Last update
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
3
The coefficient of correlation (r)
3.1
The correlation coefficient (r) and its characteristics
3.2
Using R to calculate the coeffcient of correlation
3.3
Hypothesis test for correlation (r)
4
The straight-line model
4.1
The simple linear model
4.2
The least squares method
4.2.1
How do I interpret the slope
\(\hat{\beta_{1}}\)
of the estimated regression model?
4.3
Using R to find the regression line
4.4
The coefficient of determination
\((R^2)\)
4.5
Model assumptions
4.6
An estimator of the Random Error
\((\epsilon)\)
4.7
Inference about the slope
4.8
The t-test for the slope
4.8.1
R output
4.8.2
Using R for the correlation test of significance
5
Confidence intervals
5.1
Confidence interval for the simple linear regression slope
\((\beta_{1})\)
5.2
Confidence interval for prediction
6
Introduction to multiple regression
6.1
General form of a multiple regression model
6.2
First-Order Model
6.3
A confidence interval for a single beta parameter in a multiple regression model
7
An interaction model with quantitative predictors
8
A quadratic (second-order) model with a quantitative predictor
9
Second-order model for two or more independent variables
10
Linear model with one independent qualitative variable
10.1
R example
11
A Test for Comparing Nested Models
11.1
The general F test for comparing nested models
12
Variable selection
12.0.1
Akaike’s information criterion (AIC)
12.1
Model selection in R
12.1.1
Forward Stepwise Segression
12.1.2
Backward Stepwise Segression
12.1.3
Both-Direction Stepwise Regression
13
Extra exercises
13.1
Multivariate regression model with quantitatives independent variables
13.2
Regression model with quantitative and qualitative variables
13.3
Multiple regression model with quantitative and qualitative variables
Applied regression analysis
Applied regression analysis
Prof. Fabio M. Correa
Last update
12-02-2026
The text is under development and updates are constant