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Statistics
Statistical Inference
1. Foundations of Statistical Inference
2. Sampling and Sampling Distributions
3. Point Estimation
4. Interval Estimation and Confidence Intervals
5. Hypothesis Testing Framework
6. One-Sample Parametric Tests
7. Two-Sample Parametric Tests
8. Categorical Data Analysis
9. Analysis of Variance (ANOVA)
10. Simple Linear Regression Inference
11. Introduction to Bayesian Inference
12. Non-parametric Methods
10.
Simple Linear Regression Inference
10.1.
The Simple Linear Regression Model
10.1.1.
Model Specification
10.1.2.
Population Regression Line
10.1.3.
Random Error Component
10.1.4.
Assumptions of the Model
10.1.4.1.
Linearity
10.1.4.2.
Independence
10.1.4.3.
Homoscedasticity
10.1.4.4.
Normality of Errors
10.2.
Least Squares Estimation
10.2.1.
Principle of Least Squares
10.2.2.
Estimating Slope and Intercept
10.2.3.
Properties of Least Squares Estimators
10.2.4.
Residuals and Fitted Values
10.3.
Sampling Distributions of Estimators
10.3.1.
Distribution of Slope Estimator
10.3.2.
Distribution of Intercept Estimator
10.3.3.
Standard Errors
10.3.4.
Correlation Between Estimators
10.4.
Inference for Regression Coefficients
10.4.1.
Inference for the Slope
10.4.1.1.
Confidence Interval for Slope
10.4.1.2.
Hypothesis Test for Slope
10.4.1.3.
Testing for No Linear Relationship
10.4.2.
Inference for the Intercept
10.4.2.1.
Confidence Interval for Intercept
10.4.2.2.
Hypothesis Test for Intercept
10.4.2.3.
Practical Interpretation
10.5.
Inference for Correlation
10.5.1.
Population Correlation Coefficient
10.5.2.
Sample Correlation Coefficient
10.5.3.
Testing for Linear Association
10.5.4.
Confidence Interval for Correlation
10.5.5.
Fisher's Z-Transformation
10.6.
Prediction and Confidence Intervals
10.6.1.
Confidence Interval for Mean Response
10.6.1.1.
Formula and Interpretation
10.6.1.2.
Confidence Band
10.6.2.
Prediction Interval for Individual Response
10.6.2.1.
Formula and Interpretation
10.6.2.2.
Prediction vs Confidence Intervals
10.6.3.
Extrapolation Concerns
10.7.
Model Adequacy and Diagnostics
10.7.1.
Residual Analysis
10.7.2.
Checking Model Assumptions
10.7.3.
Outliers and Influential Points
10.7.4.
Goodness of Fit Measures
10.7.4.1.
Coefficient of Determination
10.7.4.2.
Standard Error of Regression
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9. Analysis of Variance (ANOVA)
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11. Introduction to Bayesian Inference