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![Basic R Commands
Arithmetic
Operations
x <- 10
y <- 3
x + y # Addition
x - y # Subtraction
x * y # Multiplication
x / y # Division
x ^ y # Power
Creating Vectors(c())
v <- c(2, 4, 6, 8, 10)
print(v)
Indexing and Subsetting
v[1] # First element
v[2:4] # Elements 2 to 4
v[v > 5] # Elements greater than 5](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-13-2048.jpg)
![Descriptive Statistics
2. Measures of Central Tendency
mean(data) # Mean
median(data) # Median
Output:
[1] 86.6
[1] 88](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-23-2048.jpg)
![Descriptive Statistics
3. Measures of Spread (Dispersion)
var(data) # Variance
sd(data) # Standard Deviation
range(data) # Min & Max
Output:
[1] 34.3
[1] 5.86
[1] 78 92](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-24-2048.jpg)
![# Probability of 5 successes in 10 trials with p=0.5
dbinom(5, size=10, prob=0.5)
# Generate random binomial values
rbinom(10, size=10, prob=0.5)
Output Example:
[1] 0.246 # Probability of exactly 5 successes
[1] 6 5 4 7 5 6 5 4 3 7 # Random outcomes
Probability Distributions in R](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-38-2048.jpg)
![# 1. Probability of exactly 5 calls
dpois(5, lambda = 3)
[1] 0.1008188
# 2. Probability of at most 2 calls
> ppois(2, lambda = 3)
[1] 0.4231901
# 3. Simulate number of calls in 10 minutes
rpois(10, lambda = 3)
[1] 3 3 1 4 2 2 3 2 0 8
Probability Distributions in R](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-42-2048.jpg)
![P(X < 80):
pnorm(80, mean = 70, sd = 10)
# [1] 0.8413447
There is about 84.13% chance that a student scores less than 80.
P(60 < X < 75):
pnorm(75, mean = 70, sd = 10) - pnorm(60, mean = 70, sd = 10)
# [1] 0.5328072
There is about 53.28% chance that a student scores between 60 and 75.
Probability Distributions in R](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-46-2048.jpg)
![Simulated scores:
rnorm(10, mean = 70, sd = 10)
# Example output: [1] 68.5 72.3 81.0 59.4 74.2 65.8 69.1 77.6 62.8 71.4
These are 10 randomly generated exam scores based on the normal distribution.
Conclusion
Most students are likely to score below 80 (84% probability).
Over half the students (53% probability) will fall between 60 and 75.
The simulated results reflect how scores cluster around the mean (70) with some variation due to
standard deviation.
Probability Distributions in R](https://image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-47-2048.jpg)
![Basic R Commands
Arithmetic
Operations
x <- 10
y <- 3
x + y # Addition
x - y # Subtraction
x * y # Multiplication
x / y # Division
x ^ y # Power
Creating Vectors(c())
v <- c(2, 4, 6, 8, 10)
print(v)
Indexing and Subsetting
v[1] # First element
v[2:4] # Elements 2 to 4
v[v > 5] # Elements greater than 5](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-13-2048.jpg)
![Descriptive Statistics
2. Measures of Central Tendency
mean(data) # Mean
median(data) # Median
Output:
[1] 86.6
[1] 88](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-23-2048.jpg)
![Descriptive Statistics
3. Measures of Spread (Dispersion)
var(data) # Variance
sd(data) # Standard Deviation
range(data) # Min & Max
Output:
[1] 34.3
[1] 5.86
[1] 78 92](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-24-2048.jpg)
![# Probability of 5 successes in 10 trials with p=0.5
dbinom(5, size=10, prob=0.5)
# Generate random binomial values
rbinom(10, size=10, prob=0.5)
Output Example:
[1] 0.246 # Probability of exactly 5 successes
[1] 6 5 4 7 5 6 5 4 3 7 # Random outcomes
Probability Distributions in R](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-38-2048.jpg)
![# 1. Probability of exactly 5 calls
dpois(5, lambda = 3)
[1] 0.1008188
# 2. Probability of at most 2 calls
> ppois(2, lambda = 3)
[1] 0.4231901
# 3. Simulate number of calls in 10 minutes
rpois(10, lambda = 3)
[1] 3 3 1 4 2 2 3 2 0 8
Probability Distributions in R](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-42-2048.jpg)
![P(X < 80):
pnorm(80, mean = 70, sd = 10)
# [1] 0.8413447
There is about 84.13% chance that a student scores less than 80.
P(60 < X < 75):
pnorm(75, mean = 70, sd = 10) - pnorm(60, mean = 70, sd = 10)
# [1] 0.5328072
There is about 53.28% chance that a student scores between 60 and 75.
Probability Distributions in R](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-46-2048.jpg)
![Simulated scores:
rnorm(10, mean = 70, sd = 10)
# Example output: [1] 68.5 72.3 81.0 59.4 74.2 65.8 69.1 77.6 62.8 71.4
These are 10 randomly generated exam scores based on the normal distribution.
Conclusion
Most students are likely to score below 80 (84% probability).
Over half the students (53% probability) will fall between 60 and 75.
The simulated results reflect how scores cluster around the mean (70) with some variation due to
standard deviation.
Probability Distributions in R](https://crownmelresort.com/image.slidesharecdn.com/rsoftwareppt-251117152232-5c81c487/75/HARNESSING-R-STATISTICAL-TECHNIQUES-FOR-DATA-DRIVEN-ENTREPRENEURSHIP-47-2048.jpg)
![Basics of R programming for analytics [Autosaved] (1).pdf](https://cdn.slidesharecdn.com/ss_thumbnails/basicsofrprogrammingforanalyticsautosaved1-240916080545-0682f8c8-thumbnail.jpg?width=640&height=640&fit=bounds)
![[Redis Released]- FalkorDB - Redis + Graph Agentic Memory’s Secret Sauce](https://cdn.slidesharecdn.com/ss_thumbnails/redisreleased-falkordbslidedeck-1125-251115194922-e1c0046b-thumbnail.jpg?width=640&height=640&fit=bounds)
HARNESSING R: STATISTICAL TECHNIQUES FOR DATA-DRIVEN ENTREPRENEURSHIP
- 1. HARNESSING R: STATISTICAL TECHNIQUESFOR DATA- DRIVEN ENTREPRENEURSHIP DR. SABERUNNISA. A ASSISTANT PROFESSOR THE MADURA COLLEGE(AUTONOMOUS) MADURAI
- 2. WHAT IS R? Open-sourcestatistical software: Free to use, developed under the GNU license. Programming language & environment: Specifically designed for statistical computing and graphics. Widely used in Data Science, Machine Learning, and Statistics for: Data manipulation & cleaning Statistical modeling Visualization (graphs, charts, plots) Predictive analytics Community-driven: Thousands of user-contributed packages on CRAN.
- 3. History and Backgroundof R Developed by Ross Ihaka and Robert Gentleman in 1993 at the University of Auckland, New Zealand. Based on the S programming language, originally developed at Bell Laboratories. First official release in 1995; Version 1.0.0 was launched in 2000. Supported by the R Foundation for Statistical Computing (established in 2003). Today, R is globally recognized as one of the leading tools for statistical computing, data science, and research.
- 4. Features of R Free and Open Source Available at no cost, licensed under GNU. Huge Package Ecosystem (CRAN) 19,000+ packages covering statistics, ML, data visualization, bioinformatics, etc. Cross-Platform Compatibility Runs smoothly on Windows, Mac, and Linux systems. Strong Visualization Libraries Base R graphics and advanced tools like ggplot2, lattice, plotly. Highly Extensible Users can develop custom functions and packages. Active Community Support Global network of developers and researchers.
- 5. Installing and UsingR Download from CRAN (Comprehensive R Archive Network) ◦ Official website: https://cran.r-project.org ◦ Choose installer for Windows, Mac, or Linux. RStudio IDE (Integrated Development Environment) ◦ Provides a user-friendly interface for coding in R. ◦ Features: script editor, console, plots, package manager.
- 6.
- 7. Installing Packages tidyverse –a collection of packages for data wrangling & visualization. install.packages("tidyverse") (includes ggplot2, dplyr, readr, tidyr, tibble, stringr, forcats) data.table – for super-fast data manipulation. install.packages("data.table")
- 8. Installing Packages readxl &openxlsx – to import/export Excel files. install.packages("readxl") install.packages("openxlsx") haven – to read SPSS, SAS, and Stata files. install.packages("haven")
- 9. Statistical Analysis Packages car– regression & ANOVA tools. install.packages("car") MASS – classic stats and datasets. install.packages("MASS") psych – psychological statistics (descriptive, factor analysis). install.packages("psych")
- 10. Data Types inR Basic Data Types: Numeric → Decimal values (e.g., 3.14) Integer → Whole numbers (e.g., 5L) Character → Text values (e.g., "Hello") Logical → Boolean values (TRUE, FALSE)
- 11. Data Structures Vector →Collection of elements of the same type Matrix → 2D array of numbers (rows × columns) Factor → Categorical data (e.g., "Male", "Female") List → Collection of mixed data types Data Frame → Tabular structure (rows × columns), similar to Excel
- 12. Data Import Read thedata from Excel > library(readxl) > data <- read_excel("C:/Users/D E L L/OneDrive/Desktop/data.xlsx") > View(data) READ CSV FILE >DATA<-read.csv("C:/Users/D E L L/OneDrive/Desktop/data/data - Copy.csv") > View(DATA)
- 13. Basic R Commands Arithmetic Operations x<- 10 y <- 3 x + y # Addition x - y # Subtraction x * y # Multiplication x / y # Division x ^ y # Power Creating Vectors(c()) v <- c(2, 4, 6, 8, 10) print(v) Indexing and Subsetting v[1] # First element v[2:4] # Elements 2 to 4 v[v > 5] # Elements greater than 5
- 14. Data Visualization inR 1. Base R Plots Simple and built-in plotting system x<-c(1,2,3,4,5) y<-c(2,4,6,8,10) plot(x, y, type=“o", col="blue", main="Base R Plot")
- 15.
- 16. 2. Advanced Graphicswith ggplot2 library(ggplot2) data <- data.frame(Name=c("A","B","C"), Score=c(85,90,78)) ggplot(data, aes(x=Name, y=Score)) + geom_bar(stat="identity", fill="skyblue") + ggtitle("Bar Chart ")
- 17.
- 18. Scatter Plot library(ggplot2) ggplot(mtcars, aes(x=wt,y=mpg)) + geom_point(color="red") + ggtitle("Scatter Plot: mpg vs wt")
- 19.
- 20. Introduction to StatisticalAnalysis Role of Statistics in Data Analysis ◦ Helps in collecting, organizing, analyzing, and interpreting data. ◦ Converts raw data into meaningful insights. ◦ Essential for decision-making, prediction, and research validation.
- 21. Types of StatisticalAnalysis Descriptive Statistics ◦ Summarizes data. ◦ Measures: mean, median, mode, variance, standard deviation. ◦ Example: Average exam score of a class. Inferential Statistics ◦ Draws conclusions about a population from a sample. ◦ Techniques: hypothesis testing, confidence intervals, regression analysis. ◦ Example: Predicting election results from a survey.
- 22. Descriptive Statistics Descriptive Statisticsin R 1. Summary of Data data <- c(85, 90, 78, 92, 88) summary(data) Output: Min. 1st Qu. Median Mean 3rd Qu. Max. 78 85 88 86.6 90 92
- 23. Descriptive Statistics 2. Measuresof Central Tendency mean(data) # Mean median(data) # Median Output: [1] 86.6 [1] 88
- 24. Descriptive Statistics 3. Measuresof Spread (Dispersion) var(data) # Variance sd(data) # Standard Deviation range(data) # Min & Max Output: [1] 34.3 [1] 5.86 [1] 78 92
- 25. Descriptive Statistics 4. FrequencyTable table(data) Output: data 78 85 88 90 92 1 1 1 1 1
- 26. Inferential statistics A manufacturerclaims that the average fuel efficiency of their new car model is 25 mpg. A random sample of 10 cars gave the following mileages: 23, 25, 27, 24, 26, 22, 28, 25, 24, 23 Test at 5% significance level whether the claim is true using a one-sample t-test. Step 1: State Hypotheses Null Hypothesis (H ): ₀ μ = 25 (average mileage = 25 mpg) Alternative Hypothesis (H ): ₁ μ ≠ 25 (average mileage is different from 25 mpg) This is a two-tailed test. .
- 27. Inferential statistics #Sample data mileage<- c(23, 25, 27, 24, 26, 22, 28, 25, 24, 23) # Perform one-sample t-test t.test(mileage, mu = 25)
- 28. Inferential statistics One Samplet-test data: mileage t = -0.50233, df = 9, p-value = 0.6275 alternative hypothesis: true mean is not equal to 25 95 percent confidence interval: 23.349 26.051 sample estimates: mean of x : 24.7
- 29. Inferential statistics Step 4:Inference Test statistic t = -0.50233, p-value = 0.6275 Since p > 0.05, we fail to reject H₀. Conclusion: At 5% significance level, there is no significant evidence to say that the mean mileage is different from 25 mpg. The manufacturer’s claim is reasonable.
- 30. Inferential statistics Chi-Square Test Adie is suspected to be biased. To test this, it is rolled 60 times, and the observed frequencies of outcomes are: Test at the 5% significance level whether the die is fair using the Chi-square goodness of fit test. Face 1 2 3 4 5 6 Observed (O) 8 9 10 12 11 10
- 31. •To find thegoodness of fit # Observed frequencies observed <- c(8, 9, 10, 12, 11, 10) # Expected frequencies expected_prob <- rep(1/6, 6) # probabilities for 6 faces # Chi-square Goodness of Fit Test test <- chisq.test(x = observed, p = expected_prob) print(test) Inferential statistics
- 32. Inferential statistics Chi-squared testfor given probabilities data: observed X-squared = 1, df = 5, p-value = 0.9626 Here , p-value = 0.9626 >0.05 . Therefore fail to reject null hypothesis. Conclusion: At 5% significance level, there is no significant evidence to say that the die is unfair. The die appears fair.
- 33. Inferential statistics A researcherwants to test whether the mean test scores differ among three different teaching methods. The scores of students are recorded as follows: Group A (Method 1): 85, 90, 88 Group B (Method 2): 70, 75, 80 Group C (Method 3): 95, 92, 89 Is there a significant difference in mean scores among the three teaching methods at the 5% significance level?
- 34. Step 1: Hypotheses NullHypothesis (H ): ₀ μ = μ = μ (all groups have equal mean scores). ₁ ₂ ₃ Alternative Hypothesis (H ): ₁ At least one group mean differs. ANOVA (Analysis of Variance) •Compare means across 3+ groups df <- data.frame( score = c(85,90,88,70,75,80,95,92,89), group = rep(c("A","B","C"), each=3)) aov_res <- aov(score ~ group, data=df) summary(aov_res) Inferential statistics
- 35.
- 36. This tells ushow much larger the between-group variance is compared to the within-group variance. The probability of getting an F-value as large as 17.41 (or larger) if H is true ₀ . Since p = 0.00317 < 0.05, we reject the null hypothesis. Conclusion: At least one group mean is significantly different. Inferential statistics
- 37. Probability Distributions inR Binomial Distribution A fair coin (p = 0.5 for heads) is tossed 10 times. Find the probability of getting exactly 5 heads. Simulate 10 random outcomes of tossing the coin 10 times. Here, n= 10 (number of trials) K=5 (success) p=0.5
- 38. # Probability of5 successes in 10 trials with p=0.5 dbinom(5, size=10, prob=0.5) # Generate random binomial values rbinom(10, size=10, prob=0.5) Output Example: [1] 0.246 # Probability of exactly 5 successes [1] 6 5 4 7 5 6 5 4 3 7 # Random outcomes Probability Distributions in R
- 39. Conclusion for theProblem The probability of getting exactly 5 heads in 10 coin tosses is 0.2461 (≈ 24.6%). ◦ This means if we repeat the experiment many times, about 1 in 4 trials will result in exactly 5 heads. The random simulation using rbinom() shows how the number of heads can vary across repeated experiments of 10 tosses each. ◦ The values fluctuate around 5, consistent with the theoretical expectation . Overall: The binomial model confirms that getting exactly 5 successes (heads) in 10 fair coin tosses is the most likely outcome, but not guaranteed—it occurs about 25% of the time. Probability Distributions in R
- 40. Probability Distributions inR Poisson Distribution A call center receives an average of 3 calls per minute. Find the probability that exactly 5 calls are received in a given minute. Find the probability that at most 2 calls are received in a given minute. Simulate the number of calls received in 10 minutes using the Poisson distribution.
- 41. # 1. Probabilityof exactly 5 calls (lambda = 3) dpois(5, lambda = 3) # 2. Probability of at most 2 calls ppois(2, lambda = 3) # 3. Simulate number of calls in 10 minutes rpois(10, lambda = 3) Probability Distributions in R
- 42. # 1. Probabilityof exactly 5 calls dpois(5, lambda = 3) [1] 0.1008188 # 2. Probability of at most 2 calls > ppois(2, lambda = 3) [1] 0.4231901 # 3. Simulate number of calls in 10 minutes rpois(10, lambda = 3) [1] 3 3 1 4 2 2 3 2 0 8 Probability Distributions in R
- 43. Conclusion The probability ofgetting exactly 5 calls in one minute is ≈ 10%. The probability of getting at most 2 calls is ≈ 42%. The simulation shows how the number of calls fluctuates around the average (). . Probability Distributions in R
- 44. Probability Distributions inR 1. Normal Distribution The exam scores of students in a class are normally distributed with a mean (μ) = 70 and a standard deviation (σ) = 10. Find the probability that a randomly selected student scores less than 80. Find the probability that a student scores between 60 and 75. Simulate the exam scores of 10 students using the given distribution.
- 45. # 1. Probabilityof scoring less than 80 pnorm(80, mean = 70, sd = 10) # 2. Probability of scoring between 60 and 75 pnorm(75, mean = 70, sd = 10) - pnorm(60, mean = 70, sd = 10) # 3. Simulate exam scores for 10 students rnorm(10, mean = 70, sd = 10) Probability Distributions in R
- 46. P(X < 80): pnorm(80,mean = 70, sd = 10) # [1] 0.8413447 There is about 84.13% chance that a student scores less than 80. P(60 < X < 75): pnorm(75, mean = 70, sd = 10) - pnorm(60, mean = 70, sd = 10) # [1] 0.5328072 There is about 53.28% chance that a student scores between 60 and 75. Probability Distributions in R
- 47. Simulated scores: rnorm(10, mean= 70, sd = 10) # Example output: [1] 68.5 72.3 81.0 59.4 74.2 65.8 69.1 77.6 62.8 71.4 These are 10 randomly generated exam scores based on the normal distribution. Conclusion Most students are likely to score below 80 (84% probability). Over half the students (53% probability) will fall between 60 and 75. The simulated results reflect how scores cluster around the mean (70) with some variation due to standard deviation. Probability Distributions in R
- 48. Entrepreneurship With Rsoftware Entrepreneurship utilizes the R software for business analytics, enabling data-driven decision-making through powerful statistical analysis, forecasting, and visualization of trends in customer behavior, sales, and system performance. Entrepreneurs can leverage R to load, manipulate, and visualize complex datasets, identify patterns, conduct predictive modeling, and generate actionable insights from market and operational data to gain a competitive edge. Business Analytics & Data Mining: R is an open-source statistical software environment used for high-end graphics and statistical computations, making it a powerful tool for business analytics and data mining.
- 49. Entrepreneurship With Rsoftware Data Visualization: Entrepreneurs can use packages like ggplot2 to create clear, easy-to-read charts and graphs that transform raw data into impactful visualizations, helping to identify trends and patterns in data. Predictive Analytics: R enables businesses to forecast trends, classify outcomes, and analyze time-dependent data using regression analysis, classification models, and time series forecasting. Customer Behavior Analysis: By analyzing customer data, entrepreneurs can understand needs and preferences, leading to more tailored products and services.
- 50. Sales & PerformanceForecasting: R can be used to forecast sales, model system performance, and predict potential losses, supporting smarter, data-driven business decisions. Quantitative Research: R facilitates the analysis of public and proprietary datasets, helping entrepreneurs conduct research, test theories, and generate strategic insights. Market Trend Analysis: Entrepreneurs can analyze social media trends and market data to refine strategies, improve customer engagement, and make informed business decisions. Entrepreneurship With R software