MBASkills.In

Advertising Experiments at Restaurant Grades

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PART 1: Basic R Commands

Q.1a Write R code to get the dimensions of the dataframe

# dimension of the dataframe "df"
dim(SubAdvData)

## [1] 15000     6

Q.1b Write R code to list the column names of the dataframe

# column names of the dataframe 
colnames(SubAdvData)

## [1] "adType"         "pageViews"      "phoneCalls"     "reservations"  
## [5] "businessID"     "restaurantType"

Q.1c Write R code to list the data structures of the columns in the dataframe

str(SubAdvData)

## 'data.frame':    15000 obs. of  6 variables:
##  $ adType        : Factor w/ 3 levels "Curr Ads","New Ads",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ pageViews     : int  643 592 648 507 591 563 629 646 649 649 ...
##  $ phoneCalls    : int  44 35 45 40 42 43 46 39 49 41 ...
##  $ reservations  : int  39 31 46 30 37 38 38 39 41 40 ...
##  $ businessID    : int  1 4 5 9 12 17 20 21 23 24 ...
##  $ restaurantType: Factor w/ 2 levels "chain","independent": 1 1 1 1 1 1 1 1 1 1 ...

Q.1d Write R code to display the summary statistics of the dataframe, as shown below

summary(SubAdvData)

##       adType       pageViews       phoneCalls     reservations  
##  Curr Ads:4925   Min.   :145.0   Min.   :17.00   Min.   :17.00  
##  New Ads :5073   1st Qu.:328.0   1st Qu.:32.00   1st Qu.:31.00  
##  No Ads  :5002   Median :392.0   Median :37.00   Median :36.00  
##                  Mean   :467.8   Mean   :37.73   Mean   :36.58  
##                  3rd Qu.:635.0   3rd Qu.:42.00   3rd Qu.:41.00  
##                  Max.   :913.0   Max.   :75.00   Max.   :78.00  
##    businessID        restaurantType
##  Min.   :    1   chain      :5990  
##  1st Qu.: 7630   independent:9010  
##  Median :14954                     
##  Mean   :15029                     
##  3rd Qu.:22558                     
##  Max.   :30000

Q.1e Write R code to display the descriptive statistics of the dataframe, as shown below

library(psych)
describe(SubAdvData)

##                 vars     n     mean      sd  median  trimmed      mad min
## adType*            1 15000     2.01    0.81     2.0     2.01     1.48   1
## pageViews          2 15000   467.82  168.46   392.0   457.83   152.71 145
## phoneCalls         3 15000    37.73    8.02    37.0    37.19     7.41  17
## reservations       4 15000    36.58    8.05    36.0    35.97     7.41  17
## businessID         5 15000 15029.49 8647.64 14953.5 15031.39 11059.45   1
## restaurantType*    6 15000     1.60    0.49     2.0     1.63     0.00   1
##                   max range  skew kurtosis    se
## adType*             3     2 -0.01    -1.49  0.01
## pageViews         913   768  0.45    -1.29  1.38
## phoneCalls         75    58  0.69     0.61  0.07
## reservations       78    61  0.78     0.81  0.07
## businessID      30000 29999  0.00    -1.20 70.61
## restaurantType*     2     1 -0.41    -1.83  0.00

Q.1f Write R code to display the levels of variable adType

levels(advData$adType)

## [1] "Curr Ads" "New Ads"  "No Ads"

PART 2: Frequency Tables

Q.2a Write R to generate the frequency table of variable adType

tab1 <- table(SubAdvData$adType)
tab1

## 
## Curr Ads  New Ads   No Ads 
##     4925     5073     5002

Q.2b Write R to generate the proportion table of variable adType

round(prop.table(tab1)*100,2)

## 
## Curr Ads  New Ads   No Ads 
##    32.83    33.82    33.35

Q.2c Write R code to generate the contingency table between the variables adType & restaurantType

tab <- table(SubAdvData$adType,SubAdvData$restaurantType)
addmargins(tab)

##           
##            chain independent   Sum
##   Curr Ads  1959        2966  4925
##   New Ads   2060        3013  5073
##   No Ads    1971        3031  5002
##   Sum       5990        9010 15000

Q.2d Write R to generate the contingency table of proportions between the variables adType & restaurantType

tab1 <- table(SubAdvData$adType,SubAdvData$restaurantType)
tab2 <- round(addmargins(prop.table(tab1,1),2),2)
tab2

##           
##            chain independent  Sum
##   Curr Ads  0.40        0.60 1.00
##   New Ads   0.41        0.59 1.00
##   No Ads    0.39        0.61 1.00

PART 3: Summary Tables

Q.3a Write R code to measure the average reservation, for each Restaurant Type

# descriptive Statistics using aggregate() fuction
avb <- aggregate(SubAdvData["reservations"],
          by = list(restaurantType = SubAdvData$restaurantType), mean)
avb

##   restaurantType reservations
## 1          chain     42.77462
## 2    independent     32.45705

Q.3b Write R code to measure the average reservation, for each advertisement type

# descriptive Statistics using aggregate() fuction
avb <- aggregate(SubAdvData["reservations"],
          by = list(adType = SubAdvData$adType), mean)
avb

##     adType reservations
## 1 Curr Ads     34.00528
## 2  New Ads     41.77252
## 3   No Ads     33.84046

Q.3c Write R code to get a breakdown of the mean and standard deviation of the the reservations, with respect to variables restaurantType & adType, as shown in the following output

# summary statistics by groups
library(data.table)
SubAdvData1 <- data.table(SubAdvData)
tab1 <- SubAdvData1[, .(N = .N,
              Meanreservation = round(mean(reservations),2),
                SDreservation = round(sd(reservations),2)),
                by = .(restaurantType,adType)][order(restaurantType)]
tab1

##    restaurantType   adType    N Meanreservation SDreservation
## 1:          chain   No Ads 1971           39.82          5.11
## 2:          chain Curr Ads 1959           40.15          4.99
## 3:          chain  New Ads 2060           48.10          8.60
## 4:    independent   No Ads 3031           29.95          4.01
## 5:    independent Curr Ads 2966           29.95          3.55
## 6:    independent  New Ads 3013           37.45          4.05

PART 4: Correlation

Q.4a Find Pearson correlation coefficient between the Variable reservations & phoneCalls using cor()

cor(reservations, phoneCalls, method = "pearson")

## [1] 0.662667

Q.4b Write R code to find out Pearson correlation coefficient & significance value between Variable reservations & phoneCalls as shown below.

cor.test(reservations, phoneCalls, method = "pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  reservations and phoneCalls
## t = 108.36, df = 14998, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6535950 0.6715486
## sample estimates:
##      cor 
## 0.662667

Q.4c Write R code draw correlation matrix for all the continuous variables in the dataframe, as shown below.

# taking a subset of continuous variables
Subset.df <- advData[
                ,c('reservations','pageViews','phoneCalls')]

# correlation matrix on new dataframe 
corMat <- cor(Subset.df, use = "complete")
# round off upto 2 decimal places
round(corMat, 3)

##              reservations pageViews phoneCalls
## reservations        1.000     0.686      0.658
## pageViews           0.686     1.000      0.722
## phoneCalls          0.658     0.722      1.000

PART 5: Comparing Proportions

Q.5a Compare whether the proportion of Curr Ads is equal to 40% ?

# one-proportion z-test
prop.test(x = 4989 , n = 15000 ,p = 0.40, correct = FALSE)

## 
##  1-sample proportions test without continuity correction
## 
## data:  4989 out of 15000, null probability 0.4
## X-squared = 283.92, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.4
## 95 percent confidence interval:
##  0.3251040 0.3401818
## sample estimates:
##      p 
## 0.3326

Q.5b Compare whether the proportions of Curr Ads, New Ads & No Ads are equal ?

tab1 <- table(SubAdvData$adType)
chisqTest <- chisq.test(prop.table(tab1), p = c(1/3,1/3,1/3))

## Warning in chisq.test(prop.table(tab1), p = c(1/3, 1/3, 1/3)): Chi-squared
## approximation may be incorrect

chisqTest

## 
##  Chi-squared test for given probabilities
## 
## data:  prop.table(tab1)
## X-squared = 0.00014611, df = 2, p-value = 0.9999

Q.5c Compare whether the proportions of Curr Ads in chain restaurants is equal to the independent restaurants ?

# two-proportions Z-Test
prop.test(x = c(1993,2996), n = c(5966, 9034))

## 
##  2-sample test for equality of proportions with continuity
##  correction
## 
## data:  c(1993, 2996) out of c(5966, 9034)
## X-squared = 0.084477, df = 1, p-value = 0.7713
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.01312639  0.01797365
## sample estimates:
##    prop 1    prop 2 
## 0.3340597 0.3316360

Q.5d Check whether there is any association between the two variables restaurantType & adType?

chisq <- chisq.test(tab)
chisq

## 
##  Pearson's Chi-squared test
## 
## data:  tab
## X-squared = 1.5944, df = 2, p-value = 0.4506

PART 6: Comparing Means

Q.6a Compare whether the mean reservation is equal to 40.00?

# One-sample t-test
res <- t.test(reservations, mu = 40.00)
# Printing the results
res 

## 
##  One Sample t-test
## 
## data:  reservations
## t = -52.06, df = 14999, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 40
## 95 percent confidence interval:
##  36.44833 36.70607
## sample estimates:
## mean of x 
##   36.5772

Q.6b Compare whether the mean reservation of chain restaurants equal to the independent restaurants?

 # using subset function
# creating a subset of dataset including only Airline = Air India
restaurantsOfChain <- subset(SubAdvData, 
                            restaurantType == "chain", select = "reservations")
# creating a subset of dataset including only Airline = IndiGo
restaurantsOfindependent <- subset(SubAdvData,
                          restaurantType == "independent", select = "reservations")

# Computing t-test
tst <- t.test(restaurantsOfChain, restaurantsOfindependent, var.equal = TRUE)
tst

## 
##  Two Sample t-test
## 
## data:  restaurantsOfChain and restaurantsOfindependent
## t = 98.711, df = 14998, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  10.11270 10.52245
## sample estimates:
## mean of x mean of y 
##  42.77462  32.45705