13

class of Auto?

Answer 13

‘data.frame’

Question 14

structure of data?

Answer 14

str(Auto)

Question 15

headers of data?

Answer 15

head(Auto)

Question 16

names of variables?

Answer 16

names(Auto)

Question 17

number of observations and variables?

Answer 17

dim(Auto)

Question 18

frequency of each observation under a origin variable?

Answer 18

table(Auto$origin)

Question 19

recoding data for ‘origin’? (check using table(Auto$originf)

Answer 19

Auto$originf = factor(Auto$origin,

labels = c(“USA”, “Europe”, “Japan”))

Question 20

create new data.frame without variable ‘origin’?

Answer 20

new_data=subset(Auto,select=c(-origin))

Question 21

identify number of rows with missing values (NA)?

Answer 21

sum(is.na(Auto))

Question 22

locate entries (which row and column) with missing values

Answer 22

which(is.na(Auto),arr.ind=TRUE)

Question 23

remove rows with missing values?

Answer 23

Auto=na.omit(Auto)

Question 24

summarising data for a variable?

Answer 24

mean(Auto$variable)
median(Auto$variable) –> quantile(Auto$variable,0.5)
max(Auto$variable),min(Auto$variable) (minus will range)
var(Auto$variable)
sd(Auto$variable)

Question 25

5 number summary?

Answer 25

quantile(Auto$variable) OR summary(Auto$variable)

Question 26

interquartile range?

Answer 26

IQR(Auto$variable)

Question 27

covariance n correspondance of variable?

Answer 27

attach(Auto)
cov(var1,var2)
cor(var1,var2)

Question 28

barplot of variable?

Answer 28

barplot(summary(Auto$variable), xlab= ‘label’, ylab=’frequency’,col ‘wheat’)

Question 29

histogram of variable?

Answer 29

hist(Auto$variable, breaks=20, xlab=’variable (#bin=20)’, ylab=’frequency’, main=’’, col=’wheat’)

Question 30

side by side graphs with 1 row n 2 columns?

Answer 30

par(mfrow=c(1,2))

Question 31

box plot of variable?

Answer 31

boxplot(Auto$variable, col=’wheat’, main=’title’, horizontal=TRUE)

Question 32

Detect outliers based on IQR: [Q1 - 1.5IQR, Q3 + 1.5IQR]?

Answer 32

boxplot.stats(Auto$variable)$out

Question 33

Locate the outliers in the dataset

Answer 33

outlier= boxplot.stats(Auto$variable)$out
outlier_row=which(Auto$variable)%int%c(outlier))
Auto[outlier_row, ]

Question 34

Detect outliers based on percentile: 2.5% - 97.5%

Answer 34

lower=quantile(Auto$variable,0.025)
upper=quantile(Auto$variable,0.975)
outlier_row=which(Auto$variable>upper|Auto$variable)

Question 35

scatterplot?

Answer 35

plot(Auto$var1,Auto$var2, xlab=’var1’, ylab=’var2’)