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1
Introduction
1.1
General Examples of Relationships
1.2
More About the Variables
1.3
Collecting the Data for Regression
1.3.1
Observational data
1.3.2
Experimental data
2
Simple linear regression
2.1
Scatter plots
2.2
Association between X and Y
2.3
The straight-line model
2.4
The simple linear model
2.5
The least squares method
2.5.1
How do I interpret the slope
\(\hat{\beta_{1}}\)
of the estimated regression model?
2.6
Using R to find the regression line
2.7
The correlation coefficient (r) and the coefficient of determination
\((R^{2})\)
2.7.1
The correlation coefficient (r) and its characteristics
2.7.2
Using R to calculate the coeffcient of correlation
2.7.3
The coefficient of determination
\((R^2)\)
2.8
Model assumptions
2.9
An estimator of the Random Error
\((\epsilon)\)
2.10
Inference about the slope
2.11
The t-test for the slope
2.11.1
R output
2.12
Hypothesis test for correlation (r)
2.12.1
Using R for the correlation test of significance
3
Confidence intervals
3.1
Confidence interval for the simple linear regression slope
\((\beta_{1})\)
3.2
Confidence interval for prediction
4
Introduction to multiple regression
4.1
General form of a multiple regression model
4.2
First-Order Model
4.3
A confidence interval for a single beta parameter in a multiple regression model
5
An interaction model with quantitative predictors
6
A quadratic (second-order) model with a quantitative predictor
7
Second-order model for two or more independent variables
8
Linear model with one independent qualitative variable
8.1
R example
9
A Test for Comparing Nested Models
9.1
The general F test for comparing nested models
10
Variable selection
10.0.1
Akaike’s information criterion (AIC)
10.1
Model selection in R
10.1.1
Forward Stepwise Segression
10.1.2
Backward Stepwise Segression
10.1.3
Both-Direction Stepwise Regression
11
Extra exercises
11.1
Multivariate regression model with quantitatives independent variables
11.2
Regression model with quantitative and qualitative variables
11.3
Multiple regression model with quantitative and qualitative variables
Applied regression analysis
Applied regression analysis
Prof. Fabio M. Correa
Last update
22-05-2025
The text is under development and updates are constant
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