UsefulLinks
Statistics
Statistics with R
1. Introduction to R and Statistical Computing
2. R Fundamentals and Basic Operations
3. R Package System
4. R Data Structures
5. Data Import and Export
6. Data Cleaning and Preprocessing
7. Data Manipulation with dplyr
8. Descriptive Statistics
9. Data Visualization Fundamentals
10. Advanced Data Visualization with ggplot2
11. Probability Theory
12. Probability Distributions
13. Sampling and Sampling Distributions
14. Statistical Inference Foundations
15. Hypothesis Testing Framework
16. One-Sample Tests
17. Two-Sample Tests
18. Chi-squared Tests
19. Analysis of Variance (ANOVA)
20. Correlation Analysis
21. Simple Linear Regression
22. Regression Diagnostics
23. Multiple Linear Regression
24. Generalized Linear Models
25. Nonparametric Statistics
26. Introduction to Time Series Analysis
27. Introduction to Machine Learning
28. Reproducible Research
29. Statistical Computing Best Practices
21.
Simple Linear Regression
21.1.
Regression Concepts
21.1.1.
Dependent and Independent Variables
21.1.2.
Linear Relationships
21.1.3.
Prediction vs Explanation
21.2.
Simple Linear Regression Model
21.2.1.
Population Model
21.2.2.
Sample Model
21.2.3.
Error Term
21.2.4.
Assumptions
21.3.
Least Squares Estimation
21.3.1.
Method of Least Squares
21.3.2.
Regression Coefficients
21.3.3.
Fitted Values
21.3.4.
Residuals
21.4.
Implementation in R
21.4.1.
lm() Function
21.4.2.
Model Formula Syntax
21.4.3.
Model Objects
21.5.
Interpreting Regression Output
21.5.1.
Coefficient Interpretation
21.5.2.
Intercept and Slope
21.5.3.
Standard Errors
21.5.4.
t-statistics
21.5.5.
p-values
21.6.
Assessing Model Fit
21.6.1.
R-squared
21.6.2.
Adjusted R-squared
21.6.3.
Residual Standard Error
21.6.4.
F-statistic
21.7.
Confidence and Prediction Intervals
21.7.1.
Confidence Intervals for Coefficients
21.7.2.
Confidence Intervals for Mean Response
21.7.3.
Prediction Intervals for Individual Observations
21.8.
Making Predictions
21.8.1.
predict() Function
21.8.2.
New Data Prediction
21.8.3.
Extrapolation Concerns
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20. Correlation Analysis
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22. Regression Diagnostics