1. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

2. 1.1 Regression and Model Building
Regression analysis is a statistical technique for investigating and modeling the relationship between variables.
Equation of a straight line (classical)
y = mx +b
we usually write this as
y = 0 +1x
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

3. 1.1 Regression and Model Building
Not all observations will fall exactly on a straight line.
y = 0 + 1x + 
where  represents error
it is a random variable that accounts for the failure of the model to fit the data exactly.
 ~ N(0, 2)
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

4. 1.1 Regression and Model Building
Delivery time example
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

5. 1.1 Regression and Model Building
Simple Linear Regression Model
where y – dependent (response) variable
x – independent (regressor/predictor) variable
0 - intercept
1 - slope
 - random error term
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

6. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

7. 1.1 Regression and Model Building
The mean response at any value, x, of the regressor variable is
The variance of y at any given x is
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

8. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

9. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
Figure 1.3 Linear regression approximation of a complex relationship.
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

10. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
Figure 1.4 Piecewise linear approximation of a complex relationship.
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

11. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
Figure 1.5 The danger of extrapolation in regression.
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

12. 1.1 Regression and Model Building
Multiple Linear Regression Model
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

13. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
1.2 Data Collection
Your analysis/model is only as good as the data
Three different methods can be used for data collection
A retrospective study based on historical data
An observational study
A designed experiment
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

14. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
1.2 Data Collection
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

15. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

16. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

17. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

18. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

19. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
Designed Experiment
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

20. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
1.3 Uses of Regression
There are many uses of regression, including:
Data description
Parameter estimation
Prediction and estimation
Control
Regression analysis is perhaps the most widely used statistical technique, and probably the most widely misused.
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

21. Linear Regression Analysis 5th edition Montgomery, Peck & Vining
1.3 Uses of Regression
Cause and Effect Relationships
Caution: just because you can fit a linear model to a set of data, does not mean you should.
It is relatively easy to build “nonsense” relationships between variables
Regression does not necessarily imply causality
Linear Regression Analysis 5th edition Montgomery, Peck & Vining

22. Model building in regression
Linear Regression Analysis 5th edition Montgomery, Peck & Vining