R Studio - Data Screening Assessment Answer

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Subject Name : Rstudio

Data Screening Assessment Answer

lab3$Gender[lab3$Gender == "male"] "Male" lab3$Gender[lab3$Gender == "female"] "Female"

lab3$Information[lab3$Information == "info poor"] "Poor Information" lab3$Information[lab3$Information == "info rich"] "Rich Information" lab3$Gender as.factor(lab3$Gender)

lab3$Information as.factor(lab3$Information) summary(lab3)

Part 1

Gender Information likeability externalatt Female:18 PoorInformation:18 Min. : 0.00 Min. :5.000 Male :17 RichInformation:20 1stQu.:76.00 1st Qu.:7.000 NA's :3 Median:83.00 Median:7.000

Mean : 80.21 Mean :7.289 3rd Qu.: 91.50 3rd Qu.:8.000 Max. :100.00 Max. :9.000

interalatt ovcompt selfesteem negmood Min. :3.000 Min. :11.00 Min. :0.3894 Min. : 2.000 1stQu.:6.000 1stQu.:13.00 1stQu.:1.8349 1st Qu.:2.000

Median:7.000 Median:14.00 Median:3.2733 Median :3.000

Mean :6.763 Mean :14.11 Mean :3.7119 Mean : 4.297 3rd Qu.:8.000 3rd Qu.:16.00 3rd Qu.:4.8068 3rd Qu.: 6.000 Max. :9.000 Max. :18.00 Max. :9.3132 Max. :12.000

NA's :1 NA's :1

Gender: each participant’s gender. There are 18 females and 3 males in the dataset, we dont have gender of 3data-instances.
Information:whichcategoryeachsubjectwasassigned.Informationpoorparticipantswereonly

given a few pieces of information about a person (short resume), while information rich participants were given more information about a person (long resume). The dataset assign category to all the 38 subjects

Likability : each participant rated how likeable a person was given some information and a shorttime

talking to them (scale is in percentages). This column/feature/attribute is not out of range as it is between 0%-100%.

Externalatt:Explicitratingofaparticipant’sattitudeassessedbyaskingtheparticipanthowthey

felt about the person on a 9 point Likert scale. This column/feature/attribute is not out of range as it is between 0-9.

Internalatt:Implicitratingofaparticipant’sattitudeaboutapersonassessedbytheimplicitattitudes

test on a 9 point Likert scale. This column/feature/attribute is not out of range as it is between 0-9.

Ovcompt:aratingscaleabouthowmuchaparticipantthoughttheparticipantwasovercompensating for a flaw on their resume on a 0-20 scale. This column/feature/attribute is not out of range as it is between0-20,withamaxof18andwearemissingtheratingforonesubject.
Selfesteem:anaverageratingofeachparticipant’sselfesteemona0-10scale.Thiscol-

umn/feature/attribute is not out of range as it is between 0-10 with a max of 9.3132.

Negmood:aratingofhownegative/positiveaparticipantwasduringthefakeinterviewwherelower numbersaremorepositiveona0-10scale.Thiscolumn/feature/attributeisoutofrangeasitis

correct.indexes $negmood <= 10 correct.indexes[is.na(correct.indexes)] TRUE lab3

summary(lab3)

between 2-12, however, as explained the scale is between 0-10.

Gender Information likeability externalatt Female:17 Poor Information:16 Min. : 0.00 Min. :5.00 Male :16 Rich Information:20 1st Qu.: 75.50 1st Qu.:7.00 NA's :3 Median : 85.00 Median:7.00

Mean : 80.33 Mean :7.25 3rd Qu.: 92.00 3rd Qu.:8.00 Max. :100.00 Max. :9.00

interalatt ovcompt selfesteem negmood Min. :3.000 Min. :11.0 Min. :0.3894 Min. :2.000 1stQu.:6.000 1stQu.:12.5 1stQu.:2.0669 1stQu.:2.000

Median:7.000 Median:14.0 Median:3.7072 Median:3.000

Mean :6.694 Mean :14.0 Mean :3.8183 Mean :3.886 3rd Qu.:8.000 3rd Qu.:16.0 3rd Qu.:5.0288 3rd Qu.:6.000 Max. :9.000 Max. :18.0 Max. :9.3132 Max. :9.000

NA's :1 NA's :1

Part 2

table(lab3$Gender)

Female Male

17 16

table(lab3$Information)

Poor Information Rich Information

16 20

Part 3

Everyone is not skipping the same question, it appears to be random in nature.

Part 4

(percentage.missing<-apply(is.na(lab3),2,sum)/nrow(lab3)*100)

Gender Information likeability externalatt interalatt ovcompt 8.333333 0.000000 0.000000 0.000000 0.000000 2.777778

selfesteem negmood 0.000000 2.777778

lab3<-lab3[!apply(is.na(lab3),1,sum)>1,]

(percentage.missing<-apply(is.na(lab3),2,sum)/nrow(lab3)*100)

Part 5

Gender Information likeability externalatt interalatt ovcompt 8.333333 0.000000 0.000000 0.000000 0.000000 2.777778

selfesteem negmood 0.000000 2.777778

Part 6

md.pattern(lab3)

InformatiolinkeabiliteyxternalaitntteralasttelfesteemovcompntegmoodGender

31									0
3									1
1									1
1									1
	0	0	0	0	0	1	1	3	5

	Information	likeability		externalatt	interalatt	selfesteem	ovcompt
31	1	1		1	1	1	1
3	1	1		1	1	1	1
1	1	1		1	1	1	1
1	1	1		1	1	1	0
	0	0		0	0	0	1
	negmood Gender
31	1	1	0
3	1	0	1
1	0	1	1
1	1	1	1
	1	3	5

Let’sunderstandthistable. Thereare33observationswithnomissingvalues. Thereare3observationswith missingvaluesinGenderSimilarly,thereare1missingvalueswithnegmoodandsoon.

lab3 complete.cases(lab3), ] nums unlist(lapply(lab3, is.numeric)) numeric.lab3

(mahalanobis.dist maha_dist(numeric.lab3))

Part 7

[1] 2.3394832 2.4654131 4.7297569 6.8506185 2.0964151 6.1884968

[7] 2.6946912 1.3369857 1.208658419.3674108 2.8973412 1.3472412

[13] 1.4970120 3.6756000 4.3838732 6.911943611.0801184 1.3391054

[19] 7.4482359 6.8308977 0.9715782 5.3983499 4.0121421 7.5310089

[25] 4.3361726 4.5433479 5.2215257 7.0104954 5.5647990 5.8809187

[31] 2.8403632

hist(mahalanobis.dist, main="Mahalanobis distance", xlab="distance")

Frequency

Mahalanobis distance

0 5 10 15 20

distance

The above function returned a vector, with the same length as the number of rows of the provided data frame, corresponding to the average mahalanobis distances of each row from the whole data set.

numeric.lab3

quantile(mahalanobis.dist, 0.95), ]

lab3

quantile(mahalanobis.dist, 0.95), ]

Now, removing the outliers by selecting 95% quantile as the cutoff score.

Part 8

symnum(cor(numeric.lab3),abbr.colnames=FALSE)

likeability externalatt interalatt ovcompt selfesteem negmood likeability 1

externalatt 1

interalatt . 1

ovcompt + * 1

selfesteem 1

negmood 1

attr(,"legend")

[1]0''0.3'.'0.6','0.8'+'0.9'*'0.95'B'1

As indicated in the legend, the correlation coefficients between 0 and 0.3 are replaced by a space (" “); correlation coefficients between 0.3 and 0.6 are replace by”.“; etc .

Part 9

The variable ovcompt is highly correlated to externalatt and interalatt.

result<-mvn(data=numeric.lab3,

mvnTest = "royston", univariatePlot = "histogram")

Part 10

Density

0.000

0.015

0.030

Density

0.0

0.4

0.8

Density

0.0

0.1 0.2 0.3

50 60 70 80 90 100

5 6 7 8 9

4 5 6 7 8 9

0.15

0.6

likeability

externalatt

interalatt

Density

0.00

0.10 0.20

Density

0.00

0.05 0.10

Density

0.0

0.2 0.4

11 13 15 17

0 2 4 6 8 10

2 3 4 5 6 7 8 9

ovcompt

selfesteem

negmood

Part 11

As seen from Figure above, negmood has a right-skewed distribution and likeability and interalatt has a left-skewed distribution whereas other variables have approximately normal distributions. Thus, we can concludethatproblemswithmultivariatenormalityarisefromtheskeweddistributionsmentionedabove.

result<-mvn(data=numeric.lab3,

mvnTest = "royston", univariatePlot = "qqplot",

Part 12

multivariatePlot="qq")

10 12 14

Chi−Square Q−Q Plot

Chi−Square Quantile

2 4 6 8 10

Squared Mahalanobis Distance

100

Normal Q−Q Plot (likeability)

Normal Q−Q Plot (externalatt)

Normal Q−Q Plot (interalatt)

Sample Quantiles

4 5 6 7 8 9

−2 −1 0 1 2

Theoretical Quantiles

Normal Q−Q Plot (ovcompt)

Normal Q−Q Plot (selfesteem

Normal Q−Q Plot (negmood)

Sample Quantiles

11 13 15 17

Sample Quantiles

2 4 6 8

Sample Quantiles

−2 −1 0 1 2

Theoretical Quantiles

Part 13

Except for the likeabililty and self esteem, the other variables do not show multivariate normality.

Inadditiontotheunivariateplots,onecanalsoperformunivariatenormalitytestsusingtheunivariateTest argumentinthemvnfunction.Itprovidesseveralwidelyusedunivariatenormalitytests,including“SW”(do notapplyShapiro-Wilk’stest,ifdatasetincludesmorethan5000casesorlessthan3cases.) forShapiro-Wilk test, “CVM” for Cramer-von Mises test, texttt“Lillie” for Lilliefors test, “SF” for Shapiro-Francia test and “AD” Anderson-Darlingtest.

par(mfrow=c(3,2))

plot(lm(likeability~.,data=numeric.lab3)$residuals, type = "l",

main="residuals", ylab="likeability")

plot(lm(externalatt~.,data=numeric.lab3)$residuals, type = "l",

main="residuals", ylab="externalatt")

plot(lm(interalatt~.,data=numeric.lab3)$residuals, type = "l",

main="residuals", ylab="interalatt")

plot(lm(ovcompt~.,data=numeric.lab3)$residuals, type = "l",

main="residuals",

Part 14

ylab="ovcompt")

plot(lm(selfesteem~.,data=numeric.lab3)$residuals, type = "l",

main="residuals", ylab="selfesteem")

plot(lm(negmood~.,data=numeric.lab3)$residuals, type = "l",

main="residuals", ylab="negmood")

likeability

externalatt

residuals residuals

−30

−1e−14

0 5 10 15 20 25 30 0 5 10 15 20 25 30

Index Index

interalatt

ovcompt

0e+00

residuals residuals

0 5 10 15 20 25 30 0 5 10 15 20 25 30

−1e−14

Index Index

negmood

residuals residuals

selfesteem

−2

−2 4

0 5 10 15 20 25 30 0 5 10 15 20 25 30

Index Index

Part 15

All the graph indicates homogeneity.

Part 16

None of the graph indicates homoscedasticity.

Part 17

The study is all about an imaginary situation of interviewing a person for a job by the selected participants of the study. Participants were given a resume of the job candidate and allowed to talk to that candidate. Finally they were given a questionnaire with few variables stated below. Gender is a participants gender. The variable Information states the category each subject was assigned with two categories of poor and rich. Information poor participants were only given a few pieces of information about a person, while information rich participants were given more information about a person.

Part 18

The variable Likability defines participants rating of likeability of a person given some information and a short time talking to them (scale is in percentages). The variable Externalatt defines explicit rating of a participants attitude assessed by asking the participant how they felt about the person on a 9 point Likert scale. The Internalatt defines implicit rating of a participants attitude about a person assessed by the implicit attitudes test on a 9 point Likert scale. Ovcompt defines rating scale about how much a participant thought the participant was overcompensating for a flaw on their résumé on a 0-20 scale. Selfesteem defines an average rating of each participants self esteemon a 0-10 scale. Negmood defines a rating of how negative/positive a participant was during the fake interview where lower numbers are more positive on a 0-10 scale.

Part 19

Gender has 3 missing observations. Selfesteem and negmood each have one observation missing. Missing observations are excluded from the study. Information, likeability, externalatt, internalatt, ovcompt have no missing observations. The data set has 17 female and 16 male participants. We have 16 poor information and 20 rich information. Likebility has a median of 85 with a minimum and maximum of 0 and 100 respectively. Externalatt has a median of 7 with a minimum and maximum of 5 and 9 respectively. In a similar way interalatt has a median of 7 with a minimum and maximum of 3 and 9 respectively. Ovcompt has a median of 14 with a range of 7. Selfesteem has a median of 3.7 with a range of almost 9. Negmood has a median of 3 with range of 7.

Part 20

There are 33 observations with no missing values. There are 3 observations with missing values in Gender Similarly, there are 1 missing values with negmood and so on.

Part 21

I have used mahalanobis to solve for the outliers and clearly mentioned that while doing it.Looking at the histogram of Mahalanobis distance reveals no presence of outliers (regardless of cutoff) in the data set. The variable ovcompt is highly correlated to externalatt and interalatt. The histograms of the variables reveal that likebility and interalatt have left-skewed distributions whereas negmood has a right-skewed distribution. All other variables approximately follow the normal distribution.

Part 22

No I didnt had any issue. I simply use the MVN package of R

Part 23

The assumption of multivariate normality has not been satisfied. Only likeabililty and self esteem show multivariate normality whereas other variables do not show multivariate normality. The residuals show no specific patterns. Therefore, the assumption of homoscedasticity is satisfied and all the graph shows homogeneity

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