Descriptive statistics P RACTICIN G S TATIS TICS IN TERVIEW QUES - - PowerPoint PPT Presentation

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Descriptive statistics P RACTICIN G S TATIS TICS IN TERVIEW QUES - - PowerPoint PPT Presentation

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Descriptive statistics P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R Zuzanna Chmielewska Actuary Descriptive statistics PRACTICING STATISTICS INTERVIEW QUESTIONS IN R Descriptive statistics PRACTICING STATISTICS INTERVIEW

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Descriptive statistics

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Descriptive statistics

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Descriptive statistics

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Descriptive statistics

central tendency measures variability measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Descriptive statistics

central tendency measures variability measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Central tendency measures

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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Descriptive statistics

central tendency variability

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Variability

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Variability

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Variability

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Variability measures

variance standard deviation range

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Variability measures

variance

σ =

2

n (x − μ) ∑

i 2

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Variance - numerical example

x = 2,x = 5,x = 11 μ = = = 6 (x − μ) = (2 − 6) = (−4) = 16 (x − μ) = (5 − 6) = (−1) = 1 (x − μ) = (11 − 6) = (5) = 25 (x − μ) = 16 + 1 + 25 = 42 = = 14

1 2 3 n x ∑i=1

n i

3 2+5+11 1 2 2 2 2 2 2 2 3 2 2 2

∑i=1

n i 2 n (x −μ) ∑i=1

n i 2

3 42

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Variability measures

variance

σ =

standard deviation

σ =

2

n (x − μ) ∑

i 2

√ σ2

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Variability measures

variance

σ =

standard deviation

σ =

range

range = max − min

2

n (x − μ) ∑

i 2

√ σ2

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Summary

central tendency measures mean median mode skewness variability measures variance standard deviation range

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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Categorical data

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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Factors in R

x1 <- c("AB", "A", "O", "AB", "B", "B") lvls <- c("A", "B", "AB", "O") x2 <- factor(x1, levels = lvls) print(x2) [1] AB A O AB B B Levels: A B AB O

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Factors in R

x1 <- c("M", "L" , "L", "XS", "XL", "S") lvls <- c("XS", "S", "M", "L", "XL") x2 <- factor(x1, levels = lvls, ordered = TRUE) print(x2) [1] M L L XS XL S Levels: XS < S < M < L < XL

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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tapply(df$value, df$level, mean)

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Categorical data encoding

label encoding

  • ne hot encoding

many more!

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Label encoding

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Label encoding

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Label encoding

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Label encoding

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Label encoding

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One hot encoding

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One hot encoding

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

One hot encoding

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One hot encoding

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One hot encoding

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Summary

types of categorical data factors in R categorical data analysis

table() barplot() tapply()

data encoding label encoding

  • ne hot encoding
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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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Time series

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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Time series

Application of time series: nance agriculture energy etc.

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Time series

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Time series

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Time series

Time series analysis: trends seasonal variation serial correlation prediction model (e.g. ARIMA)

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Time series - object

ts <- xts(x = values, order.by = dates)

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plot(ts)

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Analysis - subsetting

dates <- seq(from = as.Date("2010-01-01"), to = as.Date("2010-12-31"))

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Analysis - subsetting

dates <- seq(from = as.Date("2010-01-01"), to = as.Date("2010-12-31"), by = "1 month")

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Analysis - subsetting

dates <- seq(from = as.Date("2010-01-01"), to = as.Date("2010-12-31"), by = "1 month") ts[dates]

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Analysis - merging

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Analysis - merging

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Analysis - merging

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Analysis - merging

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Analysis - applying a function by calendar period

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Analysis - applying a function by calendar period

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Analysis - applying a function by calendar period

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Summary

denition of time series

xts object in R

wrangling time series: subsetting merging functions over calendar periods

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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Principal Component Analysis

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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Principal Component Analysis

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prcomp()

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pca <- prcomp(~ v1 + v2 + v3, data = df) predict(pca)

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pca <- prcomp(~ v1 + v2 + v3, data = df) predict(pca) summary(pca)

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pca <- prcomp(~ v1 + v2 + v3, data = df, rank = 2) predict(pca) summary(pca)

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pca <- prcomp(~ v1 + v2 + v3, data = df, tol = 0.25) predict(pca) summary(pca)

Omitted if σ

≤ tol ⋅ σ

P Ci P C1

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Summary

application of PCA rotation of axes in PCA PCA in R: prcomp()

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R