Restaurant.df<-read.csv("AdvertisingDataV2.csv")
View(Restaurant.df)
attach(Restaurant.df)

Q1) Frequency table

table(adType,restaurantType)

##           restaurantType
## adType     chain independent
##   Curr Ads  4000        6000
##   New Ads   4000        6000
##   No Ads    4000        6000

Q2) Table showing mean, median, min, max

library(psych)

## Warning: package 'psych' was built under R version 3.5.1

describe(Restaurant.df)

##                 vars     n     mean      sd  median  trimmed      mad min
## adType*            1 30000     2.00    0.82     2.0     2.00     1.48   1
## pageViews          2 30000   468.06  168.16   391.0   458.18   149.74 145
## phoneCalls         3 30000    37.71    7.97    37.0    37.20     7.41  17
## reservations       4 30000    36.55    7.99    36.0    35.97     7.41  15
## businessID         5 30000 15000.50 8660.40 15000.5 15000.50 11119.50   1
## restaurantType*    6 30000     1.60    0.49     2.0     1.62     0.00   1
##                   max range  skew kurtosis    se
## adType*             3     2  0.00    -1.50  0.00
## pageViews         929   784  0.45    -1.29  0.97
## phoneCalls         77    60  0.65     0.57  0.05
## reservations       79    64  0.78     0.88  0.05
## businessID      30000 29999  0.00    -1.20 50.00
## restaurantType*     2     1 -0.41    -1.83  0.00

Q3) Box Plot

boxplot(phoneCalls~adType, ylab="phonecalls", xlab="adtype", main= "Table 1")

boxplot(pageViews~adType, ylab="pageviews", xlab="adtype", main= "Table 2")

boxplot(reservations~adType, ylab="reservations", xlab="adtype", main= "Table 3")

boxplot(phoneCalls~restaurantType, ylab="phonecalls", xlab="restaurantType", main= "Table 4")

boxplot(pageViews~restaurantType, ylab="pageviews", xlab="restaurantType", main= "Table 5")

boxplot(reservations~restaurantType, ylab="reservations", xlab="restaurantType", main= "Table 6")

Q5) One way anova

oneWayfit <- aov(phoneCalls~adType, data = Restaurant.df)
# summary of the ANOVA model
summary(oneWayfit)

##                Df  Sum Sq Mean Sq F value Pr(>F)    
## adType          2  297584  148792    2780 <2e-16 ***
## Residuals   29997 1605692      54                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p<0.05, so we reject null hypothesis. Phonecalls are not same across all adtypes

Q6) Checking ANOVA assumption

Anderson-Darling normality test

library(nortest)
ad.test(phoneCalls)

## 
##  Anderson-Darling normality test
## 
## data:  phoneCalls
## A = 172.76, p-value < 2.2e-16

P< 0.05, reject null hypohesis. We can’t assume normality

Check for homogeneity of variance

library(car)

## Warning: package 'car' was built under R version 3.5.1

## Loading required package: carData

## Warning: package 'carData' was built under R version 3.5.1

## 
## Attaching package: 'car'

## The following object is masked from 'package:psych':
## 
##     logit

leveneTest(phoneCalls ~ adType, data = Restaurant.df)

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     2  79.125 < 2.2e-16 ***
##       29997                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p< 0.05, we reject null hypothesis. There is heterogeneity in variances of phone calls

rectifying normality and homogeneity violations by applying log transformation

library(car)
leveneTest(log(phoneCalls) ~ adType, data = Restaurant.df)

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     2  31.254 2.759e-14 ***
##       29997                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Q7)Pair wise comparison test value

pairwise.t.test(phoneCalls, adType, data = Restaurant.df,
                p.adjust.method = "BH", pool.sd = FALSE)

## 
##  Pairwise comparisons using t tests with non-pooled SD 
## 
## data:  phoneCalls and adType 
## 
##         Curr Ads New Ads
## New Ads <2e-16   -      
## No Ads  <2e-16   <2e-16 
## 
## P value adjustment method: BH

Q8) one-way ANOVA

oneWayTransfit <- aov(log(phoneCalls) ~ adType, data = Restaurant.df)
# summary of the ANOVA model
summary(oneWayTransfit)

##                Df Sum Sq Mean Sq F value Pr(>F)    
## adType          2  209.9  104.93    2887 <2e-16 ***
## Residuals   29997 1090.0    0.04                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(oneWayfit,2)

plot(oneWayTransfit,2)

plot(oneWayfit,1)

plot(oneWayTransfit,1)