Notebook for ALRM
1
Preface
2
Linear regression with one predictor variable
2.1
Relations between variables
2.2
Regression Models and Their Uses
2.3
Simple linear regression model with distribution of error terms unspecified
2.4
Data for regression analysis
2.5
Overview of steps in regression analysis
2.6
Estimation of regression function
2.7
Estimation of Erro Terms Variance
\(\sigma^{2}\)
2.8
Normal Error Regression Model
3
Inferences in Regeression and Correlation Analysis
3.1
Inferences Concerning
\(\beta_{1}\)
3.2
Inferences Concerning
\(\beta_{0}\)
3.3
Some Considerations on Making Inferences Concerning
\(\beta_{0}\)
and
\(\beta_{1}\)
3.4
Interval Estimation of
\(E(Y_{h})\)
3.5
Prediction of New Observation
3.6
Confidence Band for Regression Line
3.7
Analysis of Variance Approach
3.8
General Linear Test Approach
3.9
Descriptive Measures of Linear Association between X and Y
3.10
Considerations in Applying Regression Analysis
3.11
Normal Correlation Models
3.12
R code
3.12.1
Example data
3.12.2
built-in function
3.12.3
point estimator
\(b_0\)
and
\(b_1\)
3.12.4
Residuals, SSE and MSE
3.12.5
sampling distribution of
\(b_1\)
and
\((b_1−\beta_1)/s(b_1)\)
3.12.6
F test
3.12.7
\(R^2\)
and r
3.12.8
plot
4
Diagnostics and Remedial Measures
5
Simultaneous Inferences and Other Topics in Regression Analysis
6
Matrix Approach to Simple Linear Regression Analysis
6.1
Matrices
6.2
Matrix Addition and Subtraction
6.3
Matrix Multiplication
6.4
Special Types of Matrices
6.5
Linear Dependence and Rank of Matrix
6.6
Inverse of a Matrix
6.7
Some Basic Results for Matrics
6.8
Random Vectors and Matrices
6.9
Simple Linear Regression Model in Matrix Terms
6.10
Leasst Squares Estimation of Regression Parameters
6.11
Fitted Values and Residuals
6.12
Analysis of Variance Results
6.13
Inferences in Regeression Analysis
6.14
R code
7
Multiple linear regression I
7.1
Multiple Regression Models
7.1.1
First-Order Model with Two Predictor Variables
7.1.2
First-Order Model with More than Two Predictor Variables
7.1.3
General Linear Regression Model
7.2
General Linear Regression Model in Matrix Terms
7.3
Estimation of Regression Coefficients
7.4
Fitted Values and Residuals
7.5
Analysis of Variance Results
7.6
Inferences about Regression Parameters
8
Multiple Regression II
8.1
Extra Sums of Squares
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5
Simultaneous Inferences and Other Topics in Regression Analysis