Statistical Analysis Using R

Statistical Analysis Using R

• R is an open-source statistical programming language used for robust data analysis, modeling, and visualization.
• R has a wide variety of statistical packages (over 18,000) available on CRAN (Comprehensive R Archive Network) for specialized statistical analysis.
• R offers powerful tools for creating high-quality visualizations using packages like ggplot2 and lattice.
• R can handle various data formats (vectors, matrices, data frames, lists).

Data Preparation in R

• Data preparation is crucial before analysis, involving cleaning, transforming, and organizing data.
• Common tasks include importing data from formats like CSV, Excel, databases, and web APIs.
  • Example: Importing a CSV file data <- read.csv("data.csv", header = TRUE)
• Data cleaning involves handling missing values, outliers, and duplicates.
  • Example: Removing rows with missing values data_cleaned <- na.omit(data)
• Data transformation converts data into a suitable format, e.g., factorizing categorical variables.
  • Example: Converting a column to a factor data$category <- as.factor(data$category)

Probability in R

• Probability measures the likelihood of an event occurring, ranging from 0 (impossibility) to 1 (certainty).
• Key concepts include:
  • Sample Space (S) - all possible outcomes of a random experiment
  • Event - a subset of the sample space
  • Probability of an Event - ratio of favorable outcomes to total outcomes

Probability Distributions in R

• R supports various probability distributions, describing the likelihood of different outcomes in a random experiment.
• Common distributions include:
  • Uniform Distribution - all outcomes equally likely.
  • Normal Distribution - symmetric bell-shaped curve, characterized by mean (µ) and standard deviation (σ).
• R functions for generating random numbers from distributions:
  • runif(): uniform distribution
  • rnorm(): normal distribution
  • rbinom(): binomial distribution
  • rpois(): Poisson distribution

Hypothesis Testing in R

• Hypothesis testing in R is used to validate research assumptions or hypotheses regarding data sets.
• R provides functions for testing hypotheses, including onesample T-tests.

Four Step Process of Hypothesis Testing

• Stating null and alternative hypotheses.
• Formulating an analysis plan.
• Analyzing sample data using a test statistic.
• Interpreting the results based on the significance level for a decision.

One Sample T-Test

• Compares the mean of a sample to a known population mean.
• Requires normally distributed data.
• Example syntax: t.test(x, mu) (where x is the data, mu is the hypothesized mean)

Two Sample T-Test

• Compares the means of two independent samples.
• May assume equal variances (var.equal = TRUE).
• Example syntax: t.test(x, y)

Directional Hypothesis Testing

• Specifies the direction of the hypothesis, e.g., one sample mean is greater/smaller than another.
• Example syntax: t.test(x, mu, alternative = "greater")

Linear Regression

• A statistical method to explore the relationship between a dependent variable and one or more independent variables.
• R's lm() function is used for creating linear regression models, and predict() function is used for predictions.
• Various types exist, including simple linear regression and multiple linear regression.
  • Example: model <- lm(y ~ x)
  • To predict values res <- predict(model, newdata = data.frame(x = ...))

Multiple Regression

• Similar to linear regression, but involves more than one independent variable.
• Use lm() to create the model.

Logistic Regression

• A statistical method for predicting a categorical response variable given one or more predictor variables.
• Use R's glm() function for creating logistic regression models (use family=binomial argument)

Model Fitting in Data Science

• Model fitting is crucial for assessing how well a model represents data.
• Process involves data collection, model selection, parameter estimation, and evaluation.
• Techniques for evaluation, like cross-validation and bootstrapping, help determine model performance.
• Accurate modeling aids in prediction, pattern identification, and informed decisions based on data.

Components of Time Series Data

• Trend - overall direction of the series (increase, decrease, or stable)
• Seasonality - repeating patterns at regular intervals
• Cyclical variations - longer-term fluctuations in data
• Irregularity - unpredictable fluctuations (noise)